euclaise/mathqa_programs huggingface dataset:
Problem: if an integer n is to be chosen at random from the integers 1 to 96 , inclusive , what is the probability that n ( n + 1 ) ( n + 2 ) will be divisible by 12 ?
Options: a ) 1 / 48 , b ) 234 / 8 , c ) 1 / 24 , d ) 5 / 8 , e ) 3 / 4
Rationale: "i get 5 / 8 as well 1 to 96 inclusive means we have 48 odd and 48 even integers e o e / 12 = integer , therefore we have 48 / 96 numbers divisible by 8 o e o / 12 = not integer we can not forget multiples of 12 from 1 to 96 we have 8 numbers that are multiple of 12 therefore , 48 / 96 + 8 / 96 = 23 / 48 answer : b"
Answer: b
Python program:
a = 96 / 2
b = 96 / 12
c = a + b 
d = c / 96
Problem: a theater box office sold an average ( arithmetic mean ) of 68 tickets per staff member to a particular movie . among the daytime staff , the average number sold per member was 80 , and among the evening staff , the average number sold was 60 . if there are no other employees , what was the ratio of the number of daytime staff members to the number of evening staff members ?
Options: a ) 2 : 3 , b ) 1 : 4 , c ) 5 : 6 , d ) 7 : 11 , e ) 3 : 7
Rationale: "deviation from the mean for the daytime staff = 80 - 68 = 12 . deviation from the mean for the evening staff = 68 - 60 = 8 . thus , the ratio of the number of daytime staff members to the number of evening staff members is 8 : 12 = 2 : 3 . the answer is a ."
Answer: a
Python program:
a = 68 - 60
b = 80 - 68
c = a / b
Problem: if 7 log ( 4 * 5 ^ 2 ) = x , find x
Options: a ) 12 , b ) 11 , c ) 10 , d ) 14 , e ) 13
Rationale: "7 ( log 2 ^ 2 * 5 ^ 2 ) = x 7 log ( 5 * 2 ) ^ 2 = x 7 * 2 log ( 5 * 2 ) = x 14 log 10 = x log 10 base 10 = 1 so 14 * 1 = x x = 14 answer : d"
Answer: d
Python program:
a = 5 ** 2
b = 4 * a
c = b ** 7
Problem: a bag contains 6 black and 8 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ?
Options: a ) 3 / 4 , b ) 4 / 7 , c ) 1 / 7 , d ) 1 / 8 , e ) 4 / 3
Rationale: "let number of balls = ( 6 + 8 ) = 14 . number of white balls = 8 . p ( drawing a white ball ) = 8 / 14 = 4 / 7 . option b ."
Answer: b
Python program:
a = math.factorial(8)
b = 8 - 2
c = math.factorial(b)
d = a / c
e = math.factorial(2)
f = d / e
g = math.factorial(6)
h = 6 - 2
i = math.factorial(h)
j = g / i
k = math.factorial(2)
l = j / k
m = f + l 
n = 6 + 8 
o = math.factorial(n)
p = 6 + 8 
q = p - 2
r = math.factorial(q)
s = o / r
t = math.factorial(2)
u = s / t
v = m / u
Problem: we had $ 2800 left after spending 30 % of the money that we took for shopping . how much money did we start with ?
Options: a ) $ 3700 , b ) $ 4000 , c ) $ 4300 , d ) $ 4600 , e ) $ 4900
Rationale: "let x be the amount of money we started with . 0.7 x = 2800 x = 4000 the answer is b ."
Answer: b
Python program:
a = 30 / 100
b = 1 - a
c = 2800 / b
Problem: ? x 48 = 173 x 240
Options: a ) 545 , b ) 685 , c ) 865 , d ) 495 , e ) 534
Rationale: "let y x 48 = 173 x 240 then y = ( 173 x 240 ) / 48 = 173 x 5 = 865 . answer : c"
Answer: c
Python program:
a = 173 * 240
b = a / 48
Problem: the ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm . find the ratio of the breadth and the area of the rectangle ?
Options: a ) 1 : 96
b ) 1 : 99
c ) 1 : 95
d ) 1 : 12
e ) 1 : 11
Rationale: let the length and the breadth of the rectangle be 4 x cm and 3 x respectively . ( 4 x ) ( 3 x ) = 6912 12 x 2 = 6912 x 2 = 576 = 4 * 144 = 22 * 122 ( x > 0 ) = > x = 2 * 12 = 24 ratio of the breadth and the areas = 3 x : 12 x 2 = 1 : 4 x = 1 : 96 . answer : a
Answer: a
Python program:
a = 6912 / 3
b = 4 * a
c = math.sqrt(b)
d = c / 4
e = d * 3
f = e / 6912
Problem: after an ice began to melt out from the freezer , in the first hour lost 3 / 4 , in the second hour lost 3 / 4 of its remaining . if after two hours , the volume is 0.25 cubic inches , what is the original volume of the cubic ice , in cubic inches ?
Options: a ) 2.5 , b ) 3.0 , c ) 4.0 , d ) 6.5 , e ) 8.0
Rationale: "let initial volume of ice be = x ice remaining after 1 hour = x - 0.75 x = 0.25 x ice remaining after 2 hour = ( 1 / 4 ) x - ( 3 / 4 * 1 / 4 * x ) = ( 1 / 16 ) x ( 1 / 16 ) x = 0.25 x = 4 alternate solution : try to backsolve . initial volume = 4 after one hour - - > ( 1 / 4 ) 4 = 1 after two hours - - > ( 1 / 4 ) 1 = 0.25 answer : c"
Answer: c
Python program:
a = 0 / 25
b = a / const_0_25
Problem: log 3 n + log 6 n what is 3 digit number n that will be whole number
Options: a ) 629 , b ) 729 , c ) 829 , d ) 929 , e ) 216
Rationale: "no of values n can take is 1 6 ^ 3 = 216 answer : e"
Answer: e
Python program:
a = 6 ** 3
Problem: of the total amount that rose spent on a shopping trip , excluding taxes , she spent 50 percent on clothing , 20 percent on food , and 30 percent on other items . if rose paid a 4 percent tax on the clothing , no tax on the food , and an 8 percent tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?
Options: a ) 2.8 % , b ) 4.4 % , c ) 4.6 % , d ) 5.2 % , e ) 6.0 %
Rationale: assume she has $ 200 to spend . tax clothing = 50 % = $ 100 = $ 4.00 food = 20 % = $ 40 = $ 0.00 items = 30 % = $ 60 = $ 4.80 total tax = $ 8.80 % of total amount = 8.8 / 200 * 100 = 4.4 % b )
Answer: b
Python program:
a = 4 / 100
b = a * 50
c = 8 / 100
d = c * 30
e = b + d
Problem: 33 cubic centimetres of silver is drawn into a wire 1 mm in diameter . the length of the wire in metres will be :
Options: a ) 84 m , b ) 88 m , c ) 42 m , d ) 137 m , e ) none
Rationale: "sol . let the length of the wire b h . radius = 1 / 2 mm = 1 / 20 cm . then , 22 / 7 * 1 / 20 * 1 / 20 * h = 33 ⇔ = [ 33 * 20 * 20 * 7 / 22 ] = 4200 cm = 42 m . answer c"
Answer: c
Python program:
a = 1 / 2
b = a ** 2
c = b * math.pi
d = 33 / c
Problem: in a certain game of dice , the player ’ s score is determined as a sum of 3 throws of a single die . the player with the highest score wins the round . if more than one player has the highest score , the winnings of the round are divided equally among these players . if john plays this game against 22 other players , what is the probability of the minimum score that will guarantee john some monetary payoff ?
Options: a ) 41 / 50 , b ) 1 / 216 , c ) 1 / 221 , d ) 1 / 84 , e ) 1 / 42
Rationale: to guarantee that john will get some monetary payoff he must score the maximum score of 6 + 6 + 6 = 18 , because if he gets even one less than that so 17 , someone can get 18 and john will get nothing . p ( 18 ) = 1 / 6 ^ 3 = 1 / 216 . answer : b .
Answer: b
Python program:
a = 3 * 2
b = 1 / a
c = b ** 3
Problem: if the product of the integers w , x , y and z is 68 , and if 0 < w < x < y < z , what is the value of w + z ?
Options: a ) 10 , b ) 5 , c ) 16 , d ) 18 , e ) 21
Rationale: 24 = 1 * 2 * 3 * 4 so w = 1 , x = 2 , y = 3 , z = 4 w + z = 1 + 4 = 5 answer - b
Answer: b
Python program:
a = 68 / 2
b = a / 2
c = b - 1
d = c - 1
e = d - 1
f = e - 1
g = f - 1
h = g - 1
i = h - 1
j = i - 1
k = j - 1
l = k - 1
m = l - 1
n = m - 1
Problem: what is the least number which when divided by 5 , 6 , 9 and 18 leaves remainder 4 in each care ?
Options: a ) 30 , b ) 44 , c ) 36 , d ) 56 , e ) 94
Rationale: "explanation : lcm of 5 , 6 , 9 and 18 is 90 required number = 90 + 4 = 94 answer : option e"
Answer: e
Python program:
a = math.lcm(5, 6)
b = math.lcm(9, 18)
c = math.lcm(a, b)
d = c + 4
Problem: the speed of a railway engine is 63 km per hour when no compartment is attached , and the reduction in speed is directly proportional to the square root of the number of compartments attached . if the speed of the train carried by this engine is 24 km per hour when 9 compartments are attached , the maximum number of compartments that can be carried by the engine is :
Options: a ) 19 , b ) 18 , c ) 16 , d ) 17 , e ) 23
Rationale: the reduction in speed is directly proportional to the square root of the number of compartments attached does reduction mean amount subtracted ? or percentage decrease ? there are at least two interpretations , and the wording does not provide a clear interpretation between them . evidently what the question intends is the subtraction interpretation . what is subtracted from the speed is directly proportional to the square root of the number of compartments attached . in other words , if s = speed , and n = number of compartments , then s = 63 - k * sqrt ( n ) where k is a constant of the proportionality . in general , if a is directly proportional to b , we can write a = k * b and solve for k . if n = 9 , then s = 24 24 = 63 - k * sqrt ( 9 ) = 63 - 3 k k = 13 now , we need to know : what value of n makes s go to zero ? 0 = 63 - 13 * sqrt ( n ) 13 * sqrt ( n ) = 63 n = 23 with 24 compartments , the train does not budge . therefore , it would budge if there were one fewer cars . thus , 23 is the maximum number of cars the engine can pull and still move . e
Answer: e
Python program:
a = 63 - 24
b = math.sqrt(9)
c = a / b
d = 63 / c
e = d ** 2
Problem: in a class of 79 students 41 are taking french , 22 are taking german . of the students taking french or german , 9 are taking both courses . how many students are not enrolled in either course ?
Options: a ) 6 , b ) 15 , c ) 25 , d ) 33 , e ) 54
Rationale: "formula for calculating two overlapping sets : a + b - both + not ( a or b ) = total so in our task we have equation : 41 ( french ) + 22 ( german ) - 9 ( both ) + not = 79 54 + not = 79 not = 79 - 54 = 25 so answer is c"
Answer: c
Python program:
a = 41 + 22 
b = a - 9
c = 79 - b
Problem: a train traveled the first d miles of its journey it an average speed of 60 miles per hour , the next d miles of its journey at an average speed of y miles per hour , and the final d miles of its journey at an average speed of 160 miles per hour . if the train ’ s average speed over the total distance was 98 miles per hour , what is the value of y ?
Options: a ) 68 , b ) 84 , c ) 90 , d ) 120 , e ) 125
Rationale: average speed = total distance traveled / total time taken 3 d / d / 60 + d / y + d / 160 = 98 solving for d and y , 15 y = 11 y + 480 4 y = 500 y = 125 answer e
Answer: e
Python program:
a = 4 * 2
b = a * 10
c = 100 * 4
d = b + c 
e = 4 * 2
f = e * 10
g = 100 * 4
h = f + g 
i = h * 3
j = i / 98
k = 4 * 2
l = k + 3 
m = j - l
n = d / m
Problem: a vessel of capacity 2 litre has 35 % of alcohol and another vessel of capacity 6 litre had 50 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?
Options: a ) 31 % . , b ) 71 % . , c ) 49 % . , d ) 29 % . , e ) 37 % .
Rationale: "35 % of 2 litres = 0.7 litres 50 % of 6 litres = 3 litres therefore , total quantity of alcohol is 3.7 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 37 % e"
Answer: e
Python program:
a = 35 / 100
b = a * 2
c = 50 / 100
d = c * 6
e = b + d 
f = e / 10
g = f * 100
Problem: how many integers between 324,700 and 468,600 have tens digit 1 and units digit 3 ?
Options: a ) 10,300 , b ) 10,030 , c ) 1,353 , d ) 1,352 , e ) 1,439
Rationale: "there is one number in hundred with 1 in the tens digit and 3 in the units digit : 13 , 113 , 213 , 313 , . . . the difference between 324,700 and 468,600 is 468,600 - 324,700 = 133,900 - one number per each hundred gives 143,900 / 100 = 1,439 numbers . answer : e ."
Answer: e
Python program:
a = 2 * 100
b = 3 + 4 
c = b * 10
d = a + c 
e = d + 2 
f = 468 - 600
Problem: find the unknown term 8 , x , 62 , - 4 , - 12
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 9
Rationale: 8 , x , 6,2 , - 4 , - 12 i guess each differ in d range of 2 8 - 8 = 0 8 - 6 = 2 6 - 2 = 4 2 - 6 = - 4 - 4 - 8 = - 12 answer : d
Answer: d
Python program:
a = 62 + 2 
b = a / 8
Problem: how many integers are divisible by 3 between 10 ! and 10 ! + 20 inclusive ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "0 ! is divisible by 3 - the way i look factorials is that any number included will also be divisible by the product . 10,9 , 8,7 , 6,5 , 4,3 , 2,1 are all divisors of 10 ! there are 6 numbers between 10 ! and 10 ! + 20 that are divisible by 3 . hence b : 7"
Answer: b
Python program:
a = 20 / 3
b = a + 1
Problem: a cricket bat is sold for $ 850 , making a profit of $ 205 . the profit percentage would be
Options: a ) 24 % , b ) 25 % , c ) 32 % , d ) 36 % , e ) 40 %
Rationale: "205 / ( 850 - 205 ) = 205 / 645 = 41 / 129 = 32 % . answer : c ."
Answer: c
Python program:
a = 850 - 205
b = 205 / a
c = b * 100
Problem: for the symbol , m ” n = n ^ 2 − m for all values of m and n . what is the value of 4 ” 3 ?
Options: a ) 5 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: "4 ” 3 = 9 - 4 = 5 answer : a"
Answer: a
Python program:
a = 3 ** 2
b = a - 4
Problem: a man buys an article for $ 10 . and sells it for $ 25 . find the gain percent ?
Options: a ) 25 % , b ) 50 % , c ) 20 % , d ) 150 % , e ) 300 %
Rationale: "c . p . = $ 10 s . p . = $ 25 gain = $ 15 gain % = 15 / 10 * 100 = 150 % answer is d"
Answer: d
Python program:
a = 10 / 100
b = 25 / a
c = b - 100
Problem: a can do a piece of work in 12 days . when he had worked for 2 days b joins him . if the complete work was finished in 8 days . in how many days b alone can finish the work ?
Options: a ) 28 days , b ) 76 days , c ) 16 days , d ) 18 days , e ) 19 days
Rationale: 8 / 12 + 6 / x = 1 x = 18 days answer : a
Answer: a
Python program:
a = 1 / 8
b = 1 / 12
c = 2 * b
d = 1 - c
e = a * d
f = 1 / 12
g = e - f
h = 1/(g)
i = 12 + 8 
j = h - i
Problem: if x / 4 years ago roger was 14 years old and x / 4 years from now he will be 4 x years old , how old will he be 6 x years from now ?
Options: a ) 32 , b ) 39 , c ) 30 , d ) 40 , e ) 28
Rationale: "assume the current age = a a - x / 4 = 14 ( i ) a + x / 4 = 4 x or a = 15 x / 4 ( ii ) putting the value of a from ( ii ) in ( i ) 15 x / 4 - x / 4 = 14 or 14 x / 4 = 14 therefore x = 4 and a = 15 6 x years from now , age will be 15 + 6 * 4 = 39 option b"
Answer: b
Python program:
a = 4 * 6
b = a * 4
c = 14 - 1
d = c / 2
e = b - d
Problem: sue ' s trail mix is 30 % nuts and 70 % dried fruit . jane ' s trail mix is 60 % nuts and 40 % chocolate chips . if the combined mixture of sue and jane ' s trails mix contains 48 % nuts , what percent of the combined mixture is dried fruit ?
Options: a ) 20 % , b ) 24 % , c ) 28 % , d ) 32 % , e ) 36 %
Rationale: "48 % is 18 % - points above 30 % and 12 % - points below 60 % . so the ratio of sue ' s mix to jane ' s mix is 2 : 3 . 2 / 5 * 70 % = 28 % the answer is c ."
Answer: c
Python program:
a = 100 * 2
b = 70 / a
c = b * 100
Problem: x can finish a work in 30 days . y can finish the same work in 15 days . yworked for 10 days and left the job . how many days does x alone need to finish the remaining work ?
Options: a ) 3 , b ) 10 , c ) 6 , d ) 8 , e ) 9
Rationale: "work done by x in 1 day = 1 / 30 work done by y in 1 day = 1 / 15 work done by y in 10 days = 10 / 15 = 2 / 3 remaining work = 1 – 2 / 3 = 1 / 3 number of days in which x can finish the remaining work = ( 1 / 3 ) / ( 1 / 30 ) = 10 b"
Answer: b
Python program:
a = 1 / 15
b = 10 * a
c = 1 - b
d = 1 / 30
e = c / d
Problem: what is the sum of the numbers between 1 and 10 , inclusive ?
Options: a ) 85 , b ) 95 , c ) 100 , d ) 105 , e ) 55
Rationale: "sol . add all the numbers between 1 and 10 . final answer = e , 55 ."
Answer: e
Python program:
a = 1 * 10
b = a / 4
Problem: a is thrice as good a work man as b and together they finish a piece of work in 12 days . the number of days taken by a alone to finish the work is :
Options: a ) 28 days . , b ) 14 days . , c ) 12 days . , d ) 16 days . , e ) 18 days .
Rationale: solution ( a ’ s 1 day ’ s work ) : ( b ’ s 1 day ’ s work ) = 3 : 1 . ( a + b ) ' s 1 day ’ s work = 1 / 12 divide 1 / 14 in the ratio 3 : 1 . ∴ a ’ s 1 day ’ s work = ( 1 / 12 x 2 / 3 ) = 1 / 16 hence , a alone can finish the work in 16 days . answer d
Answer: d
Python program:
a = 3 + 1 
b = 12 / 3
c = a * b
Problem: 300 first - time customers of a fashion store were surveyed for their shopping experience right after leaving the store . 60 % of the customers in the survey had purchased clothes for less than $ 100 . 40 % of the customers in the survey reported they were overall satisfied with their purchase . 55 % of the customers that had purchased clothes for less than $ 100 reported they were overall satisfied with their purchase . what percent of the customers surveyed purchased clothes for at least $ 100 and reported that they were not overall satisfied with their purchase ?
Options: a ) 7 , b ) 25 , c ) 35 , d ) 45 , e ) 75
Rationale: "out of 300 - 180 purchased for less than 100 $ 120 for more out of 300 - 120 responded as satisfied and 180 responded disatisfied out of 180 ( purchased less than 100 $ ) - 55 % = 99 responded as satisfied , so remaining satisfied are 120 - 99 = 21 so 21 is what percentage of 300 - 7 % so the answer should be a"
Answer: a
Python program:
a = 40 / 100
b = a * 300
c = 55 / 100
d = 60 / 100
e = 300 * d
f = c * e
g = b - f
h = g / 300
i = h * 100
Problem: the average age of 9 men increases by 4 years when two women are included in place of two men of ages 36 and 32 years . find the average age of the women ?
Options: a ) 78 , b ) 26 , c ) 52 , d ) 54 , e ) 56
Rationale: "explanation : 36 + 32 + 9 * 4 = 104 / 2 = 52 answer : c"
Answer: c
Python program:
a = 36 + 32 
b = 9 * 4
c = a + b 
d = c / 2
Problem: 0.014 × 0.014 = ?
Options: a ) 0.000196 , b ) 0.00196 , c ) 19.6 , d ) 196 , e ) none
Rationale: "solution sum of decimals places = 6 . 14 × 14 = 196 . = s 0.014 × 0.014 = 0.000196 answer a"
Answer: a
Python program:
a = 0 / 14
b = a * 100
Problem: of the land owned by a farmer , 90 percent was cleared for planting . of the cleared land , 30 percent was planted with soybeans and 60 percent of the cleared land was planted with wheat . if the remaining 540 acres of cleared land was planted with corn , how many acres did the farmer own ?
Options: a ) 7200 , b ) 6000 , c ) 3500 , d ) 5000 , e ) 6200
Rationale: 30 % od 90 % = 27 % , 60 % 0 f 90 % = 54 % so the remaining 90 - 27 - 54 = 9 % = 540 acres or 10 % of 90 % = 9 % - - > 540 / 9 * 100 = 6000 acres answer ( b )
Answer: b
Python program:
a = 100 - 30
b = a - 60
c = b / 100
d = 90 / 100
e = c * d
f = 540 / e
Problem: the wages earned by robin is 49 % more than that earned by erica . the wages earned by charles is 60 % more than that earned by erica . how much % is the wages earned by charles more than that earned by robin ?
Options: a ) 23 % , b ) 18.75 % , c ) 30 % , d ) 50 % , e ) 32.88 %
Rationale: "explanatory answer let the wages earned by erica be $ 100 then , wages earned by robin and charles will be $ 149 and $ 160 respectively . charles earns $ 49 more than robin who earns $ 149 . therefore , charles ' wage is 49 / 149 * 100 = 32.88 % . the correct choice is ( e )"
Answer: e
Python program:
a = 100 + 60 
b = 100 + 49 
c = a - b
d = 100 + 49 
e = c / d
f = e * 100
Problem: there are 59 people that own pets . 15 people own only dogs , 10 people own only cats , 5 people own only cats and dogs , 3 people own cats , dogs and snakes . how many total snakes are there ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 29 , e ) 32
Rationale: "lets assign variables to all the areas in venn diagram of three . three different units are dog , cat , snake = total = 59 only dog = d = 15 only cat = c = 10 only snake = s exactly dog and cat = 5 exactly dog and snake = x exactly cat and snake = y all three = 3 so 59 = 15 + 10 + 5 + 3 + x + y + s we need to know total snakes = x + y + s + 3 = 29 answer : d"
Answer: d
Python program:
a = 15 + 10 
b = a + 5 
c = b + 3 
d = 59 - c
e = d + 3
Problem: a sum of salary is distributed among a , b , c , d in the proportion of 2 : 3 : 4 : 6 . if d gets $ 700 more than c , what is the b ' s share ?
Options: a ) $ 1050 , b ) $ 2500 , c ) $ 3000 , d ) $ 3400 , e ) $ 8000
Rationale: let the shares of a , b , c , d are 2 x , 3 x , 4 x , 6 x 6 x - 4 x = 700 x = 350 b ' s share = 3 x = $ 1050 answer is a
Answer: a
Python program:
a = 6 - 4
b = 700 / a
c = 3 * b
Problem: two 6 faced dice are thrown together . the probability that all the three show the same number on them is ?
Options: a ) 1 / 32 , b ) 1 / 6 , c ) 1 / 33 , d ) 1 / 38 , e ) 1 / 34
Rationale: "the three dice can fall in 6 * 6 = 36 ways . hence the probability is 6 / 36 = 1 / 6 answer : b"
Answer: b
Python program:
a = 1 / 6
b = 1 / 6
c = a * b
d = 1 / 6
e = c * d
f = 1 / 6
g = e * f
Problem: the tax on a commodity is diminished by 27 % and its consumption increased by 16 % . the effect on revenue is ?
Options: a ) 18 , b ) 16 , c ) 5 , d ) 15 , e ) 4
Rationale: "100 * 100 = 10000 73 * 116 = 8468 - - - - - - - - - - - 10000 - - - - - - - - - - - 1532 100 - - - - - - - - - - - ? = > 15 % decrease answer : d"
Answer: d
Python program:
a = 16 / 100
b = 1 + a 
c = 27 / 100
d = 1 - c
e = b * d
f = e * 100
g = 100 - f
Problem: 5 , 10 , 13 , 26 , 29 , 58 , 61 , ( . . . . )
Options: a ) 128 , b ) 64 , c ) 122 , d ) 125 , e ) 130
Rationale: "numbers are alternatively multiplied by 2 and increased by 3 5 ã — 2 = 10 10 + 3 = 13 13 ã — 2 = 26 26 + 3 = 29 29 ã — 2 = 58 58 + 3 = 61 61 ã — 2 = 122 answer c"
Answer: c
Python program:
a = negate - (
Problem: in a class , 7 students like to play basketball and 8 like to play cricket . 5 students like to play on both basketball and cricket . how many students like to play basketball or cricket or both ?
Options: a ) 10 , 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 - 5 = 10 a )
Answer: a
Python program:
a = 7 + 8 
b = a - 5
Problem: a library has an average of 175 visitors on sundays and 75 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :
Options: a ) 80 , b ) 90 , c ) 100 , d ) 110 , e ) 120
Rationale: "explanation : since the month begins with a sunday , so there will be five sundays in the month , required average = ( 165 * 5 + 75 * 25 ) / 30 = 2700 / 30 = 90 answer : b ) 90"
Answer: b
Python program:
a = 3 + 4 
b = 30 / a
c = math.floor(b)
d = c + 1 
e = d * 175
f = 3 + 4 
g = 30 / f
h = math.floor(g)
i = h + 1 
j = 30 - i
k = j * 75
l = e + k 
m = l / 30
Problem: if { x } is the product of all even integers from 1 to x inclusive , what is the greatest prime factor of { 26 } + { 24 } ?
Options: a ) 23 , b ) 20 , c ) 27 , d ) 5 , e ) 2
Rationale: "soln : { 26 } + { 24 } = 26 * { 24 } + { 24 } = 27 * { 24 } answer : c"
Answer: c
Python program:
a = 26 + 24 
b = a / 2
c = 1 * 2
d = b + c
Problem: in a mixed college 160 students are there in one class . out of this 160 students 3 / 8 students are girls . how many boys are there ?
Options: a ) a ) 40 , b ) b ) 60 , c ) c ) 80 , d ) d ) 100 , e ) e ) 140
Rationale: "total number of students : 160 total girls : 160 * 3 / 8 = 60 total boys : 160 - 60 = 100 answer is d"
Answer: d
Python program:
a = 160 / 8
b = a * 3
Problem: a beats b by 50 m in a race of 500 m , then b beats by c by 25 m in a race of 500 m . find the distance by which a beats c in a race of 400 ?
Options: a ) 55 m , b ) 56 m , c ) 57 m , d ) 58 m , e ) 59 m
Rationale: a beats b in 500 m race by 50 m so , for every 10 m race a beat b by 1 m . . so , in 400 m race a beat b by 40 m in a case of b & c , b beats c by 25 m in 500 m race . . so , b beats c by 1 m in 20 m race now , in a 400 m race b beats c by 18 m . . in a 400 m race , a beats b by 40 m & b beats c by 18 m . . so , a beats c by 58 m answer : d
Answer: d
Python program:
a = 500 - 25
b = a / 500
c = 500 - 50
d = b * c
e = d / 500
f = e * 400
g = 400 - f
Problem: a fellow borrowed a certain sum of money at 4 % per annum at simple interest and in 4 years the interest amounted to rs . 1260 less than the sum lent . what was the sum lent ?
Options: a ) 1050 , b ) 1220 , c ) 1500 , d ) 1060 , e ) 1110
Rationale: "p - 1260 = ( p * 4 * 4 ) / 100 p = 1500 answer : c"
Answer: c
Python program:
a = 4 * 4
b = a / 100
c = 1 - b
d = 1260 / c