euclaise/mathqa_programs huggingface dataset:
Problem: when positive integer x is divided by positive integer y , the result is 59.32 . what is the sum w of all possible 2 - digit remainders for x / y ?
Options: a ) 560 , b ) 616 , c ) 672 , d ) 728 , e ) 784
Rationale: "ans b 616 . . . remainders = . 32 = 32 / 100 = 8 / 25 = 16 / 50 and so on . . so two digit remainders are 16 + 24 + 32 + . . . . + 96 . . w = 8 ( 2 + 3 + 4 . . . . + 12 ) = 616"
Answer: b
Python program:
a = math.floor(2)
b = 2 - a
c = 59 / 32
Problem: jerry ’ s average ( arithmetic mean ) score on the first 3 of 4 tests is 81 . if jerry wants to raise his average by 2 points , what score must he earn on the fourth test ?
Options: a ) 87 , b ) 89 , c ) 90 , d ) 93 , e ) 95
Rationale: "total score on 3 tests = 81 * 3 = 243 jerry wants the average to be = 83 hence total score on 4 tests should be = 83 * 4 = 332 score required on the fourth test = 332 - 243 = 89 option b"
Answer: b
Python program:
a = 81 + 2 
b = 4 * a
c = 81 * 3
d = b - c
Problem: a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 390 sq . feet , how many feet of fencing will be required ?
Options: a ) 34
b ) 59
c ) 68
d ) 88
e ) 92
Rationale: given that length and area , so we can find the breadth . length x breadth = area 20 x breadth = 390 breadth = 19.5 feet area to be fenced = 2 b + l = 2 ( 19.5 ) + 20 = 59 feet answer : b
Answer: b
Python program:
a = 390 / 20
b = a * 2
c = b + 20
Problem: in a certain apartment building , there are one - bedroom and two - bedroom apartments . the rental prices of the apartment depend on a number of factors , but on average , two - bedroom apartments have higher rental prices than do one - bedroom apartments . let m be the average rental price for all apartments in the building . if m is $ 2,000 higher than the average rental price for all one - bedroom apartments , and if the average rental price for all two - bedroom apartments is $ 8,000 higher that m , then what percentage of apartments in the building are two - bedroom apartments ?
Options: a ) 20 % , b ) 25 % , c ) 50 % , d ) 60 % , e ) 27 %
Rationale: "ratio of 2 bedroom apartment : 1 bedroom apartment = 2000 : 8000 - - - - - > 1 : 4 let total number of apartments be x no . of 2 bedroom apartment = ( 1 / 5 ) * x percentage of apartments in the building are two - bedroom apartments - - - - > ( 1 / 5 ) * 100 - - - > 20 % answer : a"
Answer: a
Python program:
a = 2 * 0
b = 2 * 1000
c = b + 100 
d = c + 2 
e = a / d
Problem: what is the smallest positive integer that can be multiplied by 1,008 to make it a perfect square ?
Options: a ) 2
b ) 3
c ) 5
d ) 7
e ) 11
Rationale: 1008 = 2 ^ 4 x 3 ^ 2 x 7 . therefore the smallest integer to multiplied to 1008 to make it a perfect square is 7 . answer d .
Answer: d
Python program:
a = 3 + 4
Problem: how many factors of 660 are odd numbers greater than 1 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 15
Rationale: when factorized , 660 has 5 prime factors . of these prime factors 4 are odd and 1 is even . hence total number of odd factors is 2 * 2 * 2 * 2 ( 16 ) , which includes 1 . the total number of odd factors greater than 1 are 15 . ( option e )
Answer: e
Python program:
a = 10 * 2
b = 660 / a
Problem: a palindrome is a number that reads the same front - to - back as it does back - to - front ( e . g . 202 , 575 , 1991 , etc . ) p is the smallest integer greater than 300 that is both a prime and a palindrome . what is the sum of the digits of p ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: given that p is smallest integer greater than 300 - assume there is a 3 - digit that satisfies the above conditions . let the number be xyx ; question asks us the values of 2 x + y we can straight away cross out options a ) and d ) - sum of digits 3 or 6 implies it is divisible by 3 - - - > we know that p is a prime number coming to option b ) 2 x + y = 4 - - > only x = 2 and y = 0 satisfy this equation ( x > 2 will never give sum of digits = 4 ) ; but 202 is divisible by 2 ; we know that p is a prime number similarly option c ) 2 x + y = 5 - - > only x = 2 and y = 1 satisfy this equation ( x > 2 will never give sum of digits = 5 ) ; but 212 is divisible by 2 ; we know that p is a prime number therefore answer option should be e - - - > can be verified by taking 2 x + y = 7 - - - > x = 3 and y = 1 ; gives 313 d
Answer: d
Python program:
a = 3 + 3
Problem: a sucrose solution contains 10 grams of sucrose per 100 cubic centimeters of solution . if 60 cubic centimeters of the solution were poured into an empty container , how many grams of sucrose would be in the container ?
Options: a ) 4.00
b ) 6.00
c ) 5.50
d ) 6.50
e ) 6.75
Rationale: we are given that a sucrose solution contains 10 grams of sucrose per 100 cubic centimeters of solution . since we are dealing with a solution , we know that the grams of sucrose is proportional to the number of cubic centimeters of solution . thus , to determine how many grams of sucrose would be in the container when we have 60 cubic centimeters of solution , we can set up a proportion . we can say : “ 10 grams of sucrose is to 100 cubic centimeters of solution as x grams of sucrose is to 60 cubic centimeters of solution . ” let ’ s now set up the proportion and solve for x . 10 / 100 = x / 60 when we cross multiply we obtain : ( 10 ) ( 60 ) = 100 x 600 = 100 x 6.00 = x there are 6.00 grams of sucrose in the solution in the container . the answer is b .
Answer: b
Python program:
a = 60 * 10
b = a / 100
Problem: a crate measures 6 feet by 8 feet by 12 feet on the inside . a stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides . what is the radius , in feet , of the pillar with the largest volume that could still fit in the crate ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 12
Rationale: "we can find the radius of all the three cases of cylinders . the only crux to find the answer faster is that : voulme is pi * r ^ 2 * h . the volume is a function of r ^ 2 . so r has to be the highest to find the largest volume . so r = 6 for the surface 8 * 12 face . volume = 216 pi answer c"
Answer: c
Python program:
a = 8 * 12
b = a * 6
c = b / 12
d = c / 8
Problem: a man can row downstream at 20 kmph and upstream at 12 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options: a ) 13 , 3 , b ) 12 , 6 , c ) 16 , 4 , d ) 14 , 4 , e ) none of these
Rationale: "explanation : let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 20 - - - ( 1 ) and x - y = 12 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 32 = > x = 16 , y = 4 . answer : option c"
Answer: c
Python program:
a = 20 + 12 
b = a / 2
c = b / 2
Problem: a and b go around a circular track of length 1200 m on a cycle at speeds of 36 kmph and 54 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 240 sec , b ) 165 sec , c ) 186 sec , d ) 167 sec , e ) 168 sec
Rationale: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 1200 / ( 36 * 5 / 18 ) , 1200 / ( 54 * 5 / 18 ) } = lcm ( 120 , 80 ) = 240 sec . answer : a"
Answer: a
Python program:
a = 54 * const_0_2778
b = 36 * const_0_2778
c = a - b
d = 1200 / c
Problem: if the number is decreased by 5 and divided by 7 the result is 7 . what would be the result if 24 is subtracted and divided by 10 ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 5 , e ) 3
Rationale: "explanation : let the number be x . then , ( x - 5 ) / 7 = 7 = > x - 5 = 49 x = 54 . : ( x - 24 ) / 10 = ( 54 - 24 ) / 10 = 3 answer : option e"
Answer: e
Python program:
a = 7 * 7
b = a + 5 
c = b - 24
d = c / 10
Problem: tom read a book containing 560 pages by reading the same number of pages each day . if he would have finished the book 5 days earlier by reading 16 pages a day more , how many days did tom spend reading the book ?
Options: a ) 19 , b ) 18 , c ) 9.12 , d ) 20 , e ) none
Rationale: "actually u can set up 2 equation p - - stands for the pages d - - stands for the days 1 ) p * d = 560 ( we want to find the days , sop = 560 / d ) 2 ) ( p + 16 ) ( d - 5 ) = 560 = > pd - 5 p + 16 d - 80 = 560 as the 1 ) stated u can put 1 ) into 2 ) = > 560 - 5 p + 16 d - 80 = 560 = > 16 d - 5 p = 80 put the bold one into it = > 16 d - 5 ( 560 / d ) = 80 the we get the final equation 16 d ^ 2 - 2800 = 80 d ( divide 16 ) = > d ^ 2 - 5 d - 175 = 0 ( d - 15 ) ( d + 10 ) = 0 so d = 9.12 days ans : c"
Answer: c
Python program:
a = 16 * 5
b = a * 4
c = 16 ** 2
d = b + c 
e = math.sqrt(d)
f = e - 16
g = f / 2
Problem: john bought 9.25 m of cloth for $ 407 . find the cost price per metre .
Options: a ) 46 , b ) 47 , c ) 58 , d ) 44 , e ) 54
Rationale: "cloth bought by john = 9.25 m cost of 9.25 m = $ 407 cost per metre = 407 ÷ 9.25 the cost of the cloth per metre = $ 44 answers : d"
Answer: d
Python program:
a = 407 / 9
Problem: how many pieces can a square pizza be cut into by making 6 linear cuts ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: "1 cut makes 2 pieces a second cut can make 4 pieces by cutting through both pieces a third cut can make 7 pieces by cutting through 3 of the pieces a fourth cut can make 11 pieces by cutting through 4 of the pieces a fifth cut can make 16 pieces by cutting through 5 of the pieces a sixth cut can make 22 pieces by cutting through 6 of the pieces c"
Answer: c
Python program:
a = 6 * 3
b = a - 1
Problem: on the xy - plane , each point on circle c has coordinates such that x 0 and y 0 . if the center of circle c is the point ( 3 ; 9 ) , what is the maximum possible area of c ?
Options: a ) 6 , b ) 9 , c ) 24 , d ) 32 , e ) 64
Rationale: i think that theintentof this question is that the circle will have no co - ordinates that fit the following 2 forms : ( 0 , y ) or ( x , 0 ) . in real basic terms , this circle will neither touch ( nor cross ) the x - axis nor will it touch ( nor cross ) the y - axis . with a center at ( 3,8 ) , the longest possible radius would almost touch the x - axis , so the radius would be a little less than 3 . if the radius was 3 exactly , then the area would be 9 pi , which is approximately 28.26 since the circle ca n ' t touch the x - axis , the area has to be less than approximately 28.26 as it ' s written , none of the answers is clearly the correct one . c
Answer: c
Python program:
a = 3 ** 2
b = 4 ** 2
c = a + b 
d = c - 2
Problem: if 10 gallons of grape juice are added to 40 gallons of a mixture , which contains 30 percent grape juice then what percent of the resulting mixture is grape juice ?
Options: a ) 14 % , b ) 25 % , c ) 48 % , d ) 34 % , e ) 50 %
Rationale: "official solution : if we start with 40 gallons of a mixture that is 10 % grape juice , then we have : 40 × 0.30 = 12 gallons of grape juice . 40 × 0.70 = 28 gallons of other components . if we add 10 gallons of grape juice , we will end up with 24 gallons of grape juice and 36 gallons of other components , and we will have a total of 50 gallons of the mixture . so 24 / 50 of the new mixture is grape juice . now we convert this to a percent : percent grape juice = 24 / 50 = 48 / 100 = 48 % . the correct answer is choice ( c )"
Answer: c
Python program:
a = 30 / 100
b = a * 40
c = b + 10 
d = 40 + 10 
e = c / d
f = e * 100
Problem: in a school 10 % of the boys are same in number as 1 / 5 th of the girls . what is the ratio of boys to the girls in the school ?
Options: a ) 5 : 2 , b ) 2 : 3 , c ) 1 : 2 , d ) 3 : 7 , e ) 2 : 5
Rationale: 10 % of b = 1 / 5 g 10 b / 100 = g / 5 b = g / 2 b / g = 1 / 2 b : g = 1 : 2 answer is c
Answer: c
Python program:
a = 10 / 100
b = 1 / 5
c = a / b
Problem: in a certain parallelogram the degree measure of one angle exceeds that of the other by 40 what is the degree measure of the smaller angle ?
Options: a ) 70 , b ) 80 , c ) 85 , d ) 90 , e ) 95
Rationale: "in a parallelogram opposite angles are equal and the angles at each side are supplementary to each other ( supplementary angles are two angles that add up to 180 ° ) . given : x + ( x + 40 ) = 180 - - > x = 70 . answer : a ."
Answer: a
Python program:
a = 3600 / 10
b = 40 * 2
c = a - b
d = c / 4
Problem: a farmer built a fence around his square plot . he used 27 fence poles on each side of the square . how many poles did he need altogether ?
Options: a ) 100
b ) 104
c ) 108
d ) 112
e ) none of these
Rationale: one side = 2 corners ( 1 nd 1 each ) plus 25 . . . 1 25 1 25 25 1 25 1 der 4 ans = 25 * 4 + 4 = 104 answer : b
Answer: b
Python program:
a = 27 - 2
b = a * 4
c = b + 4
Problem: if one positive integer is greater than another positive integer by 4 , and the difference of their cubes is 208 , what is their sum ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "1 ^ 3 = 1 2 ^ 3 = 8 3 ^ 3 = 27 4 ^ 3 = 64 5 ^ 3 = 125 6 ^ 3 = 216 the two numbers are 2 and 6 . the answer is a ."
Answer: a
Python program:
a = 4 ** 4
b = 4 ** 4
c = b ** 2
d = 4 ** 4
e = 208 - d
f = e ** 2
g = c + f 
h = math.sqrt(g)
i = a + h 
j = 4 ** 2
k = j * 2
l = i / k
m = 4 ** 4
n = 4 ** 4
o = n ** 2
p = 4 ** 4
q = 208 - p
r = q ** 2
s = o + r 
t = math.sqrt(s)
u = m + t 
v = 4 ** 2
w = v * 2
x = u / w
y = x - 4
z = l + y
Problem: if s = { 1 , 2 , 3 , 4 , 5 , 6 , 7 } , how much less is the mean of the numbers in s than the median of the numbers in s ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "mean = ( 1 + 2 + 3 + 4 + 5 + 6 + 7 ) / 7 = 4 median = 4 difference = 4 - 4 = 0 option a"
Answer: a
Python program:
a = 2 + 1 
b = a + 3 
c = b + 4 
d = c + 5 
e = d + 6 
f = 2 + 4 
g = e / f
h = 3 + 4 
i = h / 2
j = g * i
Problem: 45 x ? = 40 % of 900
Options: a ) 16.2 , b ) 4 , c ) 5 , d ) 500 , e ) 8
Rationale: "answer let 45 x a = ( 40 x 900 ) / 100 ∴ a = ( 40 x 9 ) / 45 = 8 correct option : e"
Answer: e
Python program:
a = 40 / 100
b = a * 900
c = b / 45
Problem: ramu bought an old car for rs . 42000 . he spent rs . 13000 on repairs and sold it for rs . 64900 . what is his profit percent ?
Options: a ) 22 , b ) 77 , c ) 18 , d ) 77 , e ) 65
Rationale: "total cp = rs . 42000 + rs . 13000 = rs . 55000 and sp = rs . 64900 profit ( % ) = ( 64900 - 55000 ) / 55000 * 100 = 18 % answer : c"
Answer: c
Python program:
a = 42000 + 13000 
b = 64900 - a
c = 42000 + 13000 
d = b / c
e = d * 100
Problem: a honey bee flies for 10 seconds , from a daisy to a rose . it immediately continues to a poppy , flying for 6 additional seconds . the distance the bee passed , flying from the daisy to the rose is 8 meters longer than the distance it passed flying from the rose to the poppy . the bee flies to the poppy at 3 meters per second faster than her speed flying to the rose . the bee flies how many meters per second from the daisy to the rose ?
Options: a ) 2.6 , b ) 5.6 , c ) 6.3 , d ) 8 , e ) 10
Rationale: let the speed be ' s ' and let the distance between rose and poppy be ' x ' the problem boils down to : rose to poppy : s + 3 = x / 6 - - - - - - - 1 daisy to rose : s = ( x + 8 ) / 10 - - - - - - 2 so from 1 we can re write x as x = 6 s + 18 substitute the value of x in 2 gives us s = 2.6 m / s a
Answer: a
Python program:
a = 6 * 3
b = a + 8 
c = b / 10
Problem: of the female students at barkely university , 5 / 6 are on the honor roll . of the male students , 2 / 3 are on the honor roll . if 3 / 5 of the students are female , what is ratio of male to female students on honor roll ?
Options: a ) 5 / 9 , b ) 8 / 15 , c ) 23 / 30 , d ) 43 / 60 , e ) 53 / 90
Rationale: "let the total students be 30 given 3 / 5 of the students are females = 18 then males = 2 / 5 = 12 5 / 6 of the females are on honor roll = 15 males on the honor roll = 2 / 3 = 8 ratio of m : f students on honor roll = 8 / 15 b"
Answer: b
Python program:
a = 5 * 2
b = a * 2
c = b + 3 
d = 3 * 5
e = 2 * d
f = c / e
Problem: if in a race of 90 m , a covers the distance in 20 seconds and b in 25 seconds , then a beats b by :
Options: a ) 20 m , b ) 16 m , c ) 11 m , d ) 10 m , e ) 18 m
Rationale: explanation : the difference in the timing of a and b is 5 seconds . hence , a beats b by 5 seconds . the distance covered by b in 5 seconds = ( 90 * 5 ) / 25 = 18 m hence , a beats b by 18 m . answer e
Answer: e
Python program:
a = 25 - 20
b = a / 25
c = b * 90
Problem: find the least number must be subtracted from 899830 so that remaining no . is divisible by 16 ?
Options: a ) 5 , b ) 8 , c ) 7 , d ) 6 , e ) 9
Rationale: "on dividing 899830 by 16 we get the remainder 6 , so 6 should be subtracted d"
Answer: d
Python program:
a = 899830 / 16
b = math.floor(a)
c = b * 16
d = 899830 - c
Problem: at 3 : 40 , the hour hand and the minute hand of a clock form an angle of :
Options: a ) 130 , b ) 125 , c ) 140 , d ) 154 , e ) 145
Rationale: angle traced by hour hand in 12 hrs . = 360 â ° . abgle traced it in 11 / 3 hrs = ( 360 / 12 * 11 / 3 ) = 110 angle traced by min hand in 60 min = 360 angle traced by it in 40 min = ( 360 / 60 * 40 ) = 240 req ( 240 - 110 ) = 130 d
Answer: a
Python program:
a = const_60 * 3
b = a * 2
c = 40 / const_60
d = b * c
e = const_60 * 3
f = e * 2
g = f / 3
h = g / 4
i = 40 / const_60
j = i + 3 
k = h * j
l = d - k
Problem: express 60 mps in kmph ?
Options: a ) 200 , b ) 182 , c ) 216 , d ) 127 , e ) 400
Rationale: "60 * 18 / 5 = 216 kmph answer : c"
Answer: c
Python program:
a = 60 / 1000
b = a * 3600
Problem: set a : { 1 , 3 , 4 , 6 , 9 , 12 , 15 } if 3 numbers are randomly selected from set a without replacement , what is the probability that the sum of the 3 numbers is divisible by 3 ?
Options: a ) 3 / 14 , b ) 2 / 7 , c ) 9 / 14 , d ) 5 / 7 , e ) 11 / 14
Rationale: probability of an event = ( # of favorable outcomes ) / ( total # of outcomes ) . there are 5 numbers you can choose from ( 3 , 6 , 9 , 12 , 15 ) so that the sum to be divisible by 3 and there are total of 7 numbers so p = c 35 c 37 = 27 p = c 53 c 73 = 27 . answer : b .
Answer: b
Python program:
a = 4 + 1 
b = math.factorial(a)
c = 4 + 1 
d = c - 3
e = math.factorial(d)
f = math.factorial(3)
g = e * f
h = b / g
i = 4 + 3 
j = math.factorial(i)
k = math.factorial(4)
l = math.factorial(3)
m = k * l
n = j / m
o = h / n
Problem: in a rectangular axis system , what is the area of a parallelogram with the coordinates : ( 1,3 ) , ( 5,3 ) , ( 2,6 ) , ( 6,6 ) ?
Options: a ) 21 . , b ) 12 . , c ) 35 . , d ) 49 . , e ) 52 .
Rationale: "delta x will give us the dimension of one side of the parallelogram = 5 - 1 = 4 unit delta y will give us the dimension of the other side of parallelogram = 6 - 3 = 3 unit area of parallelogram = 4 * 3 = 12 answer is b"
Answer: b
Python program:
a = 3 + 2
Problem: the banker ' s gain on a sum due 3 years hence at 12 % per year is rs . 270 . the banker ' s discount is :
Options: a ) 960 , b ) 840 , c ) 1020 , d ) 760 , e ) 920
Rationale: "t . d . = ( b . g . x 100 / r x t ) = rs . ( 270 x 100 / 12 x 3 ) = rs . 750 . therefore , b . d . = rs . ( 750 + 270 ) = rs . 1020 . answer is c"
Answer: c
Python program:
a = 270 * 100
b = 12 * 3
c = a / b
d = 270 + c
Problem: convert the 12 / 43 m / s into kilometers per hour ?
Options: a ) 3.5 kmph . , b ) 2.5 kmph . , c ) 1 kmph . , d ) 1.5 kmph . , e ) 1.9 kmph .
Rationale: "12 / 43 m / s = 12 / 43 * 18 / 5 = 1 ( 1 / 250 ) = 1 kmph . answer : c"
Answer: c
Python program:
a = 12 / 43
b = const_3_6 * a
Problem: a rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 4 per sq m ?
Options: a ) 2288 , b ) 2779 , c ) 2779 , d ) 5200 , e ) 2781
Rationale: "area = ( l + b â € “ d ) d ( 80 + 60 â € “ 10 ) 10 = > 1300 m 2 1300 * 4 = rs . 5200 answer : d"
Answer: d
Python program:
a = 80 + 60 
b = a - 10
c = b * 10
d = c * 4
Problem: a 45 ° - 45 ° - 90 ° right triangle has hypotenuse of length h . what is the area of the triangle r in terms of h ?
Options: a ) h / √ 2
b ) h / 2
c ) h / 4
d ) ( h ) ^ 2
e ) ( h ) ^ 2 / 4
Rationale: if . . . each of the two shorter sides = 3 , then the hypotenuse = h = 3 ( root 2 ) . the area r = ( 1 / 2 ) ( base ) ( height ) = ( 1 / 2 ) ( 3 ) ( 3 ) = 9 / 2 . so we ' re looking for an answer that = 9 / 2 when h = 3 ( root 2 ) . there ' s only one answer that matches . . . e
Answer: e
Python program:
a = 1/(sine)
Problem: - 88 * 49 + 100 = ?
Options: a ) - 4212 , b ) 4601 , c ) - 4801 , d ) - 3471 , e ) none of these
Rationale: "= > - 88 * ( 50 - 1 ) + 100 ; = > - ( 88 * 50 ) + 88 + 100 ; = > - 4400 + 188 = - 4212 . correct option : a"
Answer: a
Python program:
a = negate * (
b = a + 49
Problem: how many digits 2 ^ 200 has ?
Options: a ) 31 , b ) 61 , c ) 50 , d ) 99 , e ) 101
Rationale: "2 ^ 10 = 1.024 * 10 ^ 3 = > 2 ^ 100 = ( 1.024 ) ^ 10 * 10 ^ 60 therefore 61 digits would be my best guess b"
Answer: b
Python program:
a = math.log(2)
b = math.log(10)
c = a / b
d = c * 200
e = 1 + d 
f = math.floor(e)
Problem: in an intercollegiate competition that lasted for 3 days , 175 students took part on day 1 , 210 on day 2 and 150 on day 3 . if 80 took part on day 1 and day 2 and 70 took part on day 2 and day 3 and 20 took part on all three days , how many students took part only on day 1 ?
Options: a ) 25 , b ) 45 , c ) 55 , d ) 70 , e ) 30
Rationale: day 1 & 2 = 80 ; only day 1 & 2 ( 80 - 20 ) = 60 , day 2 & 3 = 70 ; only day 2 & 3 ( 70 - 20 ) = 50 , only day 1 = 175 - ( 60 + 50 + 20 ) = 45 answer : b
Answer: b
Python program:
a = 20 + 80 
b = 80 + 70 
c = b + 20 
d = 210 - c
e = 20 + d 
f = e / 2
g = a + f 
h = 175 - g
Problem: rs . 1500 is divided into two parts such that if one part is invested at 6 % and the other at 5 % the whole annual interest from both the sum is rs . 75 . how much was lent at 5 % ?
Options: a ) 388 , b ) 1500 , c ) 277 , d ) 500 , e ) 271
Rationale: "( x * 5 * 1 ) / 100 + [ ( 1500 - x ) * 6 * 1 ] / 100 = 75 5 x / 100 + 90 – 6 x / 100 = 75 x / 100 = 15 = > x = 1500 . answer : b"
Answer: b
Python program:
a = 5 + 6 
b = a * 100
Problem: a sum of money at simple interest amounts to $ 980 in 3 years and to $ 1024 in 4 years . the sum is :
Options: a ) $ 153 , b ) $ 848 , c ) $ 398 , d ) $ 549 , e ) $ 675
Rationale: "b $ 848 s . i . for 1 year = $ ( 1024 - 980 ) = $ 44 . s . i . for 3 years = $ ( 44 x 3 ) = $ 132 . principal = $ ( 980 - 132 ) = $ 848 ."
Answer: b
Python program:
a = 1024 - 980
b = a * 3
c = b / 4
d = 980 - c
Problem: the perimeter of a rectangular yard is completely surrounded by a fence that measures 18 meters . what is the length of the yard if the area of the yard is 20 meters squared ?
Options: a ) 8 , b ) 2 , c ) 7 , d ) 5 , e ) 1
Rationale: "perimeter of rectangular yard = 2 ( l + b ) = 18 - - > l + b = 9 area = l * b = 20 b = 9 - l l ( 9 - l ) = 20 29 l - l ^ 2 = 20 l ^ 2 - 9 l + 20 = 0 upon simplifying we get l = 5 or 4 . only 5 is there in the answer choice . answer : d"
Answer: d
Python program:
a = 4 - 3
Problem: the shopkeeper increased the price of a product by 25 % so that customer finds it difficult to purchase the required amount . but somehow the customer managed to purchase only 68 % of the required amount . what is the net difference in the expenditure on that product ?
Options: a ) 12.5 % , b ) 13 % , c ) 16 % , d ) 15 % , e ) 19 %
Rationale: "quantity x rate = price 1 x 1 = 1 0.68 x 1.25 = 0.85 decrease in price = ( 0.15 / 1 ) × 100 = 15 % d )"
Answer: d
Python program:
a = 100 * 100
b = 100 + 25 
c = b * 68
d = a - c
e = d * 100
f = 100 * 100
g = e / f
Problem: a store reduced the price of all items in the store by 10 % on the first day and by another 14 % on the second day . the price of items on the second day was what percent of the price before the first reduction took place ?
Options: a ) 80.0 , b ) 80.9 , c ) 77.4 , d ) 81.1 , e ) 81.9
Rationale: "consider price of the all items as $ 100 after a initial reduction of 10 % price becomes = 0.9 * 100 = $ 90 after the final reduction of 14 % price becomes = 0.86 * 90 = $ 77.4 price of all items on second day is 77.4 % of price on first day correct answer option c"
Answer: c
Python program:
a = 100 - 10
b = a / 100
c = 100 - 14
d = c / 100
e = b * d
f = e * 100