euclaise/mathqa_programs huggingface dataset:
Problem: if 7 < x < 9 < y < 15 , then what is the greatest possible positive integer difference of x and y ?
Options: a ) 7 , b ) 4 , c ) 5 , d ) 6 , e ) 3
Rationale: "let x = 7.1 and y = 14.1 greatest possible difference = 14.1 - 7.1 = 7 answer a"
Answer: a
Python program:
a = 15 - 7
b = a - 1
Problem: on the number line , the number p is twice as many units from - 2 as - 2 is from 2 . if p is less than – 2 , what is the value of p ?
Options: a ) – 18 , b ) – 10 , c ) – 6 , d ) 10 , e ) 14
Rationale: distance between - 2 and 2 = 4 since number p is twice as many units from - 2 as - 2 is from 2 , therefore p can be - 10 since , p is less than - 2 , the value of p = - 10 answer b
Answer: b
Python program:
a = negate - (
Problem: when 100 is divided by positive integer x , the remainder is 3 . what is the remainder when 197 is divided by x ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: if 100 / x leaves a reminder 3 then ( 100 - 3 ) i . e . 97 is divisible by x so ( 100 + 97 ) / x leaves a reminder rem ( 100 / x ) + rem ( 97 / x ) = > 3 + 0 = 3 answer : b
Answer: b
Python program:
a = 197 - 100
b = 100 - a
Problem: if 4 ^ k + 4 ^ k = ( 4 ^ 9 ) ^ ( 4 ^ 9 ) - 4 ^ k , then k = ?
Options: a ) 11 / 3 , b ) 4 ^ 11 - 1 , c ) 242 , d ) 3 ^ 10 , e ) 3 ^ 11 - 1
Rationale: 4 ^ k + 4 ^ k = ( 4 ^ 9 ) ^ 4 ^ 9 - 4 ^ k 4 * ( 4 ^ k ) = 4 ^ ( 16 * 4 ^ 9 ) = 4 ^ ( 4 ^ 2 * 4 ^ 9 ) = 4 ( 4 ^ 11 ) 4 ^ k + 1 = 4 ^ ( 4 ^ 11 ) so k + 1 = 4 ^ 11 so k = 4 ^ 11 - 1 answer is b
Answer: b
Python program:
a = 9 + 2 
b = 4 ** a
c = b - 1
Problem: if n is a positive integer and n ^ 2 is divisible by 212 , then the largest positive integer that must divide n is
Options: a ) 6 , b ) 12 , c ) 24 , d ) 36 , e ) 48
Rationale: "the question asks aboutthe largest positive integer that must divide n , not could divide n . since the least value of n for which n ^ 2 is a multiple of 72 is 12 then the largest positive integer that must divide n is 12 . complete solution of this question is given above . please ask if anything remains unclear . i spent a few hours on this one alone and i ' m still not clear . i chose 12 at first , but then changed to 48 . i ' m not a native speaker , so here is how i interpreted this question : the largest positive integer that must divide n = the largest positive factor of n . since n is a variable ( i . e . n is moving ) , so is its largest factor . please correct if i ' m wrong here . i know that if n = 12 , n ^ 2 = 144 = 2 * 72 ( satisfy the condition ) . when n = 12 , the largest factor of n is n itself , which is 12 . check : 12 is the largest positive number that must divide 12 - - > true however if n = 48 , n ^ 2 = 48 * 48 = 32 * 72 ( satisfy the condition too ) . when n = 48 , the largest factor of n is n itself , which is 48 . check : 48 is the largest positive number that must divide 48 - - > true so , i also notice that the keyword ismust , notcould . the question is , why is 48 notmust divide 48 , but instead onlycould divide 48 ? i ' m not clear right here . why is 12 must divide 12 ? what ' s the difference between them ? only restriction we have on positive integer n is that n ^ 2 is divisible by 72 . the least value of n for which n ^ 2 is divisible by 72 is 12 , thus nmustbe divisible by 12 ( n is in any case divisible by 12 ) . for all other values of n , for which n ^ 2 is divisible by 72 , n will still be divisible by 12 . this means that n is always divisible by 12 if n ^ 2 is divisible by 72 . now , ask yourself : if n = 36 , is n divisible by 48 ? no . so , n is not always divisible by 48 . d"
Answer: d
Python program:
a = 212 / 2
b = math.sqrt(a)
c = b * 2
Problem: a survey of employers found that during 1993 employment costs rose 3.5 percent , where employment costs consist of salary costs and fringe benefit costs . if salary costs rose 3 percent and fringe - benefit costs rose 5.5 percent during 1993 , then fringe - benefit costs represented what percent of employment costs at the beginning of 1993 ?
Options: a ) 16.5 % , b ) 20 % , c ) 35 % , d ) 55 % , e ) 65 %
Rationale: "the amount by which employment costs rose is equal to 0.035 ( salary costs + fringe benefit costs ) ; on the other hand the amount by which employment costs rose is equal to 0.03 * salary costs + 0.055 * fringe benefit costs ; so , 35 ( s + f ) = 30 s + 55 f - - > s = 4 f - - > f / s = 1 / 4 - - > f / ( s + f ) = 1 / ( 1 + 4 ) = 1 / 5 = 0.2 . answer : b ."
Answer: b
Python program:
a = 3 - 5
b = 5 - 5
c = a / b
d = c * 100
Problem: a man performs 1 / 2 of the total journey by rail , 1 / 3 by bus and the remaining 5 km on foot . his total journey is
Options: a ) 16 km , b ) 10 km , c ) 12 km , d ) 30 km , e ) 25 km
Rationale: "explanation : let the journey be x km then , 1 x / 2 + 1 x / 3 + 5 = x 5 x + 30 = 6 x x = 30 km answer : option d"
Answer: d
Python program:
a = 3 * 5
Problem: the sum of two consecutive even integers is 26 . what are the two numbers ?
Options: a ) 12 - 14 , b ) 13 - 13 , c ) 10 - 16 , d ) 9 - 17 , e ) 8 - 18
Rationale: "let 2 n be the first even integer and let 2 n + 2 be the second integer 2 n + 2 n + 2 = 26 4 n + 2 = 26 4 n + 2 - 2 = 26 - 2 4 n = 24 n = 6 so the first even integer is 2 n = 2 × 6 = 12 and the second is 12 + 2 = 14 correct answer is a ) 12 - 14"
Answer: a
Python program:
a = 26 - 10
b = a - 2
c = b / 4
d = c + 2 
e = d + 2 
f = e ** 2
g = 26 - 10
h = g - 2
i = h / 4
j = i + 2 
k = j + 2 
l = k + 2 
m = l ** 2
n = f + m 
o = 26 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 26 - 10
t = s - 2
u = t / 4
v = u + 2 
w = v ** 2
x = r + w 
y = n + x
Problem: total 75 cows 25 cow gives each 2 liter milk 25 cow gives each 3 / 4 liter milk 25 cow gives each 1 / 4 liter milk this is split into 3 son per each 25 cows & 25 liter milk how ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 25 , e ) 18
Rationale: "25 cow 2 liter each = 50 liter 25 cow 3 / 4 liter each = 3 / 4 = 0.75 * 25 = 18.75 25 cow 1 / 4 liter each = 1 / 4 = 0.25 * 25 = 6.25 add 50 + 18.75 + 6.25 = 75 milk split into 3 son each 25 liter then 75 / 3 = 25 answer : d"
Answer: d
Python program:
a = 3 / 4
b = 3 / 4
c = b * 25
d = a + c 
e = const_0_25 * 25
f = d + e
Problem: if the wheel is 14 cm then the number of revolutions to cover a distance of 968 cm is ?
Options: a ) a ) 15 , b ) b ) 10 , c ) c ) 14 , d ) d ) 12 , e ) e ) 11
Rationale: "2 * 22 / 7 * 14 * x = 968 = > x = 11 answer : e"
Answer: e
Python program:
a = 3 * 100
b = 1 * 10
c = a + b 
d = c + 4 
e = d / 100
f = 2 * e
g = f * 14
h = 968 / g
Problem: two trains 210 m and 260 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 16.92 sec , b ) 14.8 sec , c ) 10.68 sec , d ) 10.8 sec , e ) 20.8 sec
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 210 + 260 = 470 m . required time = 470 * 9 / 250 = 16.92 = 16.92 sec . answer : a"
Answer: a
Python program:
a = 210 + 260 
b = 60 + 40 
c = b * const_0_2778
d = a / c
Problem: a certain sum is invested at simple interest at 15 % p . a . for two years instead of investing at 12 % p . a . for the same time period . therefore the interest received is more by rs . 900 . find the sum ?
Options: a ) s . 7000 , b ) s . 9000 , c ) s . 15000 , d ) s . 17000 , e ) s . 27000
Rationale: "let the sum be rs . x . ( x * 15 * 2 ) / 100 - ( x * 12 * 2 ) / 100 = 900 = > 30 x / 100 - 24 x / 100 = 900 = > 6 x / 100 = 900 = > x = 15000 . answer : c"
Answer: c
Python program:
a = 15 - 12
b = a * 2
c = b / 100
d = 900 / c
Problem: a batsman scored 125 runs which included 5 boundaries and 5 sixes . what percent of his total score did he make by running between the wickets ?
Options: a ) 45 % , b ) 500 / 11 , c ) 600 / 11 , d ) 55 % , e ) 60 %
Rationale: "explanation : number of runs made by running , = > 125 − ( 5 × 4 + 5 × 6 ) . = > 125 - 50 = > 75 hence , the required percentage is : - = > 75 / 125 * 100 = > 60 % answer : e"
Answer: e
Python program:
a = 5 * 5
b = 5 * 5
c = a + b 
d = 125 - c
e = d / 125
f = e * 100
Problem: a certain basketball team that has played 2 / 3 of its games has a record of 15 wins and 5 losses . what is the greatest number of the remaining games that the team can lose and still win at least 3 / 4 of all of its games ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 2
Rationale: "15 wins , 3 losses - total 20 games played . the team has played 2 / 3 rd of all games so total number of games = 30 3 / 4 th of 30 is 22.5 so the team must win 23 games and can afford to lose at most 7 total games . it has already lost 5 games so it can lose another 2 at most . answer ( e )"
Answer: e
Python program:
a = 3 / 2
b = 15 + 5 
c = a * b
d = 3 / 4
e = 3 / 2
f = 15 + 5 
g = e * f
h = d * g
i = math.floor(h)
j = i + 1 
k = c - j
Problem: on selling 13 balls at rs . 720 , there is a loss equal to the cost price of 5 balls . the cost price of a ball is :
Options: a ) s . 45 , b ) s . 50 , c ) s . 55 , d ) s . 60 , e ) s . 90
Rationale: "( c . p . of 13 balls ) - ( s . p . of 13 balls ) = ( c . p . of 5 balls ) c . p . of 8 balls = s . p . of 13 balls = rs . 720 . c . p . of 1 ball = rs . 720 / 8 = rs . 90 . answer : option e"
Answer: e
Python program:
a = 13 - 5
b = 720 / a
Problem: 3 friends neha , sabi and mahi divide $ 1100 amongs them in such a way that if $ 5 , $ 8 and $ 4 are removed from the sums that neha , sabi and mahi received respectively , then the share of the sums that they got will be in the ratio of 2 : 8 : 6 . how much did mahi receive ?
Options: a ) $ 122 , b ) $ 152 , c ) $ 202 , d ) $ 107 , e ) $ 102
Rationale: explanatory answer let the sums of money received by a , b and c be x , y and z respectively . then x - 5 : y - 8 : z - 4 is 2 a : 8 a : 6 a when $ 5 , $ 8 and $ 4 are removed , we are removing a total of $ 17 from $ 1100 . therefore , 2 a + 8 a + 6 a = 1100 - 17 = 1093 i . e . , 16 a = 1093 or a = 68 . we know that z - 6 = 16 a = 6 * 16 = 96 therefore , z = 96 + 6 = $ 102 the correct choice is ( e )
Answer: e
Python program:
a = 8 + 12 
b = a * 4
c = b + 12 
d = c + 10
Problem: the maximum number of girls among them 2923 bags and 3239 eyeliners can be distributed in such a way that each student gets the same number of bags and eyeliners .
Options: a ) 80 , b ) 79 , c ) 78 , d ) 81 , e ) 82
Rationale: max no of girls = hcf of 2923 and 3239 = 79 answer : b
Answer: b
Python program:
a = math.gcd(2923, 3239)
Problem: for any integer n greater than 1 , n * denotes the product of all the integers from 1 to n , inclusive . how many prime numbers w are there between 6 * + 2 and 6 * + 6 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "given that n * denotes the product of all the integers from 1 to n , inclusive so , 6 * + 2 = 6 ! + 2 and 6 * + 6 = 6 ! + 6 . now , notice that we can factor out 2 our of 6 ! + 2 so it can not be a prime number , we can factor out 3 our of 6 ! + 3 so it can not be a prime number , we can factor out 4 our of 6 ! + 4 so it can not be a prime number , . . . the same way for all numbers between 6 * + 2 = 6 ! + 2 and 6 * + 6 = 6 ! + 6 , inclusive . which means that there are no primes w in this range . answer : a ."
Answer: a
Python program:
a = math.factorial(6)
b = a + 6 
c = math.factorial(6)
d = c + 6 
e = b / d
Problem: in may , the groundskeeper at spring lake golf club built a circular green with an area of 95 π square feet . in august , the groundskeeper doubled the distance from the center of the green to the edge of the green . what is the total area of the renovated green ?
Options: a ) 190 π
b ) 210 π
c ) 240 π
d ) 320 π
e ) 380 π
Rationale: area = π r ^ 2 , so doubling the radius results in an area that is 4 times the original area . 4 ( 95 π ) = 380 π the answer is e .
Answer: e
Python program:
a = math.sqrt(95)
b = a * 2
c = b ** 2
d = c * math.pi
Problem: i have a huge bed - sheet of 1 meter long . i want to cuts this role into pieces of 20 centimeter long cloth . how long will it take me to cut the bed sheet if each 20 centimeter cut took me 5 minutes ?
Options: a ) 150 min , b ) 245 min , c ) 185 min , d ) 300 min , e ) 205 min
Rationale: b it will take 49 cuts not 50 . so 49 * 5 = > 245 minutes
Answer: b
Python program:
a = 20 + 20 
b = a + 10 
c = b - 1
d = c * 5
Problem: 30 men can do a work in 40 days . when should 14 men leave the work so that the entire work is completed in 40 days after they leave the work ?
Options: a ) 87 days , b ) 16 days , c ) 55 days , d ) 44 days , e ) 22 days
Rationale: "total work to be done = 30 * 40 = 1200 let 14 men leave the work after ' p ' days , so that the remaining work is completed in 40 days after they leave the work . 40 p + ( 14 * 40 ) = 1200 40 p = 640 = > p = 16 days answer : b"
Answer: b
Python program:
a = 30 * 40
b = 40 * 14
c = a - b
d = c / 40
Problem: if the cost price of 50 articles is equal to the selling price of 32 articles , then the gain or loss percent is ?
Options: a ) 22 , b ) 56.25 , c ) 78 , d ) 33 , e ) 25
Rationale: "given that , cost price of 50 article is equal to selling price of 32 articles . let cost price of one article = rs . 1 selling price of 32 articles = rs . 50 but cost price of 32 articles = rs . 32 therefore , the trader made profit . \ percentage of profit = 18 / 32 * 100 = 56.25 % answer : b"
Answer: b
Python program:
a = 100 * 32
b = a / 50
c = 100 - b
d = 100 * 32
e = d / 50
f = c / e
g = 100 * f
Problem: on dividing 23 by a number , the quotient is 7 and the remainder is 2 . find the divisor .
Options: a ) 1 , b ) 2 , c ) 3 , d ) 6 , e ) 7
Rationale: "d = ( d - r ) / q = ( 23 - 2 ) / 7 = 21 / 7 = 3 c"
Answer: c
Python program:
a = 23 / 7
b = math.floor(a)
Problem: what is the value of 3 x ^ 2 − 1.8 x + 0.3 for x = 0.3 ?
Options: a ) − 0.3 , b ) 0 , c ) 0.03 , d ) 1.08 , e ) 2.46
Rationale: "3 x ^ 2 - 1.8 x + 0.3 for x = 0.6 = 3 ( 0.3 * 0.3 ) - 6 * 0.3 * ( 0.3 ) + 0.3 = - 3 * 0.3 * 0.3 + 0.3 = - 0.27 + 0.3 = 0.03 correct option : c"
Answer: c
Python program:
a = 3 ** 2
b = 1 ** 8
c = a - b
d = c / 1000
e = d / 1000
f = e * 3
g = 3 ** 2
h = 1 ** 8
i = g - h
j = i / 1000
k = j / 1000
l = f - k
Problem: the average of temperatures at noontime from monday to friday is 50 ; the lowest one is 42 , what is the possible maximum range of the temperatures ?
Options: a ) 20 , b ) 25 , c ) 40 , d ) 45 , e ) 86
Rationale: "there are 5 days so the sum of temperature can be 50 * 5 = 250 lowest is 42 . to find the maximum range we can say the temperature was the lowest for 4 of the 5 days so 4 * 42 = 168 . on the fifth day it is 250 - 168 = 281 range is therefore 128 - 42 = 86 answer e"
Answer: e
Python program:
a = 2 + 3 
b = 50 * a
c = 42 * 4
d = b - c
e = d - 42
Problem: a , b and c enter into a partnership and theirs shares are in the ratio 1 / 2 : 1 / 3 : 1 / 4 . after two months , a withdraws half of his capital and after 10 months , a profit of rs . 378 is divided among them . what is b ’ s share ?
Options: a ) rs . 129 , b ) rs . 144 , c ) rs . 156 , d ) rs . 168 , e ) rs . 178
Rationale: ratio of initial investments = 1 / 2 : 1 / 3 : 1 / 4 = 6 : 4 : 3 . let their initial investments be 6 x , 2 x and 3 x respectively . a : b : c = ( 6 x * 2 + 3 x * 10 ) : ( 4 x * 12 ) : ( 3 x * 12 ) = 42 : 48 : 36 = 7 : 8 : 6 . therefore , b ’ s share = rs . 378 * 8 / 21 = rs . 144 . answer : b
Answer: b
Python program:
a = 2 * 4
b = 378 * a
c = 3 + 4 
d = c * 3
e = b / d
Problem: on a scale that measures the intensity of a certain phenomenon , a reading of d + 1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of d . on that scale , the intensity corresponding to a reading of 8 is how many times as great as the intensity corresponding to a reading of 3 ?
Options: a ) 5 , b ) 50 , c ) 10 ^ 5 , d ) 5 ^ 10 , e ) 8 ^ 10 - 3 ^ 10
Rationale: to solve this problem we need to examine the information in the first sentence . we are told that “ a reading of d + 1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of d . ” let ’ s practice this idea with some real numbers . let ’ s say d is 2 . this means that d + 1 = 3 . with the information we were given we can say that a reading of 3 is ten times as great as the intensity of a reading of 2 . furthermore , we can say that a reading of 4 is actually 10 x 10 = 10 ^ 2 times as great as the intensity of a reading of 2 . increasing one more unit , we can say that a reading of 5 is 10 x 10 x 10 = 10 ^ 3 times as great as the intensity of a reading of 2 . we have found a pattern , which can be applied to the problem presented in the stem : 3 is “ one ” unit away from 2 , and thus a reading of 3 is 10 ^ 1 times as great as the intensity of a reading of 2 . 4 is “ two ” units away from 2 , and thus a reading of 4 is 10 ^ 2 times as great as the intensity of a reading of 2 . 5 is “ three ” units away from 2 , and thus a reading of 5 is 10 ^ 3 times as great as the intensity of a measure of 2 . we can use this pattern to easily answer the question . here we are being asked for the number of times the intensity corresponding to a reading of 8 is as great as the intensity corresponding to a reading of 3 . because 8 is 5 units greater than 3 , a reading of 8 is 10 ^ 5 times as great as the intensity corresponding to a reading of 3 . answer c .
Answer: c
Python program:
a = 8 - 3
b = 10 ** a
Problem: if 6 x ^ 2 + x - 12 = ( hx + b ) ( cx + d ) , then | h | + | b | + | c | + | d | = for a complete solution and more practice problems , see this blog : http : / / magoosh . com / gmat / 2012 / algebra - on . . . to - factor /
Options: a ) 10 , b ) 12 , c ) 15 , d ) 18 , e ) 20
Rationale: 6 x ^ 2 + x - 12 = 6 x ^ 2 + 9 x - 8 x - 12 = > 3 x ( 2 x + 3 ) - 4 ( 2 x + 3 ) = > ( 2 x + 3 ) ( 3 x - 4 ) = ( hx + b ) ( cx + d ) hence h = 2 , b = c = 3 , d = - 4 so , 2 + 3 + 3 + | - 4 | = 2 + 3 + 3 + 4 = 12 answer b .
Answer: b
Python program:
a = 2 + 3 
b = a + 3 
c = b + 4
Problem: 4 men and 6 women finish a job in 8 days , while 3 men and 7 women finish it in 10 days . in how many days will 10 women working together finish it ?
Options: a ) 30 days , b ) 40 days , c ) 50 days , d ) 60 days , e ) 70 days
Rationale: explanation : let 1 man ' s 1 day work = x and 1 woman ' s 1 days work = y . then , 4 x + 6 y = 1 / 8 and 3 x + 7 y = 1 / 10 solving , we get y = 1 / 400 [ means work done by a woman in 1 day ] 10 women 1 day work = 10 / 400 = 1 / 40 10 women will finish the work in 40 days option b
Answer: b
Python program:
a = 10 * 7
b = 8 * 6
c = a - b
d = 8 * 4
e = 10 * 3
f = d - e
g = c / f
h = 8 * 4
i = g * h
j = 8 * 6
k = i + j 
l = k / 10
Problem: how many trailing zeros will be there after the rightmost non - zero digit in the value of 25 ! ( factorial 25 ) ?
Options: a ) 25 , b ) 8 , c ) 6 , d ) 5 , e ) 2
Rationale: explanatory answer 25 ! means factorial 25 whose value = 25 * 24 * 23 * 22 * . . . . * 1 when a number that has 5 as its factor is multiplied by an even number , it results in a trailing zero . ( product of 5 and 2 is 10 and any number when multiplied with 10 or a power of 10 will have one or as many zeroes as the power of 10 with which it has been multiplied ) in 25 ! , the following numbers have 5 as their factor : 5 , 10 , 15 , 20 , and 25 . 25 is the square of 5 and hence it has two 5 s in it . in toto , it is equivalent of having six 5 s . there are at least 6 even numbers in 25 ! hence , the number 25 ! will have 6 trailing zeroes in it . choice c
Answer: c
Python program:
a = math.sqrt(25)
b = a + 1
Problem: alice leaves her home and walks toward bob ' s house . one hour later , bob leaves his home and walks toward alice ' s house . the distance between their homes is 41 kilometers , alice ' s walking speed is 5 km / h , and bob ' s walking speed is 4 km / h . how many kilometers will alice walk before she meets bob ?
Options: a ) 22 , b ) 25 , c ) 27 , d ) 38 , e ) 30
Rationale: alice walks 5 km in the first hour so there are 36 km remaining . when bob starts walking , they complete a total of 9 km per hour . they will meet four hours after bob starts walking . since alice walks for 5 hours , she walks 25 km . the answer is b .
Answer: b
Python program:
a = 41 - 5
b = 5 + 4 
c = a / b
d = c * 5
e = d + 5
Problem: the average of 1 st 3 of 4 numbers is 6 and of the last 3 are 5 . if the sum of the first and the last number is 17 . what is the last numbers ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "a + b + c = 18 b + c + d = 15 a + d = 17 a – d = 3 a + d = 17 2 d = 14 d = 7 answer : d"
Answer: d
Python program:
a = 3 * 6
b = 17 - 6
c = b + 3 
d = a - c
e = d - 6
Problem: a man can row 7 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and back . what is the total distance traveled by the man ?
Options: a ) 6.24 km , b ) 6 km , c ) 6.79 km , d ) 5.66 km , e ) 10 km
Rationale: "m = 7 s = 1.2 ds = 8.2 us = 5.8 x / 8.2 + x / 5.8 = 1 x = 3.40 d = 3.40 * 2 = 6.79 answer : c"
Answer: c
Python program:
a = 7 + 1 
b = 7 - 1
c = a * b
d = 7 + 1 
e = 7 - 1
f = d + e 
g = c / f
h = g * 2
Problem: how many prime numbers between 1 and 100 are factors of 67830 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 3 , e ) 2
Rationale: "factor of 67830 = 2 * 3 * 5 * 7 * 17 * 19 - - - 6 prime numbers c"
Answer: c
Python program:
a = 4 * 1
Problem: the speed of a car is 20 km in the first hour and 30 km in the second hour . what is the average speed of the car ?
Options: a ) 25 kmph , b ) 85 kmph , c ) 34 kmph , d ) 23 kmph , e ) 45 kmph
Rationale: "s = ( 20 + 30 ) / 2 = 25 kmph answer : a"
Answer: a
Python program:
a = 20 + 30 
b = a / 2
Problem: how many shots of 1 cm radius can be prepared from a sphere of 4 cm radius ?
Options: a ) 33 , b ) 88 , c ) 27 , d ) 64 , e ) 99
Rationale: "4 / 3 ï € * 4 * 4 * 4 = 4 / 3 ï € * 1 * 1 * 1 * x x = 64 answer : d"
Answer: d
Python program:
a = 4 ** 2
b = a * 4
Problem: in a class , 7 students like to play basketball and 8 like to play cricket . 3 students like to play on both basketball and cricket . how many students like to play basketball or cricket or both ?
Options: a ) 12 , b ) 15 , c ) 16 , d ) 18 , e ) 22
Rationale: "draw a venn diagram yourself ! b + c - bc = number of students that play either basketball or cricket 7 + 8 - 3 = 12 a )"
Answer: a
Python program:
a = 7 + 8 
b = a - 3
Problem: p has $ 42 more than what q and r together would have had if both b and c had 1 / 8 of what p has . how much does p have ?
Options: a ) $ 44 , b ) $ 48 , c ) $ 52 , d ) $ 56 , e ) $ 60
Rationale: "p = ( 2 / 8 ) * p + 42 ( 6 / 8 ) * p = 42 p = 56 the answer is d ."
Answer: d
Python program:
a = 1 / 8
b = a * 2
c = 1 - b
d = 42 / c
Problem: one hour after yolanda started walking from x to y , a distance of 24 miles , bob started walking along the same road from y to x . if yolanda ' s walking rate was 3 miles per hour and bob т ' s was 4 miles per hour , how many miles had bob walked when they met ?
Options: a ) 24 , b ) 23 , c ) 22 , d ) 21 , e ) 12
Rationale: "when b started walking y already has covered 3 miles out of 24 , hence the distance at that time between them was 24 - 3 = 21 miles . combined rate of b and y was 3 + 4 = 7 miles per hour , hence they would meet each other in 21 / 7 = 3 hours . in 6 hours b walked 3 * 4 = 12 miles . answer : e ."
Answer: e
Python program:
a = 24 - 3
b = 3 + 4 
c = a / b
d = c * 4
Problem: the cost of an article is decreased by 10 % . if the original cost is $ 100 , find the decrease cost .
Options: a ) 33 , b ) 11 , c ) 68 , d ) 36 , e ) 90
Rationale: "original cost = $ 100 decrease in it = 10 % of $ 100 = 10 / 100 ã — 100 = 1000 / 100 = $ 10 therefore , decrease cost = $ 100 - $ 10 = $ 90 answer : e"
Answer: e
Python program:
a = 100 * 10
b = a / 100
Problem: how long will a boy take to run round a square field of side 35 metres . if he runs at the rate of 9 km / hr ?
Options: a ) 56 sec , b ) 1 minute , c ) 45 sec , d ) 58 sec , e ) 50 sec
Rationale: "speed = 9 km / hr = 9 * 5 / 18 = 5 / 2 m / sec distance = 35 * 4 = 140 m time taken = 140 * 2 / 5 = 56 sec . answer is a"
Answer: a
Python program:
a = 35 * 4
b = 1000 / 3600
c = 9 * b
d = a / c