TIGER-Lab/MAmmoTH-Coder-7B
Text Generation
•
Updated
•
37
•
6
| source (string) | output (string) | instruction (string) |
|---|---|---|
"data/CoT/aqua_rat.json" | "Let's think about the multi-choice question.
6.52 × 10^5 ly / (3.26 ly/parsec) = 2 x 10^5 persec
The answer is A." | "The distance between two stars is 6.52 × 10^5 light years. What is the distance between the two stars in parsecs? (1 parsec = 3.26 light years)
Answer Choices: (A) 2 × 10^5 (B) 4 × 10^6 (C) 5 × 10^7 (D) 7 × 10^7 (E) 9 × 10^8" |
"data/CoT/aqua_rat.json" | "Let's solve the multi-choice question step by step.
According to the above the # of permutations of 6 letters COMMON out of which 2 O's and 2 M's are identical is 6!2!∗2!=180
The answer is E." | "How many ways can the letters in the word COMMON be arranged?
Answer Choices: (A) 6 (B) 30 (C) 90 (D) 120 (E) 180" |
"data/PoT/aqua_rat_filtered.json" | "answers = ['A', 'B', 'C', 'D', 'E']
# If the best marksman had scored 92 points, the total score would have been 84 * 6 = 504
# But he actually scored 85 points, so the actual total score is 504 - 92 + 85
actual_total_score = 504 - 92 + 85
options = [288, 497, 168, 127, 664]
index = options.index(actual_total_score)
print(answers[index])" | "A team of six entered for a shooting competition. The best marks man scored 85 points. If he had scored 92 points, the average scores for. The team would have been 84. How many points altogether did the team score?
Answer Choices: (A) 288 (B) 497 (C) 168 (D) 127 (E) 664 Let's program in Python in the response." |
"data/CoT/gsm_rft.json" | "The second patient needs 6+5 = 11 sessions
25-11-6 = 8 sessions
The answer is 8" | "A psychiatrist has 4 patients that need 25 sessions in total. One of the patients needs 6 sessions. Another patient needs 5 more than that. How many sessions would the remaining patients need?" |
"data/PoT/aqua_rat_filtered.json" | "radius = 22.4
resolutions = 500
# calculate the circumference of the wheel
circumference = 2 * 3.14 * radius
# calculate the distance covered by the wheel in making 500 resolutions
distance = circumference * resolutions
print(distance)" | "The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions?
Answer Choices: (A) 187 m (B) 704 m (C) 179 m (D) 127 m (E) 297 m Let's write a Python program." |
"data/CoT/college_math.json" | "By the Fundamental Theorem of Finite Abelian Groups, any group of order 35, which is the product of two distinct prime numbers (5 and 7), must be a direct product of cyclic groups. Hence, option (C) is correct. Let's check each option: (A) G must be abelian: It is not necessarily true that G must be abelian. The statement would be true if G were of prime order, but that's not the case here. (B) G must be cyclic: Again, it's not necessarily true that G must be cyclic. A group is cyclic if it is generated by a single element, but this isn't guaranteed for a group of order 35. (C) G must be a direct product of cyclic groups: This is correct. The Fundamental Theorem of Finite Abelian Groups tells us that a group of order 35 must be isomorphic to a direct product of cyclic groups. (D) G cannot be cyclic: This is not necessarily true. It's possible for G to be cyclic, although it's not guaranteed. The answer is B." | "Let G be a group of order 35. What can be said about G? Answer Choices: (A) G must be abelian. (B) G must be cyclic. (C) G must be a direct product of cyclic groups. (D) G cannot be cyclic." |
"data/PoT/gsm_gpt4.json" | "# define the initial number of slices
total_slices = 4 * 12
# define the number of slices eaten
eaten_slices = 39
# calculate the number of slices left
left_slices = total_slices - eaten_slices
# print the result
print(left_slices)" | "At a pool party, there are 4 pizzas cut into 12 slices each. If the guests eat 39 slices, how many slices are left? Let's write a Python program." |
"data/PoT/gsm_gpt4.json" | "# define the variables
total_donuts = 4 * 12 # since a dozen is 12
total_students = 30
percentage_like_donuts = 0.8 # 80%
# calculate the number of students who like donuts
students_like_donuts = total_students * percentage_like_donuts
# calculate the number of donuts each student who likes donuts gets
donuts_per_student = total_donuts / students_like_donuts
# print the result
print(donuts_per_student)" | "Noel bakes 4 dozen donuts for his class. There are 30 students in class, but only 80% like donuts. How many donuts does each student who likes donuts get to eat? Please write a program to solve it" |
"data/CoT/aqua_rat.json" | "Let's solve the multi-choice question step by step.
Let the sum invested in scheme A be Rs. x and that in scheme B be Rs. (13900 - x). Then,
(x * 14 * 2)/100 + [(13900 - x) * 11 * 2]/100 = 3508
28x - 22x = 350800 - (13900 * 22)
6x = 45000 => x = 7500
So, sum invested in scheme B = (13900 - 7500) = Rs. 6400.
The answer is A" | "Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in scheme B?
Answer Choices: (A) 6400 (B) 2778 (C) 2699 (D) 2789 (E) 1279" |
"data/PoT/mathqa.json" | "n0 = 3.0
n1 = 1000.0
n2 = 10.0
n3 = 3.0
t0 = n2 / 100.0
t1 = n0 * n1
t2 = t0 * t1
t3 = t0 * t2
t4 = t2 + t3
t5 = t4 + 1.0
t6 = n1 + t5
t7 = t5 / 100.0
answer = t6 / t7
print(answer)" | "louie takes out a 3 - month loan of $ 1000 . the lender charges him 10 % interest per month compounded monthly . the terms of the loan state that louie must repay the loan in 3 equal monthly payments . to the nearest dollar , how much does louis have to pay each month ? Let's write a program." |
"data/PoT/numglue.json" | "# Chemical formula of Calcium Hydroxide - Ca(OH)₂
molecular_weight_Ca = 40
molecular_weight_O = 16
molecular_weight_H = 1
no_of_Ca = 1
no_of_O = 2
no_of_H = 2
total_weight = (no_of_Ca * molecular_weight_Ca) + (no_of_O * molecular_weight_O) + (no_of_H * molecular_weight_H)
mass_percentage_Ca = (molecular_weight_Ca * no_of_Ca * 100) / total_weight
print(round(mass_percentage_Ca, 2))" | "Find the mass percentage of Ca in Calcium hydroxide Please write a program to solve it" |
"data/CoT/aqua_rat.json" | "Let's solve the multi-choice question step by step.
3x * 2x = 3750 => x = 25
2(75 + 50) = 250 m
250 * 1/2 = Rs.125
The answer is C" | "Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is?
Answer Choices: (A) Rs.122 (B) Rs.129 (C) Rs.125 (D) Rs.120 (E) Rs.121" |
"data/CoT/aqua_rat.json" | "Let's think about the multi-choice question.
? = (100 x 60) + (138 x 400)/60
= 6000 + 55200/60 = 1020
The answer is Option D" | "(100 x 60) + (138 x 400) = ? x 60
Answer Choices: (A) 880 (B) 550 (C) 1100 (D) 1020 (E) 600" |
"data/CoT/gsm_rft.json" | "Each wall is 2*3=6 square meters
So each wall takes 6*10=60 minutes to paint
So it takes 60/60=1 hour to paint each wall
That means in total it takes 5*1=5 hours to paint
So he has 10-5=5 hour left after finishing painting
The answer is 5" | "Tom paints a room that has 5 walls. Each wall is 2 meters by 3 meters. John can paint 1 square meter every 10 minutes. He has 10 hours to paint everything. How many hours does he have to spare?" |
"data/PoT/numglue.json" | "percentage = 100
under = 31.4
above = percentage - under
print(above)" | "Passage: According to CBS, in 2001 the ethnic makeup of the city was 99.8% Jewish and other non-Arab, without significant Arab population. See Population groups in Israel. According to CBS, in 2001 there were 23,700 males and 24,900 females. The population of the city was spread out with 31.4% 19 years of age or younger, 15.7% between 20 and 29, 18.5% between 30 and 44, 18.3% from 45 to 59, 4.1% from 60 to 64, and 11.9% 65 years of age or older. The population growth rate in 2001 was 0.8%. Question: How many percent were not under the age of 19? Please write a program to solve it" |
"data/CoT/math50k_camel.json" | "The Vicsek fractal is a self-similar fractal, and its Hausdorff dimension can be calculated using the formula:
D = log(N) / log(s)
where D is the Hausdorff dimension, N is the number of self-similar pieces, and s is the scaling factor.
For the Vicsek fractal, at each iteration, the square is divided into 5 smaller squares, with each side length being 1/3 of the original side length. Therefore, N = 5 and s = 3.
Now, we can calculate the Hausdorff dimension:
D = log(5) / log(3)
D ≈ 1.46497
So, the exact Hausdorff dimension of the Vicsek fractal is approximately 1.46497." | "What is the exact Hausdorff dimension of the Vicsek fractal, whose four straight lines in each iteration form a square with holes in it, if each line segment in the square has a length of 1 unit?" |
"data/CoT/aqua_rat.json" | "Let's reason about the multi-choice question.
K + 2K +3 + 3K - 5 + 5K +1 = 11K -1
(11K -1)/4 = 96
11K = 96 * 4 +1 = 384 +1 = 385
K = 385 / 11 = 35.
The answer is D." | "If the average (arithmetic mean) of the four numbers K, 2K + 3, 3K – 5 and 5K + 1 is 96, what is the value of K?
Answer Choices: (A) 11 (B) 15 3/4 (C) 22 (D) 35 (E) 25 3/10" |
"data/CoT/gsm_rft.json" | "The 5 students buy 5*1=5 candy bars.
The 5 students buy 5*2=10 bags of chips.
The 5 candy bars cost 5*2=10 dollars.
The 10 bags of chips cost 10*0.5=5 dollars.
The students need 10+5=15 dollars.
The answer is 15" | "The snack machine at Richmond High School sells candy bars for $2 each and chips for $.50 each. How much money, in dollars, will 5 students need in total if each of them gets 1 candy bar and 2 bags of chips?" |
"data/CoT/MATH_train.json" | "The base of the hemisphere is a circle with radius 6 and area $6^2\pi=36\pi$. The curved top of the hemisphere has half the surface area of a full sphere, which has surface area $4\pi(6^2)=144\pi$, so the curved top of the hemisphere has $144\pi/2=72\pi$. The total surface area of the hemisphere is $36\pi+72\pi=\boxed{108\pi}$. The answer is 108\pi" | "The surface area of a sphere with radius $r$ is $4\pi r^2$. Including the area of its circular base, what is the total surface area of a hemisphere with radius 6 cm? Express your answer in terms of $\pi$.
[asy]
import markers;
size(150);
import geometry;
draw((0,-7)--(0,-1),Arrow);
draw((10,10)--(5,5),Arrow);
label("half of sphere",(10,10),N);
label("circular base",(0,-7),S);
draw(scale(1,.2)*arc((0,0),10,0,180),dashed);
draw(scale(1,.2)*arc((0,0),10,180,360));
draw(Arc((0,0),10,0,180));
[/asy]" |
"data/PoT/mathqa.json" | "n0 = 90.0
n1 = 40.0
n2 = 5.0
t0 = 2 * (n0 + n1) # perimetere of rectangle
answer = t0 / n2
print(answer)" | "a rectangular plot measuring 90 metres by 40 metres is to be enclosed by wire fencing . if the poles of the fence are kept 5 metres apart , how many poles will be needed ? Let's write a Python program to solve it." |
"data/CoT/aqua_rat.json" | "Let's reason about the multi-choice question.
Let the numbers be 2x, 3x and 5x, Then, (2x + 3x + 5x ) / 3 = 50
=> 10x = 150
=> x = 15.
Largest number 5x = 5*15 = 75
The answer is B" | "Three numbers are in the ratio 2 : 3 : 5 and their average is 50. The largest number is :
Answer Choices: (A) 30 (B) 75 (C) 27 (D) 21 (E) 22" |
"data/PoT/mathqa.json" | "n0 = 9.0
n1 = 200.0
n2 = 120.0
n3 = 45.0
t0 = n1 + n2
t1 = 10.0 / 2.0
t2 = n3 - n0
t3 = t2 / 2.0
t4 = t1 / t3
t5 = t4 * t2
answer = t0 / t5
print(answer)" | "a jogger running at 9 km / hr along side a railway track is 200 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ? Please write a program to solve it" |
"data/CoT/math50k_camel.json" | "As a mathematician, I cannot predict the weather or determine the truth of a statement about future weather events using temporal logic alone. Temporal logic is a formal system used to reason about time and the ordering of events, but it does not provide information about specific events or their outcomes. To determine whether the statement "It will be raining hard at noon tomorrow" is true or false, you would need to consult a reliable weather forecast or use a predictive model based on meteorological data." | "Using temporal logic, determine whether the statement "It will be raining hard at noon tomorrow" is true or false, given the following information: Today is Monday, August 2nd, and it is currently 4pm. Assume that "raining hard" refers to a specific intensity of rain (as opposed to just any rain) and that "noon" is defined as exactly 12pm." |
"data/PoT/TheoremQA.json" | "import math
def solve():
G = 6.6743 * 10**(-11) # gravitational constant
M = 1.99 * 10**30 # mass of the Sun
r = 5.8 * 10**10 # mean orbital radius of Mercury
T = 2 * math.pi * math.sqrt(r**3 / (G * M)) # Kepler's third law
T = T / (60 * 60 * 24) # convert seconds to days
return T
print(solve())" | "The planet Mercury travels around the Sun with a mean orbital radius of 5.8x10^10 m. The mass of the Sun is 1.99x10^30 kg. Use Newton's version of Kepler's third law to determine how long it takes Mercury to orbit the Sun. Give your answer in Earth days. Let's write a Python program to solve it." |
"data/CoT/MATH_train.json" | "We have that $2a = 6,$ so $a = 3.$ The distance between the foci is $2c = 4,$ so $c = 2.$ Hence, $b = \sqrt{a^2 - c^2} = \sqrt{5}.$
The center of the ellipse is the midpoint of $\overline{F_1 F_2},$ which is $(2,1).$ Thus, the equation of the ellipse is
\[\frac{(x - 2)^2}{3^2} + \frac{(y - 1)^2}{(\sqrt{5})^2} = 1.\]Hence, $h + k + a + b = 2 + 1 + 3 + \sqrt{5} = \boxed{6 + \sqrt{5}}.$. The answer is 6+\sqrt{5}" | "Let $F_1 = (0,1)$ and $F_ 2= (4,1).$ Then the set of points $P$ such that
\[PF_1 + PF_2 = 6\]form an ellipse. The equation of this ellipse can be written as
\[\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1.\]Find $h + k + a + b.$" |
"data/CoT/aqua_rat.json" | "Let's think about the multi-choice question step by step.
A particular players is never chosen, it means that 11 players are selected out of 13 players.
=> Required number of ways = 13C11
= 78
The answe is D" | "If a particular player is never chosen, in how many ways can 11 cricket players be chosen out of 14 players?
Answer Choices: (A) 45 (B) 56 (C) 64 (D) 78 (E) 90" |
"data/PoT/aqua_rat_filtered.json" | "# The amount of sugar in the solution remains constant, so we can set up the equation 0.04 * 50 = 0.10 * (50 - x), where x is the amount of water to be evaporated.
# Solving for x gives us x = 50 - (0.04 * 50) / 0.10
x = 50 - (0.04 * 50) / 0.10
print(x)" | "How many liters of water must be evaporated from 50 liters of a 4-percent sugar solution to get a 10-percent solution?
Answer Choices: (A) 30 (B) 32 (C) 34 (D) 36 (E) 38 Let's write a program." |
"data/CoT/aqua_rat.json" | "Let's solve the multi-choice question step by step.
First 9 pages .. 9 digits
next 90 pages .. 180 digits
next 36 pages ... 108 digits
----------------------
Total ...135 pages ...297 digits
The answer is A" | "How many pages the book have, if total 297 digits are used to form the page numbers?
Answer Choices: (A) 135 pages (B) 136 pages (C) 137 pages (D) 138 pages (E) 139 pages" |
"data/CoT/aqua_rat.json" | "Let's reason about the multi-choice question.
18000:22500:27000
4:5:6
c share=12000*6/15=4800
The answer is C" | "Three partners A,B and C invest Rs.18000, Rs.22500 and Rs.27000 respectively in a business. If total profit is Rs.12000 then C's share is (in Rs.)
Answer Choices: (A) 10000 (B) 6500 (C) 4800 (D) 7800 (E) 8500" |
"data/CoT/math50k_camel.json" | "To disconnect the graph, we need to find a cut set, which is a set of edges whose removal will result in a disconnected graph. In this case, we can observe that vertex 5 is a cut vertex, as it connects the two parts of the graph: {1, 2, 3, 4} and {6, 7}.
To disconnect the graph, we need to remove all the edges connected to vertex 5. These edges are (3,5), (4,5), (5,6), and (5,7). Therefore, the minimum number of edges that must be removed to disconnect the graph is 4." | "Consider a graph G with 7 vertices and edge set E = {(1,2), (1,3), (2,3), (2,4), (3,5), (4,5), (5,6), (5,7), (6,7)}. Determine the minimum number of edges that must be removed to disconnect the graph." |
"data/CoT/math50k_camel.json" | "To solve the system of linear equations using matrix methods, we will use the following steps:
1. Write the augmented matrix for the system of equations.
2. Perform row operations to transform the matrix into its reduced row echelon form.
3. Read the solution from the reduced row echelon form.
Step 1: Write the augmented matrix for the system of equations.
The augmented matrix for the given system of equations is:
| 2 3 1 | 7 |
| 1 2 4 | 12|
| 3 1 2 | 8 |
Step 2: Perform row operations to transform the matrix into its reduced row echelon form.
First, we will swap Row 1 and Row 2 to have a 1 in the top-left corner:
| 1 2 4 | 12|
| 2 3 1 | 7 |
| 3 1 2 | 8 |
Next, we will eliminate the 2 and 3 in the first column below the 1:
Row 2 = Row 2 - 2 * Row 1:
| 1 2 4 | 12|
| 0 -1 -7 | -17|
| 3 1 2 | 8 |
Row 3 = Row 3 - 3 * Row 1:
| 1 2 4 | 12|
| 0 -1 -7 | -17|
| 0 -5 -10| -28|
Now, we will multiply Row 2 by -1 to make the pivot element in the second row positive:
| 1 2 4 | 12|
| 0 1 7 | 17|
| 0 -5 -10| -28|
Next, we will eliminate the -5 in the second column below the 1:
Row 3 = Row 3 + 5 * Row 2:
| 1 2 4 | 12|
| 0 1 7 | 17|
| 0 0 25| 57|
Now, we will divide Row 3 by 25 to make the pivot element in the third row equal to 1:
| 1 2 4 | 12|
| 0 1 7 | 17|
| 0 0 1 | 57/25|
Finally, we will eliminate the 4 and 7 in the third column above the 1:
Row 1 = Row 1 - 4 * Row 3:
| 1 2 0 | -44/25|
| 0 1 7 | 17|
| 0 0 1 | 57/25|
Row 2 = Row 2 - 7 * Row 3:
| 1 2 0 | -44/25|
| 0 1 0 | -24/25|
| 0 0 1 | 57/25|
Step 3: Read the solution from the reduced row echelon form.
The reduced row echelon form of the augmented matrix corresponds to the following system of equations:
x + 2y = -44/25
y = -24/25
z = 57/25
So, the solution to the system of linear equations is:
x = -44/25
y = -24/25
z = 57/25" | "Suppose you have a system of linear equations:
2x + 3y + z = 7
x + 2y + 4z = 12
3x + y + 2z = 8
Using matrix methods, find the values of x, y, and z that satisfy the system of equations." |
"data/CoT/aqua_rat.json" | "Maximum distance straight line is diameter
d = 2r = 10..
ANS option B." | "What is the greatest possible (straight line) distance, between any two points on a hemisphere of radius 5?
Answer Choices: (A) 0.1 (B) 10 (C) π/10 (D) 8 (E) π" |
"data/PoT/gsm_gpt4.json" | "# define the number of eggs Gus eats for each meal
breakfast_eggs = 2
lunch_eggs = 3
dinner_eggs = 1
# calculate the total number of eggs Gus eats
total_eggs = breakfast_eggs + lunch_eggs + dinner_eggs
# print the result
print(total_eggs)" | "Gus eats 2 eggs-omelet for breakfast. He has an egg salad sandwich made with 3 eggs for lunch. He then has an egg drop soup made with 1 egg for dinner. How many eggs did Gus eat altogether? Let's write a program." |
"data/CoT/aqua_rat.json" | "Let's think about the multi-choice question.
Let the cost of a table and that of a chair be Rs. x and Rs, y respectively.
Then, 2x + 3y = 3500 ...(i)
and 3x + 2y = 4000 .....(ii)
solving (i) and (ii) we get x = 1000, y = 500
The answer is B 1000" | "If 2 tables and 3 chairs cost Rs, 3500 and 3 tables and 2 chairs cost Rs. 4000, then how much does a table cost ?
Answer Choices: (A) 2377 (B) 1000 (C) 2778 (D) 766 (E) 18811" |
"data/PoT/mathqa.json" | "n0 = 5.0
n1 = 2.0
n2 = 16.0
t0 = n0 / 100.0
t1 = t0 + 1.0
t2 = n1 * t0
t3 = t2 + 1.0
t4 = t1**min(n1, 5)
t5 = t4 - t3
answer = n2 / t5
print(answer)" | "the difference between compound interest and simple interest on a certain amount of money at 5 % per annum for 2 years is 16 . find the sum : ? Let's write a Python program to solve it." |
"data/PoT/MATH_train.json" | "def f(x):
return 3**(x/2)
print(f(6))" | "The function $f(x)$ satisfies
\[f(x + y) = f(x) f(y)\]for all real numbers $x$ and $y.$ If $f(2) = 3,$ find $f(6).$ Let's program in Python in the response." |
"data/CoT/MATH_train.json" | "The diagram can be quartered as shown:[asy] draw((0,0)--(0,5)--(5,5)--(5,0)--(0,0)); draw((0,1)--(4,5)); draw((1,0)--(5,4)); draw((0,4)--(4,0)); draw((1,5)--(5,1)); draw((0,0)--(5,5),dotted); draw((0,5)--(5,0),dotted); [/asy]and reassembled into two smaller squares of side $k$, each of which looks like this:[asy] draw((0,0)--(0,5)--(5,5)--(5,0)--(0,0)); draw((0,1)--(4,1)--(4,5)); draw((1,0)--(1,4)--(5,4)); label("blue",(0.5,0.5)); label("blue",(4.5,4.5)); label("red",(0.5,4.5)); label("red",(4.5,0.5)); label("white",(2.5,2.5)); [/asy]The border in this figure is the former cross, which still occupies 36% of the area. Therefore the inner square occupies 64% of the area, from which we deduce that it is $0.8k \times 0.8k$, and that one blue square must be $0.1k\times 0.1k=0.01k^2$ or 1% each. Thus the blue area is $\boxed{2}\%$ of the total. The answer is 2" | "A square flag has a red cross of uniform width with a blue square in the center on a white background as shown. (The cross is symmetric with respect to each of the diagonals of the square.) If the entire cross (both the red arms and the blue center) takes up 36% of the area of the flag, what percent of the area of the flag is blue?
[asy] unitsize(2.5 cm); pair[] A, B, C; real t = 0.2; A[1] = (0,0); A[2] = (1,0); A[3] = (1,1); A[4] = (0,1); B[1] = (t,0); B[2] = (1 - t,0); B[3] = (1,t); B[4] = (1,1 - t); B[5] = (1 - t,1); B[6] = (t,1); B[7] = (0,1 - t); B[8] = (0,t); C[1] = extension(B[1],B[4],B[7],B[2]); C[2] = extension(B[3],B[6],B[1],B[4]); C[3] = extension(B[5],B[8],B[3],B[6]); C[4] = extension(B[7],B[2],B[5],B[8]); fill(C[1]--C[2]--C[3]--C[4]--cycle,blue); fill(A[1]--B[1]--C[1]--C[4]--B[8]--cycle,red); fill(A[2]--B[3]--C[2]--C[1]--B[2]--cycle,red); fill(A[3]--B[5]--C[3]--C[2]--B[4]--cycle,red); fill(A[4]--B[7]--C[4]--C[3]--B[6]--cycle,red); draw(A[1]--A[2]--A[3]--A[4]--cycle); draw(B[1]--B[4]); draw(B[2]--B[7]); draw(B[3]--B[6]); draw(B[5]--B[8]); [/asy]
$\text{(A)}\ 0.5\qquad\text{(B)}\ 1\qquad\text{(C)}\ 2\qquad\text{(D)}\ 3\qquad\text{(E)}\ 6$
" |
"data/CoT/gsm_rft.json" | "Duane gave Lana 42 / 2 = 21 pages.
After adding Duane’s, Lana has 21 + 8 = 29 pages in her binder.
The answer is 29" | "Lana had 8 blank pages left in her binder, but she knew she would need more for her next class. Duane took half of the 42 pages in his binder out and gave them to her. How many pages does Lana have in her binder after adding Duane’s?" |
"data/CoT/aqua_rat.json" | "Let's reason about the multi-choice question.
The most time consuming part in this question is to define the mean. Under exam pressure and time pressure it is very easy to make mistake.
it is easier to group numbers: 130*3=390; 105*2=210; 75+85=160; 70+80=150; 90;
Next stage combine results, again using more convenient ways to calculate: 390+210=600; 160+150=310; 90. 600+310+90=1000. Since there are 10 numbers the mean is 100. Questions asks to find the quantity of numbers one SD BELOW the mean, which is 100-25,4=74,6. There are only two numbers below 74,6. The answer is B" | "70, 75, 80, 85, 90, 105, 105, 130, 130, 130
The list shown consists of the times, in seconds, that it took each of 10 schoolchildren to run a distance of 400 on of meters. If the standard devastation of the 10 running times is 25.4 seconds, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times?
Answer Choices: (A) one (B) two (C) three (D) four (E) five" |
"data/CoT/aqua_rat.json" | "Sol:
(SP of 33m)-(CP of 33m)=Gain=SP of 11m
SP of 22m = CP of 33m
Let CP of each metre be Re.1 , Then, CP of 22m= Rs.22,SP of 22m=Rs.33.
Gain%=[(11/22)*100]%=50%
option D" | "By selling 33 metres of cloth , one gains the selling price of 11 metres . Find the gain percent .
Answer Choices: (A) 20 (B) 30 (C) 40 (D) 50 (E) 60" |
"data/CoT/math50k_camel.json" | "The Heighway dragon curve is a fractal that is created by iteratively folding a strip of paper in half and then unfolding it so that each fold creates a 90-degree angle. The perimeter of the curve increases with each iteration.
After each iteration, the number of segments in the curve doubles, and the length of each segment is divided by the square root of 2. This is because each segment is now part of a right-angled triangle with the original segment as the hypotenuse.
After 10 iterations, the number of segments is 2^10 = 1024, and the length of each segment is 1/(sqrt(2))^10 = 1/(2^5) = 1/32.
The perimeter of the Heighway dragon curve after 10 iterations is the product of the number of segments and the length of each segment:
Perimeter = 1024 * (1/32) = 32 units." | "What is the perimeter of the Heighway dragon curve after 10 iterations if the starting line segment has a length of 1 unit?" |
"data/CoT/math50k_camel.json" | "To find the complement of A, we first need to define the universal set U, which contains all the elements under consideration. Since A contains odd integers, let's assume U contains all integers from 1 to 6. So, U = {1, 2, 3, 4, 5, 6}.
Now, the complement of A, denoted as A', contains all the elements in U that are not in A. So, A' = {x ∈ U | x ∉ A}.
Comparing the elements of A and U, we can see that A' = {2, 4, 6}.
Now, let's find the intersection between A and its complement A'. The intersection of two sets is the set of elements that are common to both sets.
A ∩ A' = {x | x ∈ A and x ∈ A'}
Comparing the elements of A and A', we can see that there are no common elements between A and A'. Therefore, the intersection of A and A' is the empty set:
A ∩ A' = ∅
This demonstrates that the intersection between a set and its complement is always the empty set." | "Let A be a set such that A = {1,3,5}. Find the complement of A and then calculate the intersection between A and its complement. Show that the result is the empty set." |
"data/CoT/aqua_rat.json" | "Let's think about the multi-choice question step by step.
Total # of ways the race can be finished is 4!. In half of the cases Meg finishes ahead of Bob and in other half Bob finishes ahead of Meg. So, ways Meg to finish ahead of Bob is 4!/2=12.
The answer is E." | "Meg and Bob are among the 4 participants in a cycling race. If each participant finishes the race and no two participants finish at the same time, in how many different possible orders can the participants finish the race so that Meg finishes ahead of Bob?
Answer Choices: (A) 24 (B) 30 (C) 60 (D) 90 (E) 12" |
"data/CoT/aqua_rat.json" | "Let's think about the multi-choice question step by step.
Both together worked for 3 days.
In 3 days , P can do = 3 x
1
18
=
1
6
th work
In 3 days, Q can do = 3 x
1
15
=
1
5
th work
In 3 days , work finished =
1
6
+
1
5
=
11
30
Balance work =
19
30
Balance work finished by Q => Time taken by Q to finish the balance work =
19
30
x 15 = 9.5 days
The whole work was completed in 9.5 + 3 = 12.5 days
The answe is B" | "P can complete a piece of work in 18 days & B can do the same piece of work in 15 days. They started working together but after 3 days P left & Q alone completed the remaining work. The whole work was completed in how many days?
Answer Choices: (A) 12 days (B) 12.5 days (C) 13 days (D) 13.5 days (E) 15.5 days" |
"data/PoT/aqua_rat_filtered.json" | "distance = 624
time = 6.5
speed = distance / time
print(speed)" | "A car covers a distance of 624 km in 6 ½ hours. Find its speed?
Answer Choices: (A) 104 (B) 7778 (C) 266 (D) 288 (E) 121 Let's write a Python program to solve it." |
"data/CoT/aqua_rat.json" | "this is equivalent to :-
2x * 4y * 5z = 16000
y = z (given)
2x * 4y * 5y = 16000
2x * y^2 = 16000/20
2x * y^2 = 800
now from options given we will figure out which number will divide 800 and gives us a perfect square :-
which gives us x = 4 as
2* 4 * y^2 =800
y^2 = 100
y =10
Number of red balls = 4 hence D" | "In the game of Dubblefud, red balls,blue balls and green balls are each worth 2, 4 and 5 points respectively. In a certain selection of balls,the product of the point values of the balls is 16,000. If the number of blue balls in this selection equals the number of green balls, how many red balls are in the selection?
Answer Choices: (A) 1 (B) 2 (C) 3 (D) 4 (E) 5" |
"data/CoT/gsm_train.json" | "First find the total number of cloves needed to repel the vampires: 30 vampires * 3 cloves / 2 vampires = 45 cloves
Then find the total number of cloves needed to repel the wights: 12 wights * 3 cloves / 3 wights = 12 cloves
Then find the total number of cloves needed to repel the vampire bats: 40 vampire bats * 3 cloves / 8 vampire bats = 15 cloves
Then add up these three amounts to find the total number of cloves needed: 45 cloves + 12 cloves + 15 cloves = 72 cloves
The answer is 72" | "3 cloves of garlic can repel 2 vampires, 8 vampire bats or 3 wights. How many cloves of garlic are needed to repel 30 vampires, 12 wights and 40 vampire bats?" |
"data/CoT/gsm_rft.json" | "The dog that likes blueberries ate 3/4 * 60 blueberries = 45 blueberries, 3/4 as many blueberries as the number of bonnies eaten by the third dog.
The total number of fruits eaten by the dog that likes bonnies and the one that likes blueberries is 45 blueberries + 60 bonnies = 105
The first dog that likes apples ate 3 * 45 apples = 135 apples which are 3 times as many blueberries as the number eaten by the dog that likes blueberries.
In total, the three dogs ate 105 fruits + 135 apples = 240 fruits.
The answer is 240" | "There are three dogs in the backyard. They like apples, blueberries, and bonnies. The first dog, which likes apples, eats 3 times as many apples as the number of blueberries eaten by the second dog that likes blueberries. The dog that likes blueberries eats 3/4 times as many blueberries as the number of bonnies eaten by the third dog. If the dog that likes bonnies ate 60 of them, calculate the total number of fruits eaten by the three dogs?" |
"data/CoT/aqua_rat.json" | "Let's solve the multi-choice question step by step.
39 + 19 = 58/13 = 6 (Remainder)
The answer is D" | "A certain number when divided by 39 leaves a remainder 19, what is the remainder when the same number is divided by 13?
Answer Choices: (A) 7 (B) 8 (C) 9 (D) 6 (E) 4" |
"data/PoT/MATH_train.json" | "def sum_of_divisors(n):
result = 0
i = 1
while i <= n:
if (n % i==0):
result = result + i
i = i + 1
return result
def is_prime(n):
if n <= 1:
return False
if n <= 3:
return True
if n%2 == 0 or n%3 == 0:
return False
i = 5
while(i * i <= n):
if (n%i == 0 or n%(i + 2) == 0):
return False
i += 6
return True
count = 0
for n in range(1, 26):
if is_prime(sum_of_divisors(n)):
count += 1
print(count)" | "Let $f(n)$ be the sum of the positive integer divisors of $n$. For how many values of $n$, where $1 \le n \le 25$, is $f(n)$ prime? Let's write a program." |
"data/CoT/aqua_rat.json" | "Let's solve the multi-choice question step by step.
Given 1/10 and 5% that is 1/10
Let the last year's target be 20
This year's target is 5% more of last year=22
The target reached this year=1/10*20=2
Remaining target is 22-2=20
Required 20/20
The answer is C" | "A toothpaste manufacturer has set an annual production target to gain more profits. This year the target reached is 1/10 of last year's target. If the target production this year is increased 5% of the last year's target, how much percentage of the last year's target does he still need to reach to get the profit?
Answer Choices: (A) 4/5 (B) 3/6 (C) 20/20 (D) 10/5 (E) 4/3" |
"data/CoT/aqua_rat.json" | "Let's think about the multi-choice question step by step.
Let Marked price be Re. 1 each
C.P. of 54 pens = Rs. 46
S.P. of 54 pens = 99% of Rs. 54= Rs. 53.46
Profit % = (Profit /C.P.) x 100
Profit% = (7.46/46) x 100 = 16.21 %
The answer is C" | "A man buys 54 pens at marked price of 46 pens from a whole seller. If he sells these pens giving a discount of 1% , what is the profit percent?
Answer Choices: (A) 7.6 % (B) 7.7 % (C) 16.21 % (D) 13.6 % (E) 7.8 %" |
"data/CoT/aqua_rat.json" | "Let's think about the multi-choice question.
1^2+1=2
2^2+3=7
3^2+5=14
5^2+7=32
7^2+9=58
11^2+11=132
The answer is D" | "2,7,14,32,58,?
Answer Choices: (A) 112 (B) 154 (C) 123 (D) 132 (E) 144" |
"data/CoT/MATH_train.json" | "Let the sides of the triangle have lengths $3x$, $4x$, and $5x$. The triangle is a right triangle, so its hypotenuse is a diameter of the circle. Thus $5x=2\cdot 3=6$, so $x=6/5$. The area of the triangle is \[
\frac{1}{2}\cdot 3x\cdot 4x =\frac{1}{2}\cdot \frac{18}{5}\cdot \frac{24}{5}
=\frac{216}{25}=\boxed{8.64}.\]. The answer is 8.64" | "A triangle with side lengths in the ratio 3:4:5 is inscribed in a circle of radius 3. What is the area of the triangle? Provide your answer as a decimal rounded to the nearest hundredth." |
"data/CoT/aqua_rat.json" | "Let's think about the multi-choice question.
Expensive item = $100;
Cheap item = $75;
We must increase $75 to $100, so by $25, which is approximately 30% increase: (100-75)/75 = 1/3 = ~0.33
The answer is C." | "A merchant has selected two items to be placed on sale, one of which currently sells for 25 percent less than the other. If he wishes to raise the price of the cheaper item so that the two items are equally priced, by what percentage must he raise the price of the less expensive item?
Answer Choices: (A) 52 % (B) 40% (C) 30% (D) 20% (E) 10%" |
"data/PoT/aqua_rat_filtered.json" | "selling_price = 900
profit = 150
# calculate the cost price
cost_price = selling_price - profit
# calculate the profit percentage
profit_percentage = (profit / cost_price) * 100
print(profit_percentage)" | "A cricket bat is sold for $900, making a profit of $150. The profit percentage would be
Answer Choices: (A) 24% (B) 20% (C) 30% (D) 36% (E) 40% Please write a program to solve it" |
"data/CoT/aqua_rat.json" | "Let's reason about the multi-choice question.
is there other way than just listing?
25
34
43
52
59
61
68
70
77
86
95
106
115
124
14 ways..
The answe is C" | "The digital sum of a number is the sum of its digits. For how many of the positive integers 24-130 inclusive is the digital sum a multiple of 7?
Answer Choices: (A) 7 (B) 8 (C) 14 (D) 16 (E) 20" |
"data/CoT/math50k_camel.json" | "To determine the winner of this Nim game, we can use the concept of Nim-sum, which is the bitwise XOR operation of the number of stones in each pile. If the Nim-sum is non-zero, the first player has a winning strategy; otherwise, the second player has a winning strategy.
Let's calculate the Nim-sum for the given piles:
5 (in binary: 101)
6 (in binary: 110)
7 (in binary: 111)
-------------------
Nim-sum: 000
Since the Nim-sum is 0, the second player has a winning strategy, and therefore, the second player will win the game if both players make optimal moves." | "A combinatorial game called "Nim" is played between two players. In this game, there are 3 piles of stones with 5, 6, and 7 stones respectively. Players take turns removing stones from any pile of their choice, with the restriction that they can only remove one or two stones at a time. The player who takes the last stone wins. If the players are allowed to make optimal moves, who will win the game?" |
"data/CoT/math50k_camel.json" | "First, let's find the Cartesian product of A and B, denoted as A x B. This is the set of all ordered pairs (a, b) where a is in A and b is in B.
A x B = {(1, 2), (1, 3), (1, 4), (2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3, 4)}
Now let's find the intersection of A and B, denoted as A ∩ B. This is the set of elements that are common to both A and B.
A ∩ B = {2, 3}
Next, let's find the Cartesian product of B and A, denoted as B x A. This is the set of all ordered pairs (b, a) where b is in B and a is in A.
B x A = {(2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (4, 1), (4, 2), (4, 3)}
Now let's find the intersection of B and A, denoted as B ∩ A. This is the set of elements that are common to both B and A.
B ∩ A = {2, 3}
Now, let's compare the Cartesian products A x B and B x A:
A x B = {(1, 2), (1, 3), (1, 4), (2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3, 4)}
B x A = {(2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (4, 1), (4, 2), (4, 3)}
As we can see, A x B ≠ B x A, which means the Cartesian product is not commutative.
Now let's compare the intersections A ∩ B and B ∩ A:
A ∩ B = {2, 3}
B ∩ A = {2, 3}
In this case, A ∩ B = B ∩ A, which means the intersection is commutative.
However, the original question asked to show that the Cartesian product of two sets is not commutative with respect to intersection. This means we need to show that (A x B) ∩ (B x A) ≠ (B x A) ∩ (A x B).
(A x B) ∩ (B x A) = {}
(B x A) ∩ (A x B) = {}
In this case, the intersection of the Cartesian products is the empty set, which means (A x B) ∩ (B x A) = (B x A) ∩ (A x B). However, this does not contradict the fact that the Cartesian product itself is not commutative, as we have already shown that A x B ≠ B x A. The intersection operation is commutative, but the Cartesian product operation is not." | "Let A = {1, 2, 3} and B = {2, 3, 4}. Find the Cartesian product of A and B, then find the intersection of A with B. Repeat the process by finding the Cartesian product of B and A, then find the intersection of B with A. Show that the Cartesian product of two sets is not commutative with respect to intersection." |
"data/CoT/math50k_camel.json" | "To determine the stability of a control system using its transfer function H(s), we need to analyze the poles of the system. The poles are the values of s that make the denominator of the transfer function equal to zero. A system is stable if all its poles have negative real parts, and unstable if any pole has a positive real part.
Given the transfer function H(s) = (s+2)/(s^2+4s+5), let's find the poles by setting the denominator equal to zero:
s^2 + 4s + 5 = 0
This is a quadratic equation, and we can use the quadratic formula to find its roots:
s = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 1, b = 4, and c = 5. Plugging these values into the formula, we get:
s = (-4 ± √(4^2 - 4*1*5)) / 2*1
s = (-4 ± √(16 - 20)) / 2
s = (-4 ± √(-4)) / 2
Since the discriminant (b^2 - 4ac) is negative, the roots of the quadratic equation are complex conjugates:
s = -2 ± j
Both poles have negative real parts (-2), which means the system is stable." | "A control system has the transfer function H(s) = (s+2)/(s^2+4s+5). Use the Fourier transform to determine if the system is stable or unstable." |
"data/PoT/numglue.json" | "no_geese = 58
no_ducks = 37
geese_more_duck = no_geese - no_ducks
print(geese_more_duck)" | "There were 58.0 geese and 37.0 ducks in the marsh. How many more geese were in the marsh. Please write a program to solve it" |
"data/CoT/math50k_camel.json" | "In hyperbolic geometry, the area of a hyperbolic triangle can be found using the Gauss-Bonnet theorem. The formula for the area of a hyperbolic triangle with angles α, β, and γ in a hyperbolic plane with curvature K is:
Area = (π - (α + β + γ)) / |K|
In this case, the angles are 40°, 60°, and 80°, and the curvature K is -1. First, we need to convert the angles to radians:
40° = 40 * (π/180) = 2π/9 radians
60° = 60 * (π/180) = π/3 radians
80° = 80 * (π/180) = 4π/9 radians
Now, we can plug the values into the formula:
Area = (π - (2π/9 + π/3 + 4π/9)) / |-1|
Area = (π - (2π/9 + 3π/9 + 4π/9)) / 1
Area = (π - 9π/9) = π - π = 0
The area of this hyperbolic triangle is 0." | "A math student is asked to find the area of a hyperbolic triangle whose angles measure 40°, 60°, and 80°, all in hyperbolic space. If the hyperbolic plane has a curvature of -1, what is the area of this hyperbolic triangle?" |
"data/PoT/MATH_train.json" | "# Python Program
def sequence_length(x):
sequence = [1000, x]
while sequence[-1] >= 0:
next_term = sequence[-2] - sequence[-1]
sequence.append(next_term)
return len(sequence) - 1
max_length = 0
max_x = 0
for x in range(1, 1001):
length = sequence_length(x)
if length > max_length:
max_length = length
max_x = x
print(max_x)" | "Except for the first two terms, each term of the sequence $1000, x, 1000 - x,\ldots$ is obtained by subtracting the preceding term from the one before that. The last term of the sequence is the first negative term encountered. What positive integer $x$ produces a sequence of maximum length? Let's write a program." |
"data/CoT/gsm_rft.json" | "Boys:96(2/3)=64
Girls:96(1/3)=32
Boys that want to toast marshmallows:64(.50)=32
Girls that want to toast marshmallows:32(.75)=24
Total that want to toast marshmallows:32+24=56
They need 56 marshmallows
The answer is 56" | "At camp Wonka, there are 96 campers. Two-thirds of the campers are boys, and the remaining one-third are girls. 50% of the boys want to toast marshmallows and 75% of the girls want to toast marshmallows. If each camper gets one marshmallow to toast, how many marshmallows do they need?" |
"data/CoT/aqua_rat.json" | "Let's reason about the multi-choice question.
(16^7+16) / 16 =
16*(16^6+1) / 16 =
16^6 + 1
Clearly this is a number which ends with a 7 in the units place.
The answer is B." | "What is (16^7+16) / 16?
Answer Choices: (A) 15467118 (B) 16777217 (C) 17827343 (D) 18047455 (E) 19357579" |
"data/CoT/aqua_rat.json" | "Let's think about the multi-choice question step by step.
Speed of the first train = 120/8 = 15 m/sec.
Speed of the second train = 120/15 = 8 m/sec.
Relative speed = 15 + 8 = 23 m/sec.
Required time = (120 + 120)/23 = 10 sec.
The answer is D" | "Two trains of equal lengths take 8 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
Answer Choices: (A) 22 (B) 12 (C) 77 (D) 10 (E) 21" |
"data/CoT/aqua_rat.json" | "Let’s check each statement.
Statement I:Bob can buy 4 bowls of ice cream. the cost of one bowl of ice cream is $5, 4 bowls of ice cream will cost $5 * 4 = $20, in which case Statement I is be TRUE.
Statement II: Bob can buy 2 bowls of icecream and pizza. The cost of ice cream is $5 and pizza is $12, 2 bowls of ice cream will cost $5 * 2 = $10 and Pizza will cost $12. Total is $10 + $12 = $22 in which case Statement II can NEVER BE TRUE.
Statement III: Bob can buy 3 bowls of ice cream and pizza. 3 bowls of ice cream = $5 * 3 = $15 and pizza = $12. Total = $15 + $12 = $27, in which case Statement III ca NEVER BE TRUE.
Only Statement I is true.
So,the correct answer is A" | "If Bob has $20 in his pocket and a bowl of ice creams sells for $5 and pizza sells for $12, which of the following COULD be true?
I. Bob can buy 4 bowls of ice cream.
II. Bob can buy 2 bowls of ice cream and pizza.
III. Bob can buy 3 bowls of ice cream and pizza.
Answer Choices: (A) I only (B) I and II only (C) I and III only (D) II and III only (E) I, II and III" |
"data/CoT/math50k_camel.json" | "To solve for x, we can rewrite the equation as a logarithm:
$log_4{256} = x$
Now, we know that $4^2 = 16$ and $4^3 = 64$, so the value of x must be between 2 and 3. We also know that $4^4 = 256$, so:
$log_4{256} = 4$
Therefore, x = 4." | "Solve for x:
$4^x = 256$" |
"data/CoT/aqua_rat.json" | "take it as original output =100.
to meet demand increase by 10%, then output=110.
to meet holiday demand , new output increase by 60% then output equals 176
To restore new holidy demand output to original 100.
final -initial/final*100
=76/176*100=8/33*100=43% approxiamately.
option D is correct." | "The output of a factory is increased by 10% to keep up with rising demand. To handle the holiday rush, this new output is increased by 60%. By approximately what percent would the output of the factory now have to be decreased in order to restore the original output?
Answer Choices: (A) 20% (B) 24% (C) 30% (D) 43% (E) 79%" |
"data/PoT/numglue.json" | "tower_made_blocks=35
total_blocks=65
added_blocks=total_blocks-tower_made_blocks
print(added_blocks)" | "Adolfo made a tower with 35 blocks. He added some more blocks, and now he has 65 blocks. He had to add _____ blocks . Let's write a program." |
"data/CoT/aqua_rat.json" | "Let's reason about the multi-choice question.
Local value of 3 = 3 x 100 = 300
Place value of 3 = 3
There fore = 3 x 300 = 900
The answe is D" | "Find the product of the localvalue and absolutevalue of 3 in 20368?
Answer Choices: (A) 1000 (B) 1100 (C) 1200 (D) 900 (E) 10000" |
"data/CoT/math50k_camel.json" | "In a Feistel cipher with a key size of 128 bits and 16 rounds, the key is typically divided into subkeys for each round. To determine the number of key bits used in each round, we can simply divide the total key size by the number of rounds:
128 bits (total key size) / 16 rounds = 8 bits per round
So, 8 key bits are used in each round of the Feistel cipher." | "Given a Feistel cipher structure with a block size of 64 bits and a key size of 128 bits, using 16 rounds and a round function that involves a substitution-permutation network (SPN), how many key bits are used in each round?" |
"data/CoT/aqua_rat.json" | "Let's reason about the multi-choice question.
In this type of questions we first get the finishing of work in 1 day for A,B,C then we will add them to get the result, as:
Part finished by A in 1 day= 1/6
Part finished by B in 1 day = 1/8
Part finished by C in 1 day =1/12
Part finished by (A+B+C) in 1 day = 9/24
= 9/24 Remaining work =1-9/20=11/20. Number days to finish the work by A+B+C =2 2/3 days.
The answer is B" | "A, B and C can do a piece of work in 6,8 and 12 days respectively. In how many days would all of them complete the same job working together?
Answer Choices: (A) 2 3/4 days. (B) 2 2/3 days. (C) 2 3/2 days. (D) 3 1/2 days. (E) 3 3/4 days." |
"data/CoT/gsm_rft.json" | "Richard needs to pass for 90 touchdowns because 89 + 1 = 90
He has passed for 84 touchdowns because 14 x 6 = 84
He needs to pass for 6 touchdowns in the final two games because 90 - 84 = 6
He must average 3 touchdowns a game because 6 / 2 = 3
The answer is 3" | "Archie holds the school record for most touchdown passes with 89 in a season of 16 games. Richard is close to breaking the record, having averaged 6 touchdowns a game in the first 14 games. How many touchdowns per game must he average in the final two games to beat Archie's record?" |
"data/CoT/aqua_rat.json" | "Let's think about the multi-choice question.
Generally in such cases, there is always loss.
So always remember, when two materials are sold and if one material gets profit and the other gets a loss, then use the trick shown below to calculate the loss.
Loss% = Common loss and gain% 2 = x 2
10 10
Therefore, here common loss and gain % = 15%
Hence,
Loss% = 15 2 = 2.25%
The answe is C" | "Boy purchased two flats for Rs.5,00,000. On one he gains 15 % while on the other he losses 15%. How much does he gain or lose?
Answer Choices: (A) 2% (B) 2.12% (C) 2.25% (D) 2.30% (E) 2.50%" |
"data/CoT/math50k_camel.json" | "First, we need to convert the decimal numbers 45 and 68 to binary.
45 in binary is 101101
68 in binary is 1000100
To make the binary numbers have the same number of digits, we can add a leading 0 to the binary representation of 45:
045 in binary is 0101101
Now, we can add the two binary numbers using modulo 2 arithmetic:
0101101 (45)
+ 1000100 (68)
----------
1101001 (encrypted binary message)
So, the resulting encrypted binary message is 1101001." | "Suppose you need to send a secret message "45" to your friend using the one-time pad encryption key "68". Convert both the message and key from decimal to binary and add them together (using modulo 2 arithmetic). What is the resulting encrypted binary message?" |
"data/PoT/gsm_gpt4.json" | "# defining the initial variables
total_pies = 4
sold_pies = 1
given_pies = 1
pieces_per_pie = 6
# calculating the remaining pies
remaining_pies = total_pies - sold_pies - given_pies
# slicing the remaining pies into pieces
total_pieces = remaining_pies * pieces_per_pie
# the family ate 2/3 of the pieces
eaten_pieces = 2/3 * total_pieces
# calculating the remaining pieces
remaining_pieces = total_pieces - eaten_pieces
# print the result
print(int(remaining_pieces))" | "Grace baked 4 whole pumpkin pies. She sold 1 whole pumpkin pie and gave 1 whole pumpkin pie to her friend. The remaining whole pumpkin pies were each sliced into 6 pieces. Her family ate 2/3 pieces. How many pieces of pumpkin pie were left? Let's program in Python in the response." |
"data/CoT/aqua_rat.json" | "Let's reason about the multi-choice question.
The total number of ways to choose 2 children from 6 is 6C2 = 15
The number of ways to choose 1 boy and 1 girl is 3*3 = 9
P(1 boy and 1 girl) = 9/15
The answer is D." | "From a group of 3 boys and 3 girls, 2 children are to be randomly selected. What is the probability that 1 boy and 1 girl will be selected?
Answer Choices: (A) 1/10 (B) 4/9 (C) 1/2 (D) 9/15 (E) 2/3" |
"data/CoT/math50k_camel.json" | "The Lyapunov exponent (λ) for the logistic map can be calculated using the formula:
λ = ln |r - 2r * x|
where r is the parameter value, and x is the fixed point of the logistic map. The logistic map is given by the equation:
x(n+1) = r * x(n) * (1 - x(n))
For r = 3.2, we first need to find the fixed point x. To do this, we set x(n+1) = x(n) = x and solve for x:
x = 3.2 * x * (1 - x)
x - 3.2x^2 = 0
x(1 - 3.2x) = 0
This equation has two solutions: x = 0 and x = 1/3.2. Since the fixed point should be in the interval (0, 1), we choose x = 1/3.2.
Now, we can calculate the Lyapunov exponent:
λ = ln |3.2 - 2 * 3.2 * (1/3.2)|
λ = ln |3.2 - 2|
λ = ln(1.2)
λ ≈ 0.1823
So, the Lyapunov exponent for the logistic map with r = 3.2 is approximately 0.1823." | "What is the value of the Lyapunov exponent for the logistic map if r = 3.2?" |
"data/PoT/MATH_train.json" | "print(2.5 - 0.32)" | "Find $2.5-0.32.$ Let's write a Python program to solve it." |
"data/CoT/gsm_train.json" | "First find the total number of calories in the pancakes: 6 pancakes * 120 calories/pancake = 720 calories
Then find the total number of calories in the bacon: 2 strips * 100 calories/strip = 200 calories
Then add the number of calories in each food to find the total number of calories: 720 calories + 200 calories + 200 calories = 1120 calories
The answer is 1120" | "Jerry's breakfast includes 6 pancakes with 120 calories each, two strips of bacon with 100 calories each, and a bowl of cereal with 200 calories. How many calories is his breakfast total?" |
"data/PoT/numglue.json" | "connie = 323
comparison = 175
juan = comparison + connie
print(juan)" | "Connie has 323 marbles. Juan has 175 more marbles than Connie. How many marbles does Juan have? Please respond by writing a program in Python." |
"data/CoT/gsm_rft.json" | "Each step is made up of 3 blocks of stone, so each level has 8 steps * 3 blocks of stone = 24 blocks of stone.
Clara climbed past 96 blocks of stone, so she climbed past 96 / 24 = 4 levels.
The answer is 4" | "Clara is climbing to the top of a historical tower with stone stairs. Each level has eight huge steps in the stairs. Every step is made up of three massive blocks of stone. By the time she reaches the top, she has climbed past 96 blocks of stone. How many levels are there in the tower?" |
"data/CoT/aqua_rat.json" | "Let's reason about the multi-choice question.
The area of the carpet in feet is xy.
The area in square yards is xy / 9.
The price per square yard is 12 / (xy/9) = 108/(xy).
The answer is A." | "A rectangular-shaped carpet that measures x feet by y feet is priced at $12. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)
Answer Choices: (A) 108/ (xy) (B) 90xy (C) xy/90 (D) xy/10 (E) 10/ (xy) " |
"data/PoT/aqua_rat_filtered.json" | "target_runs = 282
total_overs = 50
remaining_overs = total_overs - 10
target_runs_remaining = target_runs - (3.2 * 10)
required_run_rate = target_runs_remaining / remaining_overs
print(required_run_rate)" | "In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
Answer Choices: (A) 5 (B) 6.25 (C) 6.75 (D) 7 (E) 7.25 Let's write a Python program to solve it." |
"data/CoT/aqua_rat.json" | "Let's solve the multi-choice question step by step.
10 units
as other 2 sides will be 15,15 units.
The answer is D" | "Perimeter of an equilateral and isosceles is 45 and 40 respectively. At least one of the sides of isosceles is equal to the equilateral. What's the base of isosceles triangle?
Answer Choices: (A) 7 (B) 8 (C) 9 (D) 10 (E) 11" |
"data/CoT/aqua_rat.json" | "Let's think about the multi-choice question step by step.
Let the number of boys and girls be 8x and 5x
Then , 5x = 120
x= 24
Total number of students = 13x = 13*24 = 312
The answer is A" | "In a college the ratio of the numbers of boys to the girls is 8:5. If there are 120 girls, the total number of students in the college is?
Answer Choices: (A) 312 (B) 356 (C) 452 (D) 416 (E) 512" |
"data/CoT/math50k_camel.json" | "To determine if a point is part of the Julia set, we need to iterate the function f(z) = z^2 + c, where z is a complex number and c is a constant complex number. In this case, the point (0.25, 0.5) corresponds to the complex number z = 0.25 + 0.5i, and c = -0.4 + 0.6i.
The point is considered to be in the Julia set if the magnitude of z (|z|) does not exceed a certain threshold (usually 2) after a maximum number of iterations. The number of iterations required to determine if a point is in the Julia set depends on the desired level of accuracy. A common choice for the maximum number of iterations is 1000, but it can be higher or lower depending on the desired precision.
Let's calculate the first few iterations of the function f(z) for the given point and complex number c:
1. z1 = (0.25 + 0.5i)^2 + (-0.4 + 0.6i) = (-0.015 + 0.3i) + (-0.4 + 0.6i) = -0.415 + 0.9i
2. z2 = (-0.415 + 0.9i)^2 + (-0.4 + 0.6i) = (-0.6715 - 0.747i) + (-0.4 + 0.6i) = -1.0715 - 0.147i
3. z3 = (-1.0715 - 0.147i)^2 + (-0.4 + 0.6i) = (0.01210225 - 0.31542i) + (-0.4 + 0.6i) = -0.38789775 + 0.28458i
We can continue this process for the desired number of iterations. If the magnitude of z remains below the threshold (2) after the maximum number of iterations, the point is considered to be part of the Julia set. If the magnitude of z exceeds the threshold before reaching the maximum number of iterations, the point is not part of the Julia set.
In this case, we cannot determine the exact maximum number of iterations required without specifying the desired level of accuracy. However, a common choice for the maximum number of iterations is 1000." | "What is the maximum number of iterations required to determine if a point with coordinates (0.25, 0.5) is part of the Julia set associated with the complex number c = -0.4 + 0.6i?" |
"data/CoT/gsm_rft.json" | "Each hectare of Johnson's neighbor can yield 80 x 2 = 160 corns every two months.
So the neighbor's two-hectare cornfield can yield a total of 160 x 2 = 320 corns every two months.
Therefore, the total corn they can harvest altogether every two months is 320 + 80 = 400.
Therefore, the total corn they can harvest altogether after six months is 400 x 3 = 1200.
The answer is 1200" | "Johnson owns a hectare cornfield that can yield 80 corn every two months, while his neighbor owns a two-hectare cornfield and each hectare can yield twice the amount as Johnson. How much corn can they harvest altogether after six months?" |
"data/CoT/math50k_camel.json" | "To encrypt the message "HELLO WORLD" using the described transposition cipher, we first take alternate letters:
H E L L O W O R L D
E L O O L
ELOOL
Now, we reverse the order of the resulting string:
LOOLE
So, the encrypted message is "LOOLE"." | "A message "HELLO WORLD" is encrypted using a transposition cipher by taking alternate letters and then reversing the order of the resulting string. What is the encrypted message?" |
"data/CoT/aqua_rat.json" | "Let's think about the multi-choice question.
Since minimal investments must be made for 2, 2, 3, and 4 thousand dollars into
the four mutual funds, this leaves 20-2-2-3-4 = 9 thousand dollars to invest as one
pleases. Thus, we want to determine the number of ways of dividing up 9 thousand dollars
among 4 different mutual funds. Consider 12 different boxes aligned as shown and check
three of them:Here, we have checked the first, fifth, and tenth boxes. Each such diagram corresponds to
a way of investing the remaining money as follows. We order the mutual funds. Count
the number of unchecked boxes to the left of the first checkmark. Call this number k1.
In the illustration above, k1 = 0. Next, count the number of unchecked boxes between
the first two checkmarks. Call this number k2. In the illustration, k2 = 3. Next, call
k3 the number of unchecked boxes between the second and third checkmarks, and call k4
the number of unchecked boxes after the third checkmark. Thus, k3 = 4 and k4 = 2.
Observe that k1 + k2 + k3 = 9, the total number of unchecked boxes. Make additional
investments (beyond the required minimal investments) of k1 thousand dollars in the first
fund, k2 thousand dollars in the second fund, k3 thousand dollars in the third fund, and
k4 thousand dollars in the fourth fund. Thus, the total number of dierent investments is
the same as the number of ways of choosing three blocks (to check) from among 12 blocks.
This number is(12 3)=12/3*9=12*11*10/3*2*1=220
The answer is A" | "We have 20 thousand dollars that must be invested among 4 possible
mutual funds. Each investment must be in units of 1 thousand dollars,
and there are minimal investments that need to be made if one is to
invest in these funds. The minimal investments are 2, 2, 3 and 4 thou-
sand dollars. How many dierent investment strategies are available if
an investment must be made in each mutual fund?
Answer Choices: (A) 220 (B) 240 (C) 260 (D) 280 (E) 300" |
"data/PoT/mathqa.json" | "n0 = 4.0
n1 = 10.0
n2 = 2.0
n3 = 2.0
n4 = 1.0
n5 = 3.0
n6 = 3.0
t0 = n1 - n2
t1 = t0 - n5
t2 = t1 - n3
answer = t2 / n6
print(answer)" | "harry started a 4 - mile hike with a full 10 - cup canteen of water and finished the hike in 2 hours with 2 cup of water remaining in the canteen . if the canteen leaked at the rate of 1 cup per hour and harry drank 3 cups of water during the last mile , how many cups did he drink per mile during the first 3 miles of the hike ? Let's write a Python program." |
"data/PoT/numglue.json" | "first = 1983
after = 1984
d = after - first
print(d * 12)" | "Passage: Forecasting airline interest in larger-capacity models, Boeing announced the stretched 767-300 in 1983 and the extended-range 767-300ER in 1984. Both models offered a 20 percent passenger capacity increase, while the extended-range version was capable of operating flights up to . Japan Airlines placed the first order for the 767-300 in September 1983. Following its first flight on January 30, 1986, the type entered service with Japan Airlines on October 20, 1986. The 767-300ER completed its first flight on December 9, 1986, but it was not until March 1987 that the first firm order, from American Airlines, was placed. The type entered service with American Airlines on March 3, 1988. The 767-300 and 767-300ER gained popularity after entering service, and came to account for approximately two-thirds of all 767s sold. Question: How many months after the first flight of the 767-300 was the first flight of the 767-300ER? Please write a program to solve it" |
"data/CoT/aqua_rat.json" | "Explanatory Answer
The cow can graze the area covered by the circle of radius 19m initially, as the length of the rope is 19m.
Area of a circle = π * (radius)2
Therefore, the initial area that the cow can graze = 22/7 * 19(2) sq m.
When the length of the rope is increased to 30m, grazing area becomes = 22/7 * 30(2) sq m.
The additional area it could graze when length is increased from 19m to 30m
= 22/7 * (30square - 19square) sq m.
22/7 * (30 + 19)(30 - 19) = 22/7 * 49 * 11 = 1694 sq m.
Choice B" | "The length of a rope, to which a cow is tied, is increased from 19 m to 30 m. How much additional ground will it be able to graze? Assume that the cow is able to move on all sides with equal ease. Use π = \\frac{22}{7}\\) in your calculations.
Answer Choices: (A) 1696 sq m (B) 1694 sq m (C) 1594 sq m (D) 1756 sq.m (E) 1896 sq.m" |
"data/CoT/aqua_rat.json" | "Let's solve the multi-choice question step by step.
Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (110 + X)/30 = 25/2 ==> 2(110 + X) = 750 ==> X = 265 m.The answer is C" | "The length of the bridge, which a train 110 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
Answer Choices: (A) 328 (B) 279 (C) 265 (D) 288 (E) 211" |
"data/CoT/math50k_camel.json" | "A Sophie Germain prime is a prime number p such that 2p + 1 is also prime. The smallest Sophie Germain prime greater than 100 is 113, since 113 is prime and 2(113) + 1 = 227, which is also prime." | "What is the smallest Sophie Germain prime greater than 100?" |
"data/CoT/aqua_rat.json" | "Let's reason about the multi-choice question.
Let avg for 11 mos. = 10
Therefore, Dec = 70
Year total = 11*10 + 70 = 180
The answer is 70/180 = 7/18 = D" | "Last year Department Store X had a sales total for December that was 7 times the average (arithmetic mean) of the monthly sales totals for January through November. The sales total for December was what fraction of the sales total for the year?
Answer Choices: (A) 1/4 (B) 4/15 (C) 1/3 (D) 7/18 (E) 4/5" |
"data/CoT/gsm_train.json" | "The total weight of 100 bags of lemons is 100 x 8 = 800 kilograms.
So, 900 - 800 = 100 kilograms can still be loaded into the truck.
The answer is 100" | "A farmer hires small trucks to transport his lemons to the markets. The load on a truck may not be more than 900 kilograms. One bag of lemons has a mass of 8 kilograms. If there are 100 bags of lemons, how many more kilograms can still be loaded into the truck?" |
"data/CoT/gsm_train.json" | "Kendy transferred $60 x 1/2 = $30 to her sister.
So, She transferred a total of $60 + $30 = $90.
Therefore, Kendy has $100 + $90 = $190 in the account before the transfer.
The answer is 190" | "Kendy made 2 online bank transactions. She transferred $60 to her mom and half that amount to her sister. As a result, her account now has $100 left in it. How much money was in the account before the transfer?" |
"data/CoT/math50k_camel.json" | "To find the correlation coefficient between the sales of the two products, we will use the Pearson correlation coefficient formula:
r = Σ[(xi - x̄)(yi - ȳ)] / sqrt(Σ(xi - x̄)² * Σ(yi - ȳ)²)
where xi and yi are the individual sales data points for products A and B, x̄ and ȳ are the mean sales of products A and B, and Σ denotes the sum over all data points.
First, let's calculate the mean sales for products A and B:
x̄ = (50 + 60 + 65 + 70 + 75 + 80 + 85 + 90 + 95 + 100 + 105 + 110) / 12 = 935 / 12 = 77.92 (rounded to 2 decimal places)
ȳ = (70 + 80 + 90 + 95 + 100 + 110 + 120 + 130 + 140 + 150 + 160 + 170) / 12 = 1415 / 12 = 117.92 (rounded to 2 decimal places)
Now, let's calculate the numerator and denominator of the correlation coefficient formula:
Numerator:
Σ[(xi - x̄)(yi - ȳ)] = (50-77.92)(70-117.92) + (60-77.92)(80-117.92) + ... + (110-77.92)(170-117.92)
= -27.92 * -47.92 + -17.92 * -37.92 + ... + 32.08 * 52.08
= 1337.1264 + 679.5264 + ... + 1670.3264
= 1337.1264 + 679.5264 + 1080.3264 + 1337.1264 + 1593.9264 + 1850.7264 + 2107.5264 + 2364.3264 + 2621.1264 + 2877.9264 + 3134.7264
= 17984
Denominator:
Σ(xi - x̄)² = (-27.92)² + (-17.92)² + ... + (32.08)²
= 779.8464 + 321.1264 + ... + 1029.1264
= 779.8464 + 321.1264 + 1080.3264 + 1337.1264 + 1593.9264 + 1850.7264 + 2107.5264 + 2364.3264 + 2621.1264 + 2877.9264 + 3134.7264
= 17984
Σ(yi - ȳ)² = (-47.92)² + (-37.92)² + ... + (52.08)²
= 2296.1664 + 1437.9264 + ... + 2712.3264
= 2296.1664 + 1437.9264 + 1080.3264 + 1337.1264 + 1593.9264 + 1850.7264 + 2107.5264 + 2364.3264 + 2621.1264 + 2877.9264 + 3134.7264
= 26901
Now, let's plug these values into the correlation coefficient formula:
r = 17984 / sqrt(17984 * 26901)
= 17984 / sqrt(483397584)
= 17984 / 21986.32
= 0.818 (rounded to 3 decimal places)
The correlation coefficient between the sales of the two products is 0.818, which indicates a strong positive correlation between the sales of products A and B." | "A company wants to analyze the relationship between the sales of their two products A and B. For the last 12 months, the sales data is given below:
| Month | Product A (units sold) | Product B (units sold) |
|-------|-----------------------|-----------------------|
| Jan | 50 | 70 |
| Feb | 60 | 80 |
| Mar | 65 | 90 |
| Apr | 70 | 95 |
| May | 75 | 100 |
| Jun | 80 | 110 |
| Jul | 85 | 120 |
| Aug | 90 | 130 |
| Sep | 95 | 140 |
| Oct | 100 | 150 |
| Nov | 105 | 160 |
| Dec | 110 | 170 |
Find the correlation coefficient between the sales of the two products using multivariate analysis." |
🦣 MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning
MathInstruct is a meticulously curated instruction tuning dataset that is lightweight yet generalizable. MathInstruct is compiled from 13 math rationale datasets, six of which are newly curated by this work. It uniquely focuses on the hybrid use of chain-of-thought (CoT) and program-of-thought (PoT) rationales, and ensures extensive coverage of diverse mathematical fields.
Project Page: https://tiger-ai-lab.github.io/MAmmoTH/
Paper: https://arxiv.org/pdf/2309.05653.pdf
Code: https://github.com/TIGER-AI-Lab/MAmmoTH
Models:
| Base Model: Llama-2 | Base Model: Code Llama | |
|---|---|---|
| 7B | 🦣 MAmmoTH-7B | 🦣 MAmmoTH-Coder-7B |
| 13B | 🦣 MAmmoTH-13B | 🦣 MAmmoTH-Coder-13B |
| 34B | - | 🦣 MAmmoTH-Coder-34B |
| 70B | 🦣 MAmmoTH-70B | - |
License
Please check out the license of each subset in our curated dataset MathInstruct.
| Dataset Name | License Type |
|---|---|
| GSM8K | MIT |
| GSM8K-RFT | Non listed |
| AQuA-RAT | Apache 2.0 |
| MATH | MIT |
| TheoremQA | MIT |
| Camel-Math | Attribution-NonCommercial 4.0 International |
| NumGLUE | Apache-2.0 |
| CrowdSourced (Lila) | Attribution 4.0 International |
| MathQA | Apache-2.0 |
| Our Curated | MIT |
Citation
Please cite our paper if you use our data, model or code. Please also kindly cite the original dataset papers.
@article{yue2023mammoth,
title={MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning},
author={Xiang Yue, Xingwei Qu, Ge Zhang, Yao Fu, Wenhao Huang, Huan Sun, Yu Su, Wenhu Chen},
journal={arXiv preprint arXiv:2309.05653},
year={2023}
}
- Downloads last month
- 164
Size of downloaded dataset files:
209 MB
Size of the auto-converted Parquet files:
99.3 MB
Number of rows:
262,785