instruction stringlengths 16 4.34k | output stringlengths 5 6.77k | dataset stringclasses 8
values |
|---|---|---|
The average speed of a car is 1 4/5 times the avg speed of a bike. A tractor covers 575km in 23hrs. How much distance will the car cover in 4hrs if the speed of the bike is twice speed of the tractor?
Answer Choices: (A) 300 km (B) 320 km (C) 360 km (D) 420 km (E) 460 km | Let's reason about the multi-choice question.
Sol. Average speed of a tractor = 25 km / h
The speed of a bus in an hour = 25 × 2 = 50 km
The speed of a car in an hour = 9/5 * 50 = 90 km
So, the distance covered by car in 4 h is
90 × 4 = 360 km
The answer is C | MathInstruct |
The running time of Beast of War: Armoured Command is 10 minutes longer than that of Alpha Epsilon, which is 30 minutes shorter than that of Millennium. If Millennium runs for 2 hours, what is the running time of Beast of War: Armoured Command in minutes? | Since 60 minutes is equivalent to 1 hour, then 2 hours is equivalent to 2*60 = 120 minutes.
Thus, the running time of Alpha Epsilon is 120-30 = 90 minutes.
Therefore, Beast of War: Armoured Command runs for 90+10 = 100 minutes.
The answer is 100 | MathInstruct |
If the ratio of the roots of the equation x2+px+q=0 is equal to that of the roots x2+rx+s=0, then:
Answer Choices: (A) sq=pr (B) qp=sr (C) sq=p (D) ps=qr (E) none | Let's solve the multi-choice question step by step.
x2+px+q=0 for this eqn... roots are R1=-p R2=-q
x2+rx+s=0 for this eqn... roots are R3=-r R4=-s
As per Question, -p/-q=-r/-s
=> ps=qr
The answer is D | MathInstruct |
Two men can complete a piece of work in four days. Two women can complete the same work in eight days. Four boys can complete the same work in five days. If four men, eight women and 20 boys work together in how many days can the work be completed?
Answer Choices: (A) 1/2 day (B) 2 1/2 days (C) 1 1/2 days (D) 3 1/2 day... | A
1/2 day
Two men take four days to complete the work four men would take (2 * 4)/4 = 2 days to complete it.
Similarly four women would take two days to complete it and 20 children would take one day to complete it.
All the three groups working togerther will complete 1/2 + 1/2 + 1/1 work in a day
= 2 times the unit wo... | MathInstruct |
1, 1, 3, 9, 11, 121,?
Answer Choices: (A) 122 (B) 123 (C) 124 (D) 125 (E) 126 | Let's think about the multi-choice question step by step.
1^2 = 1 ......... 1+2 = 3
3^2 = 9 ....... 9+2 = 11
11^2 = 121 ...... 121+2 = 123
The answer is B | MathInstruct |
How many portions of 200 ml milk can Jasmine pour from a full 2-liter container of milk? | Since there are 1000 ml in 1 liter, then 2 liters is equal to 1000 x 2 = 2000 ml.
Thus, Jasmine can pour 2000/200 = 10 portions of 200 ml milk.
The answer is 10 | MathInstruct |
Carl has been selling watermelons on the side of the road for $3 each. This evening he went home with $105 in profit and 18 watermelons. How many watermelons did he start out with this morning? | Carl sells his watermelons for $3 each so today he sold $105 / $3 per watermelon = 35 watermelons.
He had 18 watermelons left over, so this morning he started with 18 + 35 = 53 watermelons.
The answer is 53 | MathInstruct |
Suppose that $f(z)$ is a holomorphic function on the upper half-plane $\mathbb{H}$, and that $f(\frac{1}{n}) = \frac{1}{n^2}$ for all positive integers $n$. Show that $f(z) = z^2$ for all $z\in \mathbb{H}$. | We will use the identity theorem for holomorphic functions. The identity theorem states that if two holomorphic functions agree on a set with an accumulation point, then they must be equal everywhere in their domain.
Consider the function $g(z) = f(z) - z^2$. Then $g(z)$ is also holomorphic on $\mathbb{H}$, since it i... | MathInstruct |
Let X be a non-singular projective curve over a field k with genus g(X)=3, and let L be an invertible sheaf on X such that h⁰(X, L)=2 and h¹(X, L)=1. Determine the dimension of the space H⁰(X, L²). | To determine the dimension of H⁰(X, L²), we will use the Riemann-Roch theorem for curves. The Riemann-Roch theorem states that for any divisor D on a curve X of genus g, we have:
h⁰(X, D) - h¹(X, D) = deg(D) + 1 - g
In our case, we are given h⁰(X, L) = 2 and h¹(X, L) = 1. We want to find h⁰(X, L²). Let D be the divis... | MathInstruct |
"statement 1": 200 , what will be the difference between Mani and Rani ' s share ?, "statement 2" :less than 400 , what will be the difference between Mani and Rani ' s share ?, "options: " Entailment or contradiction or neutral? Please respond by writing a program in Python. | share_s1 = 200
share_s2 = 400
if share_s1 is None or share_s2 is None:
print('neutral')
elif share_s1 < share_s2:
print('Entailment')
elif share_s1 != share_s2:
print('contradiction') | MathInstruct |
Let X be a smooth projective cubic curve in the complex projective plane, and let Y be a line intersecting X in six distinct points. Compute the dimension of the intersection cohomology group IH^3(Y) with coefficients in the field with two elements. | To compute the dimension of the intersection cohomology group IH^3(Y) with coefficients in the field with two elements, we will use the Lefschetz Hyperplane Theorem.
The Lefschetz Hyperplane Theorem states that if X is a smooth projective variety of dimension n and Y is a hyperplane section of X, then the restriction ... | MathInstruct |
town m town n town o town p town q town r ; town a town b town c town d town e town f in the table above , what is the least number of table entries that are needed to show the mileage between each town and each of the other 5 towns ? Please write a program to solve it | n0 = 5.0
t0 = 2.0 * 3.0
t1 = n0 * t0
answer = t1 / 2.0
print(answer) | MathInstruct |
A man walks 6 km at a speed of 1 1/2 kmph, runs 8 km at a speed of 2 kmph and goes by bus another 32 km. Speed of the bus is 8 kmph. Find the average speed of the man.
Answer Choices: (A) 4 (5/6) kmph (B) 3 (5/6) kmph (C) 5 (7/6) kmph (D) 6 (7/6) kmph (E) None of these | Let's solve the multi-choice question step by step.
Man walked 6 km at 1.5 kmph, again he walked 8 km at speed of 2 kmph and 32 km at a speed of 8kmph
time taken indivisually:
=> 6/1.5 = 4 m
=> 8/2 = 4 m
=> 32/8 = 4 m
Average speed of man= total distance/ total time
=> 46/12 = 3 (5/6)
The answer is B | MathInstruct |
David decides to attend a base ball game with six friends. If the party of seven sits together in seven consecutive seats, and David must NOT sit in between two of his friends, how many ways can the seven friends be arranged?
Answer Choices: (A) 360 (B) 180 (C) 90 (D) 720 (E) 1440 | Let's reason about the multi-choice question.
David have to sit at either of the ends.
If David sits on the left most corner, then other 6 friends can be arranged in 6! = 720
David can also sit on the other end, then another 6! ways we can arrange.
So total number of ways = 720+720 = 1440
The answer is E | MathInstruct |
What is the greatest prime factor of 42^2+75^2+6300
Answer Choices: (A) 3 (B) 7 (C) 11 (D) 13 (E) 79 | Let's reason about the multi-choice question.
42^2 = (50-8)(50-8) = 1764
75^2 = (100-25)(100-25) = 5625
1764+5625+6300 = 13689
this number is divisible by 3 and 9
divide by 9 and get 1521, the sum of this number is again a multiple of 9, thus we can divide it one more time by 9. we get 169, and 169 is 13^2. thus The an... | MathInstruct |
A stock option has a current market value of $5.05 and a strike price of $50. The volatility of the stock price is 0.3 and the risk-free interest rate is 0.05. Using the Black-Scholes equation, what is the theoretical value of the option? | To calculate the theoretical value of the option using the Black-Scholes equation, we need to follow these steps:
1. Calculate d1 and d2
2. Find the cumulative normal distribution values N(d1) and N(d2)
3. Calculate the theoretical value of the option
Here are the given values:
Current market value (S) = $5.05
Strik... | MathInstruct |
If a committee of 3 people is to be selected from among 7 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?
Answer Choices: (A) 20 (B) 40 (C) 50 (D) 180 (E) 280 | You now have your Committee of 3 people. But you've selected them in an order, when order doesn't matter.
Selection #1 = Jack
Selection #2 = Susan
Selection #3 = Mary
Assume this is a good committee where Jack is not married to Susan or Mary and Susan and Mary are not married. The above committee will be the same as th... | MathInstruct |
34 men can complete a piece of work in 18 days . in how many days will 17 men complete the same work ? Please write a program to solve it | n0 = 34.0
n1 = 18.0
n2 = 17.0
t0 = n0 * n1
answer = t0 / n2
print(answer) | MathInstruct |
On Blacks, Martha goes to the mall to buy clothes on sale. For every 2 jackets she buys, she gets 1 free jacket. For every 3 t-shirts she buys, she gets 1 free t-shirt. Martha decides to buy 4 jackets and 9 t-shirts. How many clothes will she take home? Let's program in Python in the response. | # define the number of bought jackets and t-shirts
bought_jackets = 4
bought_tshirts = 9
# calculate the number of free jackets and t-shirts
free_jackets = bought_jackets // 2
free_tshirts = bought_tshirts // 3
# calculate the total number of clothes
total_clothes = bought_jackets + bought_tshirts + free_jackets + fr... | MathInstruct |
There are 4 cards. 3 cards more are added. There are _____ cards in total. Let's write a program. | cards=4
added=3
total_cards=cards+added
print(total_cards) | MathInstruct |
The area of square ABCD above is 18. The shaded region is the intersection of the square and a circular region centered at C. What is the area of the shaded region?
Answer Choices: (A) 18−9/4∗π (B) 18−9/2∗π (C) 9+9/4∗π (D) 9+9/2∗π (E) 9/2−9/4∗π | Let's reason about the multi-choice question.
=Square - Quarter circle
=18- pi*18/4
=18- pi*9/2
The answer is B | MathInstruct |
Manoj borrowed Rs.3450 from Anwar at 6% p.a. simple interest for three years. He then added some more money to the borrowed sum and lent it to Ramu for the same time at 9% p.a. simple interest. If Manoj gains Rs.824.85 by way of interest on the borrowed sum as well as his own amount from the whole transaction, then wha... | Let's reason about the multi-choice question.
Let the sum lent by Manoj to Ramu be Rs.P.
Amount gained by Manoj = P. 3.9 /100 = 3450.3.6/100 = Rs.824.85
27P = 62100 = 82485
P = (82485 + 62100)/27 = 3055 + 2300 = Rs.5355
The answer is B | MathInstruct |
Gilbert, the bearded dragon, eats 4 crickets per week when the temperature averages 90 degrees F per day, but he eats twice as many crickets per week when the temperature averages 100 degrees F. How many crickets will he eat over 15 weeks if the temperature averages 90 degrees F for 80% of the time, and 100 degrees F ... | If it averages 90 degrees F for 80% of the 15 weeks, then it will be 90 degrees for 80/100 * 15 = 12 weeks.
During those 12 weeks, he will eat 12 * 4 = 48 crickets.
If it averages 100 degrees F for the remainder of the 15 weeks, then it will be 100 degrees F for 15 - 12 = 3 weeks.
During those 3 weeks, he will eat 3 * ... | MathInstruct |
a boy want to make a cuboid of dimension 5 m , 6 m , 7 m from small cubes of . 04 m 3 . later he realized he can make same cuboid by making it hollow . then it takes some cubes less . what is the no . of these cubes ? Let's write a Python program to solve it. | n0 = 5.0
n1 = 6.0
n2 = 7.0
n3 = 4.0
n4 = 3.0
t0 = n3 / 100.0
t1 = n0 * n1
t2 = n0 - 1.0
t3 = n1 - 1.0
t4 = n2 - 1.0
t5 = n2 * t1
t6 = t2 * t3
t7 = t5 / t0
t8 = t6 * t4
t9 = t8 / t0
answer = t7 - t9
print(answer) | MathInstruct |
In 2004, there were 60 kids at a cookout. In 2005, half the number of kids came to the cookout as compared to 2004. In 2006, 2/3 as many kids came to the cookout as in 2005. How many kids came to the cookout in 2006? Please respond by writing a program in Python. | # define the number of kids in 2004
kids_2004 = 60
# calculate the number of kids in 2005
kids_2005 = kids_2004 / 2
# calculate the number of kids in 2006
kids_2006 = kids_2005 * 2/3
# print the result
print(int(kids_2006)) | MathInstruct |
two trains of length 120 m and 320 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ? Let's write a Python program. | n0 = 120.0
n1 = 320.0
n2 = 42.0
n3 = 30.0
t0 = n0 + n1
t1 = n2 + n3
t2 = t1 * 0.2778
answer = t0 / t2
print(answer) | MathInstruct |
If books bought at prices ranging from Rs. 200 to Rs. 350 are sold at prices ranging from Rs. 300 to Rs. 425, what is the greatest possible profit that might be made in selling nine books ?
Answer Choices: (A) 2025 (B) 2677 (C) 1800 (D) 2778 (E) 76611 | Let's solve the multi-choice question step by step.
Least Cost Price = Rs. (200 * 9) = Rs. 1800.
Greatest Selling Price = Rs. (425 * 9) = Rs. 3825.
Required profit = Rs. (3825 - 1800) = Rs. 2025.
The answer is A 2025 | MathInstruct |
Consider the intuitionistic logic formula: "If A implies B and A implies not B, then not A." Let A be the statement "x is a rational number", and B be the statement "x^2 is rational". Determine whether or not the statement "not A" is true or false. | Let's examine the given formula and the statements A and B.
Formula: If A implies B and A implies not B, then not A.
A: x is a rational number
B: x^2 is rational
First, we need to check if A implies B. If x is a rational number, then x can be expressed as a fraction p/q, where p and q are integers and q ≠ 0. Then x^... | MathInstruct |
A boat can travel with a speed of 15 km/hr in still water. If the speed of the stream is 4 km/hr. find the time taken by the boat to go 68 km downstream?
Answer Choices: (A) 3 hours 30 minutes (B) 3 hours (C) 4 hours (D) 5 hours (E) None | Let's solve the multi-choice question step by step.
Solution
Speed Downstream = (15 + 4) km/hr
= 19 km/hr.
Time taken to travel 68 km downstream =(68 / 19)hrs
= 3 hrs 30 mins.
The answer is A | MathInstruct |
"statement 1": Benjamin skated 80.0 kilometers at 10.0 kilometers per hour, "statement 2" :Benjamin skated for 8.0 hours, "options: " Entailment or contradiction? Let's write a Python program. | benjamin_skated_s1 = 80/10
benjamin_skated_s2 = 8
if benjamin_skated_s1 is None or benjamin_skated_s2 is None:
print('neutral')
elif benjamin_skated_s1 == benjamin_skated_s2:
print('Entailment')
elif benjamin_skated_s1 != benjamin_skated_s2:
print('contradiction') | MathInstruct |
ramu bought an old car for rs . 45000 . he spent rs . 12000 on repairs and sold it for rs . 80000 . what is his profit percent ? Let's program in Python in the response. | n0 = 45000.0
n1 = 12000.0
n2 = 80000.0
t0 = n0 + n1
t1 = n2 - t0
t2 = t1 / t0
answer = t2 * 100.0
print(answer) | MathInstruct |
A construction company wants to build a rectangular garden with a perimeter of 60 meters. The company needs to find the dimensions of the garden that maximize its area. What should be the length and width of the rectangular garden? | Let the length of the rectangular garden be L meters and the width be W meters. The perimeter P is given by the formula:
P = 2L + 2W
Since the perimeter is 60 meters, we have:
60 = 2L + 2W
Now, we need to find the dimensions that maximize the area A of the rectangular garden. The area A is given by the formula:
A ... | MathInstruct |
X and Y are both integers. If X/Y = 50.60, then what is the sum of all the possible two digit remainders of X/Y?
Answer Choices: (A) 315 (B) 616 (C) 672 (D) 900 (E) 1024 | Let's think about the multi-choice question.
Remainder = 0.60 --> 60/100 --> Can be written as (60/4) / (100/4) = 15/25
So remainders can be 15, 30, 45, 60, ..... 90.
We need the sum of only 2 digit remainders --> 15 + 30 + 45 + 60 + 75 + 90 = 315
The answer is A | MathInstruct |
ramu bought an old car for rs . 42000 . he spent rs . 10000 on repairs and sold it for rs . 64900 . what is his profit percent ? Let's write a Python program. | n0 = 42000.0
n1 = 10000.0
n2 = 64900.0
t0 = n0 + n1
t1 = n2 - t0
t2 = t1 / t0
answer = t2 * 100.0
print(answer) | MathInstruct |
Set X consists of 10 integers and has median of 10 and a range of 10. What is the value of the greatest possible integer that can be present in the set?
Answer Choices: (A) 32 (B) 37 (C) C.40 (D) 20 (E) 50 | Let's reason about the multi-choice question.
Note that both median and range do not restrict too many numbers in the set. Range is only concerned with the smallest and greatest. Median only cares about the middle.
Quick check of each option starting from the largest:
E 50
Range of 20 means the smallest integer will be... | MathInstruct |
ram , who is half as efficient as krish , will take 21 days to complete a task if he worked alone . if ram and krish worked together , how long will they take to complete the task ? Let's program in Python in the response. | n0 = 21.0
t0 = 1.0 / n0
t1 = n0 / 2.0
t2 = 1.0 / t1
t3 = t0 + t2
answer = 1 / t3
print(answer) | MathInstruct |
an integer n between 1 and 99 , inclusive , is to be chosen at random . what is the probability that n ( n + 1 ) will be divisible by 2 ? Let's program in Python in the response. | n0 = 1.0
n1 = 99.0
n2 = 1.0
n3 = 2.0
t0 = n1 / 3.0
t1 = t0 / n1
answer = 2.0 * t1
print(answer) | MathInstruct |
The diagram below shows a $4\times4$ rectangular array of points, each of which is $1$ unit away from its nearest neighbors.
[asy] unitsize(0.25inch); defaultpen(linewidth(0.7)); int i, j; for(i = 0; i < 4; ++i) for(j = 0; j < 4; ++j) dot(((real)i, (real)j)); [/asy]
Define a growing path to be a sequence of distinc... | We label our points using coordinates $0 \le x,y \le 3$, with the bottom-left point being $(0,0)$. By the Pythagorean Theorem, the distance between two points is $\sqrt{d_x^2 + d_y^2}$ where $0 \le d_x, d_y \le 3$; these yield the possible distances (in decreasing order)\[\sqrt{18},\ \sqrt{13},\ \sqrt{10},\ \sqrt{9},\ ... | MathInstruct |
in a group of ducks and cows , the total number of legs are 40 more than twice the number of heads . find the total number of cows . Let's write a Python program to solve it. | n0 = 40.0
answer = n0 / 2.0
print(answer) | MathInstruct |
Let G be a group of order 9. If the center of the group G is non-trivial, prove that G is isomorphic to the cyclic group C9. Otherwise, prove that G is isomorphic to the non-abelian group of order 9. | Let G be a group of order 9. We will consider two cases: when the center of G is non-trivial and when it is trivial.
Case 1: The center of G is non-trivial.
Let Z(G) denote the center of G. Since G has order 9, we know that |G| = 9 = 3^2. By the class equation, we have |G| = |Z(G)| + ∑[G:C(x)], where the sum is taken ... | MathInstruct |
A car rents for 30 dollars per day plus 23 cents per mile. You are on a daily budget of 76 dollars. What mileage can you go and stay within your budget? Let's program in Python in the response. | carRent=30
perMileCost=0.23
dailyBudget=76
mileage=(dailyBudget-carRent)/perMileCost
print(mileage) | MathInstruct |
by selling 20 pencils for a rupee a man loses 60 % . how many for a rupee should he sell in order to gain 60 % ? Let's write a Python program to solve it. | n0 = 20.0
n1 = 60.0
n2 = 60.0
t0 = n2 + 100.0
t1 = 100.0 - n1
t2 = 1.0 / t1
t3 = t0 * t2
t4 = 1.0 / t3
answer = n0 * t4
print(answer) | MathInstruct |
What's phi(29791) where phi is Euler's Totient Function? Let's write a Python program to solve it. | def solve():
n = 29791
phi = n
i = 2
while i*i <= n:
if n % i == 0:
while n % i == 0:
n //= i
phi -= phi // i
i += 1
if n > 1:
phi -= phi // n
return phi
print(solve()) | MathInstruct |
The average age of a husband and a wife is 23 years when they were married five years ago but now the average age of the husband, wife and child is 22 years(the child was born during the interval). What is the present age of the child?
Answer Choices: (A) 7 years (B) 9 years (C) 10 years (D) 4 years (E) 5 years | Let's think about the multi-choice question.
28 * 2 = 56
22 * 3 = 66
-----------
10 years
The answer is C | MathInstruct |
The price of a certain bicycle this year is $1325, which is 6 percent greater than the cost of the bicycle last year. What was the price of the bicycle last year?
Answer Choices: (A) $1150 (B) $1175 (C) $1200 (D) $1225 (E) $1250 | Let's think about the multi-choice question step by step.
The price of the bicycle last year was $1325/1.06=$1250
The answer is E. | MathInstruct |
the first doughnut is priced at $ 1 and then if you purchase additional doughnuts as dozens then the price is $ 6 / dozen . what is the total number of doughnuts purchased if you paid $ 24 ? Let's write a program. | n0 = 1.0
n1 = 6.0
n2 = 24.0
t0 = n2 / n1
answer = t0 * 12.0
print(answer) | MathInstruct |
If after 600 grams of water were added to the 24%-solution of alcohol, the strength of the solution decreased by one-third, how much of the 24%-solution was used?
Answer Choices: (A) 180 grams (B) 220 grams (C) 250 grams (D) 350 grams (E) 1200 grams | I too think 1200 grams should be the answer.
My reasoning is
The h20 content in 200 gms of water is 1
h20 content in 24% solution is 0.76
Resulting new solution's concentration decreases by one third means. Now it becomes 16% solution which means h20 content is 0.84
Let amount of solution be X
Then the equation can be ... | MathInstruct |
Here's a combinatorial optimization problem for a math student to solve:
Suppose you have a set of 10 integers, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, and you want to select a subset of size 5 such that the sum of the numbers in the subset is minimized. What is the smallest possible sum you can achieve? | To minimize the sum of the subset of size 5, you should select the smallest 5 integers from the given set. These integers are {1, 2, 3, 4, 5}. The sum of these numbers is:
1 + 2 + 3 + 4 + 5 = 15
So, the smallest possible sum you can achieve is 15. | MathInstruct |
If n=(81! − 80! + 79!)/(79!), which of the following could be subtracted from n so that √n is an integer?
Answer Choices: (A) 1 (B) 2 (C) 3 (D) 4 (E) 5 | Let's reason about the multi-choice question.
first lets find n.
n=(81! −80! +79!)/(79!)
n=81! /79!−80!/79! +79!/79!
n=81∗80−80+1=80(81−1)+1=80^2+1
so what should be subtracted from80^2+1, so that it becomes a perfect square ..
ans is 1, as 80^2−1+1=80^2
The answer is A | MathInstruct |
Let \[f(x) =
\begin{cases}
3x + 5 &\text{if }x<-3, \\
7-4x&\text{if }x\ge -3.
\end{cases}
\]Find $f(5)$. | Because $5\ge -3$, we use the second case to determine that $f(5) = 7-4(5) = \boxed{-13}$. The answer is -13 | MathInstruct |
What is the modulo $13$ residue of $247+5 \cdot 39 + 7 \cdot 143 +4 \cdot 15?$ Please respond by writing a program in Python. | # Python program to calculate the modulo 13 residue
residue = (247 + 5*39 + 7*143 + 4*15) % 13
print(residue) | MathInstruct |
Keenan needs to write an essay that is 1200 words. Her essay is due at midnight. She writes 400 words per hour for the first two hours. After that, she writes 200 words per hour. How many hours before the deadline does she need to start to finish on time? Please respond by writing a program in Python. | # define the number of words and the rates at which she writes
total_words = 1200
initial_rate = 400
later_rate = 200
# calculate the time she needs to write at the initial rate
initial_time = 2
# calculate the remaining words after the initial time
remaining_words = total_words - (initial_rate * initial_time)
# cal... | MathInstruct |
in the first 15 overs of a cricket game , the run rate was only 3.2 . what should be the run rate in the remaining 35 overs to reach the target of 275 runs ? Let's write a program. | n0 = 15.0
n1 = 3.2
n2 = 35.0
n3 = 275.0
t0 = n0 * n1
t1 = n3 - t0
answer = t1 / n2
print(answer) | MathInstruct |
"statement 1": Dana borrows more than 4500 pounds annually for her college education, "statement 2" :Dana borrows 7500 pounds annually for her college education, "options: " Entailment or contradiction or neutral? Please write a program to solve it | Dana_borrows_s1 = None
Dana_borrows_s2 = 7500
if Dana_borrows_s1 is None or Dana_borrows_s2 is None:
print('neutral')
elif Dana_borrows_s1 == Dana_borrows_s2:
print('Entailment')
elif Dana_borrows_s1 != Dana_borrows_s2:
print('contradiction') | MathInstruct |
a library has an average of 570 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is : ? Please respond by writing a program in Python. | import math
n0 = 570.0
n1 = 240.0
n2 = 30.0
t0 = 3.0 + 4.0
t1 = n2 / t0
t2 = math.floor(t1)
t3 = t2 + 1.0
t4 = n0 * t3
t5 = n2 - t3
t6 = n1 * t5
t7 = t4 + t6
answer = t7 / n2
print(answer) | MathInstruct |
The number of real roots of the equation A2/x + B2/(x-1) = 1, where A and B are real numbers not equal to zero simultaneously is
Answer Choices: (A) None (B) 1 (C) 2 (D) 1 or 2 (E) 3 | Let's reason about the multi-choice question.
=> A2/x + B2/(x-1) = 1,
=> A2 (x-1) + B2x = x2 - x.
This is a quadratic equation.
Hence, number of roots = 2 or 1 (1 in the case when both roots are equal )
The answer is A | MathInstruct |
A fair coin is tossed 11 times. What is the probability of getting more heads than tails in 11 tosses?
Answer Choices: (A) 1/2 (B) 63/128 (C) 4/7 (D) 61/256 (E) 63/64 | Let's think about the multi-choice question step by step.
On each toss, the probability of getting a head is 1/2 and the probability of getting a tail is 1/2.
There is no way to get the same number of heads and tails on an odd number of tosses.
There will either be more heads or more tails.
Then there must be more head... | MathInstruct |
A man took some money for borrowed, for 3 years the total will be Rs.5000 and 5 years it will be Rs.6000/-. Then how much amount he borrowed?
Answer Choices: (A) s.2000/- (B) s.2500/- (C) s.2770/- (D) s.2800/- (E) s.3500/- Let's write a Python program to solve it. | # The difference in total amount after 5 years and 3 years is the interest for 2 years.
interest_2_years = 6000 - 5000
# Therefore, the annual interest is half of the interest for 2 years.
annual_interest = interest_2_years / 2
# The amount he borrowed is the total amount after 3 years minus the interest for 3 years.
b... | MathInstruct |
Find the least common multiple (LCM) of 6, 9, and 15. | To find the least common multiple (LCM) of 6, 9, and 15, we can use the prime factorization method.
1. Find the prime factors of each number:
- 6 = 2 × 3
- 9 = 3 × 3
- 15 = 3 × 5
2. Identify the highest power of each prime factor in the given numbers:
- The highest power of 2 is 2^1 (from 6)
- The highest power of 3 ... | MathInstruct |
A dealer offers a cash discount of 20% and still makes a profit of 20%, when he further allows 16 articles to a dozen to a particularly sticky bargainer. How much percent above the cost price were his wares listed?
Answer Choices: (A) 100% (B) 80% (C) 75% (D) 66 (2/3) % (E) NOne | Let's reason about the multi-choice question.
Solution: Let the CP of the article be Rs. x, since he earns a profit of 20%, hence SP= X + 20% of X = 1.2x.
It is given that he incurs loss by selling 16 articles at the cost of 12 articles [loss = (16-12)/16 = 25%]
His selling price = SP - 25% of SP = SP*0.75;
Hence, SP*0... | MathInstruct |
A man takes
5
5 hours
45
45 min in walking to a certain place and riding back. He would have gained
2
2 hours by riding both ways. The time he would take to walk both ways is
Answer Choices: (A) 11 hrs (B) 8 hrs 45 min (C) 7 hrs 45 min (D) 9 hrs 20 min (E) 8 hrs | Let's think about the multi-choice question.
Solution 1Given that time taken for riding both ways will be 22 hours lesser than the time needed for waking one way and riding back.
Therefore,
time needed for riding one way = time needed for waking one way - 22 hours
Given that time taken in walking one way and riding bac... | MathInstruct |
If there are twice as many women as men in a group and an equal number of men and women do not own cars - a group that is 40% of the total. What fraction of the total is men who own cars?
Answer Choices: (A) 3⁄20 (B) 11⁄60 (C) 2⁄15 (D) 1⁄3 (E) 11⁄20 | Let's think about the multi-choice question step by step.
Consider a group of 100 men and 200 women, a total of 300 people. 40% of them, which is 120, form a group of people who don't own a car.
Half of them are men, and the other half are women, more precisely 60.
It means that there are 100 - 60 = 40 men who own a ca... | MathInstruct |
What is the structure of a group of order 35? Is it cyclic or isomorphic to the direct product of two cyclic groups of orders 5 and 7? | A group of order 35 has the order as the product of two distinct prime numbers, 5 and 7. By the fundamental theorem of finite abelian groups, any finite abelian group can be expressed as the direct product of cyclic groups of prime power orders.
Since 5 and 7 are prime and coprime (meaning their greatest common diviso... | MathInstruct |
What percent is 240 of 90?
Answer Choices: (A) 133 1/3 % (B) 134 1/3 % (C) 135 1/3 % (D) 266 2/3 % (E) 143 1/3 % Let's write a program. | # calculate the percentage by dividing 240 by 90 and multiplying by 100
percentage = (240 / 90) * 100
print(percentage) | MathInstruct |
Wilfred eats 4 carrots on Tuesday and 6 carrots on Wednesday. If Wilfred wants to eat a total of 15 carrots from Tuesday to Thursday, how many carrots does Wilfred need to eat on Thursday? Let's write a Python program to solve it. | # The total number of carrots Wilfred needs to eat on Thursday is simply the total number of carrots he wants to eat from Tuesday to Thursday minus the number of carrots he already ate on Tuesday and Wednesday.
total_carrots = 15
carrots_eaten = 4 + 6
carrots_needed = total_carrots - carrots_eaten
print(carrots_needed) | MathInstruct |
Yoque borrowed money from her sister. She promised to pay it back in 11 months including an additional 10% of the money she borrowed. If she pays $15 per month, how much money did she borrow? Let's program in Python in the response. | # define the total amount paid and the rate
total_amount_paid = 15 * 11
rate = 1 + 10 / 100
# calculate the amount borrowed
amount_borrowed = total_amount_paid / rate
print(amount_borrowed) | MathInstruct |
What is the numerical value of the long-term solution of the discrete-time Mackey-Glass equation with the following parameters:
- The time delay tau = 17
- The feedback strength beta = 0.1
- The shape parameter gamma = 10
- The decay rate alpha = 0.2
- The initial condition x(0) = 1.5
- The time step size h = 0.01
C... | To solve the discrete-time Mackey-Glass equation, we will use the following equation:
x(t+1) = x(t) + h * ( - alpha * x(t) + beta * x(t - tau) / (1 + x(t - tau)^gamma))
We will compute the solution for 100,000 time steps with the given parameters.
```python
import numpy as np
tau = 17
beta = 0.1
gamma = 10
alpha = ... | MathInstruct |
Max likes to collect model trains. He asks for one for every birthday of his, and asks for two each Christmas. Max always gets the gifts he asks for, and asks for these same gifts every year for 5 years. At the end of the 5 years, his parents give him double the number of trains he already has. How many trains does... | Max gets 1+2=3 trains per year.
He repeats this for 5 years, meaning he gets 5*3=15 trains.
At the end of the 5 years, he is given double this amount, meaning he receives 15*2=30 trains.
Since he already had 15, this means he has 15+30=45 trains.
The answer is 45 | MathInstruct |
"statement 1": Carl can wash all the windows of his house in 6 hours, "statement 2" :Carl can wash all the windows of his house in less than 6 hours, "options: " Entailment or contradiction or neutral? Let's write a Python program. | carl_wash_s1 = 6
carl_wash_s2 = 6-1
if carl_wash_s1 is None or carl_wash_s2 is None:
print('neutral')
elif carl_wash_s1 == carl_wash_s2:
print('Entailment')
elif carl_wash_s1 != carl_wash_s2:
print('contradiction') | MathInstruct |
Bob is going to put in a vegetable garden on his property. It's going to be in one of the back corners of his land. He wants the width of the garden to be about an eighth of the width of his property, and the length to be a tenth of the length of his property. His land is 1000 feet wide and 2250 feet long. How many squ... | The width of his garden is going to be 1000 / 8 = 125 feet.
The length of his garden is going to be 2250 / 10 = 225 feet.
So the area of his garden is going to be 125 X 225 = 28125 square feet.
The answer is 28125 | MathInstruct |
If the price of petrol increases by 25% and Benson intends to spend only an additional 15% on petrol, by how much % will he reduce the quantity of petrol purchased?
Answer Choices: (A) 8% (B) 7% (C) 10% (D) 6% (E) None of these | Let's solve the multi-choice question step by step.
Assume that the initial price of 1 Litre petrol = Rs.100 ,Benson spends Rs.100 for petrol,
such that Benson buys 1 litre of petrol
After the increase by 25%, price of 1 Litre petrol = 100 × (100+25)/100 = Rs.125
Since Benson spends additional 15% on petrol,
amount spe... | MathInstruct |
June’s class has 25 students. 60% are girls and the rest are boys. 40% of the boys like playing basketball and the rest don't. The number of girls who like playing basketball is double the number of boys who don't like to. What percentage of the girls in the class like playing basketball? | The class is divided into 100 - 60 = 40% boys and girls.
The boys are divided into 40/100 * 40% = 16% who don't like playing basketball and 40/100 * 60% = 24% who do like playing basketball.
So 16% + 24% = 40% of the boys play basketball.
The girls are divided into 2 * 16% = 32% who don't like playing basketball and 24... | MathInstruct |
A woman begins bicycling with a pace of 10 kmph and she increases her pace every two hours by 2 kmph. She rests from bicycling 2 hours after her pace reaches her maximum speed of 14 kmph. She does a cool-down for the final 8 km at a pace of 2 kmph. How far in km did she bicycle?
Answer Choices: (A) 96 km (B) 100 km (C)... | Let's solve the multi-choice question step by step.
Distance covered in first two hours = 10 × 2 = 20 km
Distance covered in next two hours = 12 × 2 = 24 km
Distance covered in next two hours = 14 × 2 = 48 km
Distance covered in first six hours
20 + 24 + 48 = 92 km
Remaining distance = 8 km
92 + 8 = 100 km
The answe... | MathInstruct |
Let M be the set of all smooth functions from $\mathbb{R}$ to $\mathbb{R}$. Define a function $f \in M$ as $f(x) = e^x + \sin{x}$. Find the second derivative of f(x) at x=0. | To find the second derivative of f(x), we first need to find the first derivative of f(x).
The derivative of e^x is e^x, and the derivative of sin(x) is cos(x). So, the first derivative of f(x) is:
f'(x) = e^x + cos(x)
Now, we need to find the second derivative of f(x) by taking the derivative of f'(x):
The deriva... | MathInstruct |
What is the exact circumference of a circle with a radius of 5 cm? | The circumference of a circle is given by the formula C = 2πr, where C is the circumference, π (pi) is approximately 3.14159, and r is the radius.
For a circle with a radius of 5 cm, the circumference is:
C = 2π(5)
C = 10π
The exact circumference is 10π cm. If you want an approximate value, you can use the value of ... | MathInstruct |
Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
Answer Choices: (A) 9 a.m. (B) 10 a.m. (C) 10.30 a.m. (D) 11 a.m. (E) 12 a.m. | Let's reason about the multi-choice question.
Given that distance between two stations is 110km.
First trains speed is 20kmph and starts at 7 am
2nd trains speeed is 25kmph and starts at 8 am.
So at 8 am, the distance covered by first train is 20 kms.
Now remaining distance to cover is (110-20 = 90 km).
The relative sp... | MathInstruct |
The average age of a class of 20 students is 14 years. The average increased by 2 when the teacher's age also included. What is the age of the teacher?
Answer Choices: (A) 40 years (B) 41 years (C) 42 years (D) 43 years (E) 36 years | Let's solve the multi-choice question step by step.
If age of the teacher was 14, average would not have changed.
Since average increased by 2,
Age of the teacher=14+22×1=36
The answer is E | MathInstruct |
what is the sum of all 5 digits numbers which can be formed with the digits 0,1,2,3,4 without repetition
Answer Choices: (A) 2599980 (B) 2699980 (C) 2799980 (D) 2509980 (E) 2499980 | Let's solve the multi-choice question step by step.
There is a simplest formula for solving these type of questions when we are using numbers along with 0 for finding sum.
i,e........(sum of numbers)*{(n-1)!*(111...........n times)-(n-2)!*(111..........(n-1)times) }
so,here by putting the values as,
(0+1+2+3+4){(5-1)!*... | MathInstruct |
Alice and Bob are using Diffie-Hellman key exchange with a prime number p = 23 and primitive root α = 5. Alice's private key is a = 6 and Bob's private key is b = 15. Calculate the secret key they will share. | First, Alice and Bob will compute their public keys.
Alice's public key (A) can be calculated as follows:
A = α^a mod p
A = 5^6 mod 23
A = 15625 mod 23
A = 8
Bob's public key (B) can be calculated as follows:
B = α^b mod p
B = 5^15 mod 23
B = 30517578125 mod 23
B = 19
Now, Alice and Bob will compute the shared secr... | MathInstruct |
What is the value of $\sqrt{36+64}-\sqrt{25-16}$? | Calculating under each square root first, $\sqrt{36+64}-\sqrt{25-16}=\sqrt{100}-\sqrt{9}=10-3=\boxed{7}$. The answer is 7 | MathInstruct |
Jake buys 2-pound packages of sausages. He buys 3 of them and they are $4 a pound. How much does he pay? | He bought 2*3=6 pounds of sausage
So they cost 6*$4=$24
The answer is 24 | MathInstruct |
Jamie knows that once she has any more than 32 ounces of liquid she has to use the bathroom, and her teacher said that no one can use the bathroom during the math test. She remembers that she had a cup of milk at lunch and a pint of grape juice at recess. How many ounces can she drink from her water bottle during the t... | Jamie has had 24 ounces because 8 plus 16 equals 24.
She can drink 8 ounces because 32 - 24 equals 8.
The answer is 8 | MathInstruct |
Solve for x:
$\frac{4}{x-3} + \frac{2}{x+2}=2$ | To solve the equation $\frac{4}{x-3} + \frac{2}{x+2}=2$, we first find a common denominator, which is $(x-3)(x+2)$. Then, we rewrite the fractions with the common denominator:
$\frac{4(x+2)}{(x-3)(x+2)} + \frac{2(x-3)}{(x-3)(x+2)} = 2$
Now, we can combine the fractions:
$\frac{4(x+2) + 2(x-3)}{(x-3)(x+2)} = 2$
Next... | MathInstruct |
While reading about the history of different towns, Jared learned that Euston had 20 more carriages than Norfolk. Norwich had 100 carriages, and Flying Scotsman had 20 more carriages than Norwich. If Euston had 130 carriages, how many carriages are there in all? | If Flying Scotsman had 20 more carriages than Norwich, then it had 100 + 20 = 120 carriages.
Together, Flying Scotsman and Norwich had 120 + 100 = 220 carriages.
If Euston had 20 more carriages than Norfolk, then Norfolk had 130 - 20 = 110 carriages.
Together, Euston and Norfolk had 110 + 130 = 240 carriages.
Altogethe... | MathInstruct |
At a certain store, the price of a pair of shoes is twenty dollars more than three times the price of a pair of jeans and the price of a sweater is seventy percent more than the price of a pair of shoes. If the price of a pair of jeans is j dollars at this store, then what is the price, in dollars, of a pair of shoes, ... | Let's think about the multi-choice question step by step.
The answer is A
Given
Price of Jeans = J
Price of shoes = 20+3J
Price of Sweater = 1.7(20+3J)
Total Price of all three items = J+20+3J+1.7(20+3J) = 54+9.1J | MathInstruct |
Determine the average value of the function f(x) = 2sin(2x) over the interval [0, π/2]. | To find the average value of a function over an interval, we use the formula:
Average value = (1/(b-a)) * ∫[a, b] f(x) dx
In this case, the function f(x) = 2sin(2x) and the interval is [0, π/2]. So, a = 0 and b = π/2.
Average value = (1/(π/2 - 0)) * ∫[0, π/2] 2sin(2x) dx
Average value = (2/π) * ∫[0, π/2] 2sin(2x) d... | MathInstruct |
six boys picked up 30 mangoes .In how many ways can they divide them if all mangoes be identical?
Answer Choices: (A) A) 4^30 (B) B) 2^30 (C) C) 1^30 (D) D) 3^30 (E) E) 6^30 | Let's reason about the multi-choice question.
Each Mango can be given to any one of the four people or in other words..1 mango can be divided into 6 ways...so all 30 can be divided in 6^30 ways
The answer is E | MathInstruct |
Three friends Wolfgang, Ludo, and Michael, went to Walmart and bought marbles. Wolfgang bought 16 marbles, Ludo bought 1/4 times more marbles than Wolfgang, and Michael bought 2/3 times as many marbles as the number of marbles both Wolfgang and Ludo bought. If they combined their marbles and decided to share them equal... | If Wolfgang bought 16 marbles, then Ludo bought 1/4 more marbles than Wolfgang, a total of 16+(1/4)*16 = 16+4 = 20 marbles.
The total number of marbles that Wolfgang and Ludo bought is 20+16 = 36
If Michael bought 2/3 times the total number of marbles that Wolfgang and Ludo bought, he bought 2/3*36 = 24 marbles.
The th... | MathInstruct |
Larry spends half an hour twice a day walking and playing with his dog. He also spends a fifth of an hour every day feeding his dog. How many minutes does Larry spend on his dog each day? | Larry spends 30 * 2 = 60 minutes per day walking his dog.
Larry spends 60 / 5 = 12 minutes every day feeding his dog.
Larry spends 60 + 12 = 72 minutes per day on his dog.
The answer is 72 | MathInstruct |
Let A = {1, 2, 3} and B = {2, 3, 4}. Find A ∩ B and B ∩ A, and then determine if (A × B) ∩ (B × A) is equal to (B × A) ∩ (A × B). | First, let's find A ∩ B and B ∩ A. The intersection of two sets is the set of elements that are common to both sets.
A ∩ B = {2, 3}
B ∩ A = {2, 3}
Since the intersection of two sets is commutative, A ∩ B = B ∩ A.
Now, let's find (A × B) and (B × A). The Cartesian product of two sets is the set of all ordered pairs (... | MathInstruct |
there are two sections A and B of a class consisting of 36 and 44 students respectively. If the average weight of section A is 40kg and that of section B is 35kg, find the average weight of the whole class?
Answer Choices: (A) 15.42 (B) 37.25 (C) 12.54 (D) 32.37 (E) 23.47 | Let's think about the multi-choice question step by step.
Sol: total weight of(36+44) students=(36*40+44*35)kg =2980kg.
Therefore weight of the total class=(2980/80)kg =37.25kg.
The answer is B | MathInstruct |
John weighs twice as much as Susan. Susan's weight is 60% of Sam's weight. Mark weighs 50% of Lynn's weight. Lynn weighs 170% of John's weight. Which of these 5 people weighs the least?
Answer Choices: (A) John (B) Susan (C) Sam (D) Mark (E) Lynn | Let's think about the multi-choice question.
John weighs twice as much as Susan --> J=2S --> John cannot weigh the least;
Susan's weight is 60% of Sam's weight --> S=0.6*Sam --> Sam cannot weigh the least;
Mark weighs 50% of Lynn's weight --> M=0.5*L --> Lynn cannot weigh the least;
Lynn weighs 170% of John's weight --... | MathInstruct |
What is the least prime factor of $7^4 - 7^3$? Let's write a Python program. | def least_prime(n):
# check if number is less than 2 (not a prime)
if n < 2:
return None
# check for factors of 2 first
if n % 2 == 0:
return 2
# then check for odd factors up to the square root of n
i = 3
while i * i <= n:
if n % i == 0:
return i
... | MathInstruct |
Find the sum of the roots of $\tan^2x-9\tan x+1=0$ that are between $x=0$ and $x=2\pi$ radians. | By the quadratic formula,
\[\tan x = \frac{9 \pm \sqrt{77}}{2}.\]Let $r_1 = \frac{9 + \sqrt{77}}{2}$ and $r_2 = \frac{9 - \sqrt{77}}{2}.$ Note that $r_1 r_2 = 1.$
Graphing $y = \tan x,$ we see that $\tan x = r_1$ for two angles in $[0,2 \pi],$ and $\tan x = r_2$ for two angles in $[0,2 \pi].$
[asy]
unitsize(1 cm);
... | MathInstruct |
Consider the following system of linear equations:
2x + 3y + 4z = 3
5x + 7y + 8z = 9
3x + 4y + 6z = 6
Solve this system of equations using Gaussian Elimination method and find the values of x, y and z. | To solve the system of linear equations using Gaussian Elimination method, we will perform a series of row operations to transform the augmented matrix into its row-echelon form.
The given system of linear equations can be written as an augmented matrix:
| 2 3 4 | 3 |
| 5 7 8 | 9 |
| 3 4 6 | 6 |
Step 1: Swap R... | MathInstruct |
The number of short students in a class is 2/5 of the total number of students. If there are 90 tall students, and the class has 400 students, calculate the total number of students with average height. | There are 400*2/5 = 160 short students.
The total number of short and tall students is 160+90 = 250
Since there are 400 students in the class, the number of students with average height is 400-250 = 150
The answer is 150 | MathInstruct |
A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.6 per sq m?
Answer Choices: (A) 675, Rs.1350 (B) 575, Rs.1350 (C) 1350, Rs.675 (D) 1450, Rs.775 (E) 675, Rs.4050 | Let's reason about the multi-choice question.
Area = (l + b +2d) 2d
= (75 + 55 +2.5 * 2) 2*2.5 => 675
675 * 6 = Rs.4050
The answer is E | MathInstruct |
Calculate how many ways a woman who has 4 bags and 5 books can put the books in her bag?
Answer Choices: (A) 1034 (B) 1025 (C) 1024 (D) 1025 (E) 1324 | Let's reason about the multi-choice question.
First book can be put in 4 ways, similarly second, third ,forth and fifth books also can be put in 4 ways.
So total number of ways = 4 x 4 x 4 x 4 x 4 = 1024
The answe is C | MathInstruct |
If a computer program generates three-digit odd numbers using the numbers 5, 7, 0, 4, and 1, and the digits can be repeated, what is the probability that the number formed from the program is a multiple of three?
Answer Choices: (A) 1/1 (B) 1/2 (C) 1/3 (D) 1/6 (E) 1/7 Let's write a Python program to solve it. | # A three-digit odd number can only end with 1, 5, or 7.
# The total number of three-digit numbers that can be formed is 5*5*3 = 75.
# A number is a multiple of three if the sum of its digits is a multiple of three.
# We can calculate the number of such numbers by iterating through all possible combinations.
count = 0
... | MathInstruct |
For all integers a and b, a%b = (a + b)(a - b). If 9%x = 17, then which of the following could be a value of x?
Answer Choices: (A) -8 (B) -7 (C) 2 (D) 3 (E) 6 | Let's reason about the multi-choice question.
9%x = (9+x)(9-x)
81-x^2 = 17
x^2 = 64
x=-8,8
The answer is A | MathInstruct |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.