euclaise/mathqa_programs huggingface dataset:
Problem: what is the sum of the multiples of 5 from 80 to 140 , inclusive ?
Options: a ) 560 , b ) 780 , c ) 990 , d ) 1008 , e ) 1200
Rationale: "the formula we want to use in this type of problem is this : average * total numbers = sum first , find the average by taking the sum of the f + l number and divide it by 2 : a = ( f + l ) / 2 second , find the total numbers in our range by dividing our f and l numbers by 5 and add 1 . ( 140 / 5 ) - ( 80 / 5 ) + 1 multiply these together so what we show average * total numbers = sum ( 80 + 140 ) / 2 * ( 140 / 5 ) - ( 80 / 5 ) + 1 = sum 110 * 9 = 990 c"
Answer: c
Python program:
a = 140 - 3
b = 80 + 2 
c = a + b 
d = c / 2
e = 140 - 3
f = 80 + 2 
g = e - f
h = g / 5
i = h + 1 
j = d * i
Problem: a rectangular field is to be fenced on three sides leaving a side of 30 feet uncovered . if the area of the field is 720 sq . feet , how many feet of fencing will be required ?
Options: a ) 78 , b ) 40 , c ) 68 , d ) 88 , e ) none
Rationale: "explanation we have : l = 30 ft and lb = 720 sq . ft . so , b = 24 ft . length of fencing = ( l + 2 b ) = ( 30 + 48 ) ft = 78 ft . answer a"
Answer: a
Python program:
a = 720 / 30
b = a * 2
c = b + 30
Problem: jack and jill are marathon runners . jack can finish a marathon ( 42 km ) in 5 hours and jill can run a marathon in 4.2 hours . what is the ratio of their average running speed ? ( jack : jill )
Options: a ) 14 / 15 , b ) 15 / 14 , c ) 4 / 5 , d ) 21 / 25 , e ) can not be determined
Rationale: "average speed of jack = distance / time = 42 / 5 average speed of jill = 42 / ( 4.2 ) = 10 ratio of average speed of jack to jill = ( 42 / 5 ) / 10 = 42 / 50 = 21 / 25 answer d"
Answer: d
Python program:
a = 42 / 5
b = 42 / 4
c = a / b
Problem: a bottle contains a certain solution . in the bottled solution , the ratio of water to soap is 3 : 2 , and the ratio of soap to salt is three times this ratio . the solution is poured into an open container , and after some time , the ratio of water to soap in the open container is halved by water evaporation . at that time , what is the ratio of water to salt in the solution ?
Options: a ) 1 : 1 , b ) 2 : 3 , c ) 3 : 2 , d ) 9 : 4 , e ) 27 : 8
Rationale: "water : soap = 3 : 2 soap : salt = 9 : 2 = > for 9 soap , salt = 2 = > for 2 soap , salt = ( 2 / 9 ) * 2 = 4 / 9 so , water : soap : salt = 3 : 2 : 4 / 9 = 27 : 18 : 4 after open container , water : soap : salt = 13.5 : 18 : 4 so , water : salt = 13.5 : 4 = 27 : 8 answer : e"
Answer: e
Python program:
a = 2 * 3
b = a * 3
c = 2 * 2
d = c * 2
e = b / d
Problem: at a party , 13 guests brought wine and 14 guests brought beer . if exactly 11 guests brought only one of the two types of drinks , how many guests brought both types of drinks ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 14
Rationale: say x guests brought both drinks . ( 13 - x ) + ( 14 - x ) = 11 - - > x = 8 . answer : d .
Answer: d
Python program:
a = 13 + 14 
b = a - 11
c = b / 2
Problem: a sum of money is put out at compound interest for 2 years at 20 % . it would earn rs . 482 more if the interest were paid half - yearly . calculate the sum .
Options: a ) 2878 , b ) 279 , c ) 279 , d ) 482 , e ) 661
Rationale: p ( 11 / 10 ) 4 - p ( 6 / 5 ) 2 = 482 p = 2000 answer : d
Answer: d
Python program:
a = 20 + 1 
b = 20 + 1 
c = a * b
d = 20 + 1 
e = c + d
Problem: a broker invested her own money in the stock market . during the first year , she increased her stock market wealth by 75 percent . in the second year , largely as a result of a slump in the stock market , she suffered a 30 percent decrease in the value of her stock investments . what was the net increase or decrease on her overall stock investment wealth by the end of the second year ?
Options: a ) − 5 % , b ) 5 % , c ) 15 % , d ) 20 % , e ) 22.5 %
Rationale: "the actual answer is obtained by multiplying 175 % by 70 % and subtracting 100 % from this total . that is : 175 % × 70 % = 122.5 % ; 122.5 % − 100 % = 122.5 % . answer : e"
Answer: e
Python program:
a = 75 / 100
b = 1 + a 
c = 30 / 100
d = 1 - c
e = b * d
f = e - 1
g = f * 100
Problem: farm tax is levied on the 50 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . william . mr . william paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :
Options: a ) 15 % , b ) 25 % , c ) 0.125 % , d ) 0.2083 % , e ) none
Rationale: "this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 3840 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 50 ) = 25 % the correct answer is ( b ) ."
Answer: b
Python program:
a = 480 / 3840
b = a * 100
c = b * 100
d = c / 50
Problem: the total number of digits used in numbering the pages of a book having 266 pages is
Options: a ) 732 , b ) 990 , c ) 109 , d ) 130 , e ) 690
Rationale: "total number of digits = ( no . of digits in 1 - digit page nos . + no . of digits in 2 - digit page nos . + no . of digits in 3 - digit page nos . ) = ( 1 x 9 + 2 x 90 + 3 x 167 ) = ( 9 + 180 + 501 ) = 690 . answer : e"
Answer: e
Python program:
a = 266 * 3
b = 100 - 1
c = a - b
d = 10 - 1
e = c - d
Problem: the ratio of incomes of two person p 1 and p 2 is 5 : 4 and the ratio of their expenditures is 3 : 2 . if at the end of the year , each saves rs . 1400 , then what is the income of p 1 ?
Options: a ) s . 800 , b ) s . 2400 , c ) s . 4000 , d ) s . 3500 , e ) s . 4200
Rationale: "let the income of p 1 and p 2 be rs . 5 x and rs . 4 x respectively and let their expenditures be rs . 3 y and 2 y respectively . then , 5 x – 3 y = 1400 … ( i ) and 4 x – 2 y = 1400 … … . . ( ii ) on multiplying ( i ) by 2 , ( ii ) by 3 and subtracting , we get : 2 x = 1400 - > x = 700 p 1 ’ s income = rs 5 * 700 = rs . 3500 answer : d"
Answer: d
Python program:
a = 1400 / 2
b = a * 3
c = b - 1400
d = c * 5
Problem: the value of a machine depreciates at the rate of 10 % every year . it was purchased 3 years ago . if its present value is rs 8,748 , its purchase price was ?
Options: a ) rs 16,000 , b ) rs 18,000 , c ) rs 12,000 , d ) rs 14,000 , e ) none of these
Rationale: "we have p = 8748 , r = - 10 and n = 3 therefore , the purchase price of the machine = p / ( 1 + ( r / 100 ) ) n = 8748 / ( 1 - ( 10 / 100 ) ) 3 = 8748 x ( 100 / 90 ) x ( 100 / 90 ) x ( 100 / 90 ) = 12,000 . answer : c"
Answer: c
Python program:
a = 10 / 100
b = a * 3
c = 1 - b
d = 8 / 748
Problem: a new home buyer pays 4 % annual interest on her first mortgage and 9 % annual interest on her second mortgage . if she borrowed a total of $ 340,000 , 80 % of which was in the first mortgage , what is her approximate monthly interest payment ?
Options: a ) $ 1,416 , b ) $ 1,733 , c ) $ 3,466 , d ) $ 13,333 , e ) $ 20,796
Rationale: "0.04 x + 0.09 y = 340000 [ 1 ] 0.04 x = 0.80 * 340000 = 272000 [ 2 ] 272000 + 0.09 y = 340000 - - > 0.09 y = 64000 [ 3 ] 272000 / 12 = 22666.67 [ 4 ] 64000 / 12 = 5666.67 [ 5 ] adding [ 4,5 ] we get : 28333.33 [ 6 ] dividing [ 6 ] / 2 to get an average we get 1.416 , ans a"
Answer: a
Python program:
a = 4 * 2
b = 9 - a
Problem: a mixture of 150 liters of wine and water contains 10 % water . how much more water should be added so that water becomes 25 % of the new mixture ?
Options: a ) 10 , b ) 30 , c ) 20 , d ) 15 , e ) 16
Rationale: "number of liters of water in 150 liters of the mixture = 10 % of 150 = 10 / 100 * 150 = 15 liters . p liters of water added to the mixture to make water 25 % of the new mixture . total amount of water becomes ( 15 + p ) and total volume of mixture is ( 150 + p ) . ( 15 + p ) = 25 / 100 * ( 150 + p ) 60 + 4 p = 150 + p p = 30 liters . answer : b"
Answer: b
Python program:
a = 25 / 100
b = a * 150
c = 10 / 100
d = c * 150
e = b - d
f = 25 / 100
g = 1 - f
h = e / g
Problem: what is the difference between the local values of 8 in the number 58408 ?
Options: a ) 2992 , b ) 7992 , c ) 2877 , d ) 2077 , e ) 6229
Rationale: explanation : 8000 â € “ 8 = 7992 answer : b
Answer: b
Python program:
a = 8 * 1000
b = a - 8
Problem: three numbers are in the ratio of 2 : 3 : 4 . if the sum of the squares of the extremes is 180 , then the middle number is :
Options: a ) 6 , b ) 12 , c ) 15 , d ) 9 , e ) 7
Rationale: "number be = 2 x , 3 x , 4 x , ( 2 x ) 2 + ( 4 x ) 2 = 180 20 x = 180 ⇒ x = 9 ⇒ x = 3 , midline number = 3 × 3 = 9 answer : d"
Answer: d
Python program:
a = 2 * 4
Problem: the area of a parallelogram is 147 sq m and its base is thrice the corresponding height . then the length of the base is ?
Options: a ) 14 m , b ) 29 m , c ) 49 m , d ) 7 , e ) none
Rationale: b * h = 147 b * h = 147 = > b ^ 2 = 49 m . b = 7 answer : ( d )
Answer: d
Python program:
a = 147 / 2
b = math.sqrt(a)
Problem: a contractor undertakes to complete the construction of a tunnel 720 meters long in 240 days and employs 60 men for the purpose . after 120 days , he finds that only 240 meters of the tunnel is complete . how many more men should be employ in order to complete the work in time ?
Options: a ) 22 , b ) 27 , c ) 60 , d ) 88 , e ) 12
Rationale: in 120 days , only 240 m of the tunnel is constructed by 60 men . the remaining 120 days , 480 m of the tunnel can be constructed by 120 men . additional number of men required = 120 - 60 = 60 men . answer : b
Answer: b
Python program:
a = 120 - 60
Problem: a certain automobile company ’ s best - selling model is the speedster . the speedster , like all of their other models , comes in coupe and convertible styles . 2 / 3 of the current inventory is speedsters , of which 4 / 5 are convertibles . if there are 50 vehicles that are not speedsters , how many speedster convertibles are there ?
Options: a ) 30 , b ) 48 , c ) 60 , d ) 80 , e ) 90
Rationale: "total vehicle = 2 / 3 of speedster + 1 / 3 of others . speedster convertibles = 2 / 3 total vehicle * 4 / 5 given : 1 / 3 constitutes 50 vehicles . hence 2 / 3 constitutes 100 speedster convertibls = 100 * 4 / 5 = 80 d"
Answer: d
Python program:
a = 2 / 3
b = 1 - a
c = 50 / b
d = 2 / 3
e = c * d
f = 4 / 5
g = e * f
Problem: if there are 4 peanuts in a box and mary puts 12 more peanuts inside , how many peanuts are in the box ?
Options: a ) 8 , b ) 16 , c ) 10 , d ) 11 , e ) 12
Rationale: "12 + 4 = 16 correct answer is b ) 16"
Answer: b
Python program:
a = 4 + 12
Problem: 4 dice are thrown and the sum of the numbers noted is 10 . find the probability that all the numbers lie between 2 and 5 ( both inclusive ) ?
Options: a ) 11 / 79 , b ) 10 / 79 , c ) 12 / 79 , d ) 13 / 79 , e ) 14 / 79
Rationale: sum of numbers noted on 4 dice ( with six faces ) to be 10 will include combinations : ( 1,1 , 2,6 ) ( 1,1 , 3,5 ) ( 1,1 , 4,4 ) ( 1,1 , 5,3 ) ( 1,1 , 6,2 ) ( 1,2 , 1,6 ) ( 1,2 , 2,5 ) ( 1,2 , 3,4 ) ( 1,2 , 4,3 ) ( 1,2 , 5,2 ) ( 1,2 , 6,1 ) ( 1,3 , 1,5 ) ( 1,3 , 2,4 ) ( 1,3 , 3,3 ) ( 1,3 , 4,2 ) ( 1,3 , 5,1 ) ( 1,4 , 1,4 ) ( 1,4 , 2,3 ) ( 1,4 , 3,2 ) ( 1,4 , 4,1 ) ( 1,5 , 1,3 ) ( 1,5 , 2,2 ) ( 1,5 , 3,1 ) ( 1,6 , 1,2 ) ( 1,6 , 2,1 ) ( 2,1 , 1,6 ) ( 2,1 , 2,5 ) ( 2,1 , 3,4 ) ( 2,1 , 4,3 ) ( 2,1 , 5,2 ) ( 2,1 , 6,1 ) ( 2,2 , 1,5 ) ( 2,2 , 2,4 ) ( 2,2 , 3,3 ) ( 2,2 , 4,2 ) ( 2,2 , 5,1 ) ( 2,3 , 1,4 ) ( 2,3 , 2,3 ) ( 2,3 , 3,2 ) ( 2,3 , 4,1 ) ( 2,4 , 1,3 ) ( 2,4 , 2,2 ) ( 2,4 , 3,1 ) ( 2,5 , 1,2 ) ( 2,5 , 2,1 ) ( 2,6 , 1,1 ) ( 3,1 , 1,5 ) ( 3,1 , 2,4 ) ( 3,1 , 3,3 ) ( 3,1 , 4,2 ) ( 3,1 , 5,1 ) ( 3,2 , 1,4 ) ( 3,2 , 2,3 ) ( 3,2 , 3,2 ) ( 3,2 , 4,1 ) ( 3,3 , 1,3 ) ( 3,3 , 2,2 ) ( 3,3 , 3,1 ) ( 3,4 , 1,2 ) ( 3,4 , 2,1 ) ( 3,5 , 1,1 ) ( 4,1 , 1,4 ) ( 4,1 , 2,3 ) ( 4,1 , 3,2 ) ( 4,1 , 4,1 ) ( 4,2 , 1,3 ) ( 4,2 , 2,2 ) ( 4,2 , 3,1 ) ( 4,3 , 1,2 ) ( 4,3 , 2,1 ) ( 4,4 , 1,1 ) ( 5,1 , 1,3 ) ( 5,1 , 2,2 ) ( 5,1 , 3,1 ) ( 5,2 , 1,2 ) ( 5,2 , 2,1 ) ( 5,3 , 1,1 ) ( 6,1 , 1,2 ) ( 6,1 , 2,1 ) - - - - - - - total 79 combinations with all the numbers lie between 2 and 5 are ( 2,2 , 2,4 ) ( 2,2 , 3,3 ) ( 2,2 , 4,2 ) ( 2,3 , 2,3 ) ( 2,3 , 3,2 ) ( 2,4 , 2,2 ) ( 3,2 , 2,3 ) ( 3,2 , 3,2 ) ( 3,3 , 2,2 ) ( 4,2 , 2,2 ) - - - - - - total 10 so probability = 10 / 79 answer : b
Answer: b
Python program:
a = 2 * 4
b = a * 10
c = b - 1
d = 10 / c
Problem: a truck covers a distance of 200 metres in 1 minute whereas a bus covers a distance of 100 kms in 50 minutes . the ratio of their speeds is ?
Options: a ) 2 : 3 , b ) ratio 1 : 5 , c ) ratio 1 : 10 , d ) ratio 9 : 13 , e ) ratio 7 : 15
Rationale: "ratio of speeds = ( 200 / 60 ) 18 / 5 : 60 * 100 / 50 = 12 : 120 = 1 : 10 answer is c"
Answer: c
Python program:
a = 100 / 50
b = a * 1000
c = 200 / b
Problem: a reduction of 30 % in the price of oil enables a house wife to obtain 9 kgs more for rs . 900 , what is the reduced price for kg ?
Options: a ) 72 , b ) 27 , c ) 40 , d ) 30 , e ) 20
Rationale: "900 * ( 30 / 100 ) = 270 - - - - 9 ? - - - - 1 = > rs . 30 answer : d"
Answer: d
Python program:
a = 900 * 30
b = a / 100
c = b / 9
Problem: in how many ways 6 boys and 4 girls can be seated in a row so that they are alternative ?
Options: a ) 14420 , b ) 12620 , c ) 17280 , d ) 21200 , e ) 24560
Rationale: "6 boys can be seated in 6 ! 4 girls can be seated in 4 ! required number = 6 ! 4 ! = 17280 answer is c"
Answer: c
Python program:
a = math.factorial(6)
b = math.factorial(4)
c = a * b
Problem: total dinning bill of 7 people was $ 139.00 and 10 % tip divided the bill evenly ? what is the bill amount each person shared .
Options: a ) 21.84 , b ) 22.84 , c ) 23.84 , d ) 24.84 , e ) 25.84
Rationale: "dinner bill of 7 person = 139 + 10 % tip so , 10 % of 139 = ( 139 * 10 ) / 100 = 13.9 so , the actual total amount = 139 + 13.9 = $ 152.9 so per head bill = 152.9 / 7 = $ 21.84 answer : a"
Answer: a
Python program:
a = 1 / 10
b = a + 1 
c = 139 * 0
d = c / 7
Problem: city x has a population 3 times as great as the population of city y , which has a population twice as great as the population of city z . what is the ratio of the population of city x to the population of city z ?
Options: a ) 1 : 8 , b ) 1 : 4 , c ) 2 : 1 , d ) 6 : 1 , e ) 8 : 1
Rationale: "x = 3 y , y = 2 * z x : y , y : z 3 : 1 , 2 : 1 6 : 2 , 2 : 1 so , x : z = 6 : 1 ( d )"
Answer: d
Python program:
a = 3 * 2
Problem: what is the dividend ? the divisor is 800 , the quotient is 594 , and the remainder is - 968 .
Options: a ) 6623 , b ) 43036 , c ) 51515 , d ) 474232 , e ) 2025
Rationale: dividend = ? ? = d * q + r ? = 800 * 594 + - 968 ? = 475,200 + - 968 ? = 474,232
Answer: d
Python program:
a = 800 * 594
b = a - 968
Problem: working independently , tina can do a certain job in 12 hours . working independently , ann can do the same job in 9 hours . if tina works independently at the job for 8 hours and then ann works independently , how many hours will it take ann to complete the remainder of the jobs ?
Options: a ) 2 / 3 , b ) 3 / 4 , c ) 1 , d ) 2 , e ) 3
Rationale: work done by tina in 1 hr = 1 / 12 work done by tina in 8 hr = 1 / 12 * 8 which is 2 / 3 now , the remaining work is 1 / 3 which is completed by ann in 1 / 3 * 9 which is 3 hr answer : e
Answer: e
Python program:
a = 12 - 8
b = 12 / a
c = 9 / b
Problem: sum of 24 odd numbers is ?
Options: a ) 572 , b ) 573 , c ) 574 , d ) 575 , e ) 576
Rationale: "sum of 1 st n odd no . s = 1 + 3 + 5 + 7 + . . . = n ^ 2 so , sum of 1 st 24 odd numbers = 24 ^ 2 = 576 answer : e"
Answer: e
Python program:
a = 24 * 2
b = 24 / 2
c = a * b
Problem: set x consists of all two - digit primes and set y consists of all positive odd multiples of 9 less than 100 . if the two sets are combined into one , what will be the range of the new set ?
Options: a ) 84 , b ) 89 , c ) 90 , d ) 92 , e ) 95
Rationale: "set x = { 11 , 13 , 17 , . . . . . . . . . . . . . , 83 , 89 , 97 } set y = { 9 , 27 , 45 , . . . . . . . . . . . . . . . , 63 , 81 , 99 } combining two sets , say set z set z = { 9 , 11 , 13 , 17 , 27 , . . . . . . . . . . . . . . . . . . . , 63 , 81 , 83 , 89 , 97,99 } range = max value - min value range ( z ) = 99 - 9 = 90 oa c is the answer ."
Answer: c
Python program:
a = 100 - 3
b = a - 9
Problem: the duplicate ratio of 6 : 4 is ?
Options: a ) 1 : 2 , b ) 9 : 4 , c ) 1 : 8 , d ) 1 : 18 , e ) 1 : 13
Rationale: "36 ^ 2 : 4 ^ 2 = 36 : 16 = 9 : 4 answer : b"
Answer: b
Python program:
a = 6 ** 2
b = 4 ** 2
c = a / b
Problem: find 4 + 7 + 10 + 13 + 16 + . . . up to 20 terms
Options: a ) 650 , b ) 640 , c ) 630 , d ) 620 , e ) 610
Rationale: a = 4 d = 7 – 4 = 3 sum of first 20 terms , s 20 answer is a
Answer: a
Python program:
a = 20 * 16
b = 13 * 10
c = a + b 
d = 7 * 4
e = 10 - 2
f = d - e
g = 10 * f
h = c + g
Problem: there are 10 slate rocks , 11 pumice rocks , and 4 granite rocks randomly distributed in a certain field . if 2 rocks are chosen at random and without replacement , what is the probability that both rocks will be slate rocks ?
Options: a ) 3 / 20 , b ) 5 / 26 , c ) 7 / 34 , d ) 9 / 37 , e ) 11 / 49
Rationale: "10 / 25 * 9 / 24 = 3 / 20 the answer is a ."
Answer: a
Python program:
a = 10 + 11 
b = a + 4 
c = 10 / b
d = 10 - 1
e = 10 + 11 
f = e + 4 
g = f - 1
h = d / g
i = c * h
Problem: if 100 % of j is equal to 25 % of k , 150 % of k is equal to 50 % of l , and 125 % of l is equal to 75 % of m , then 20 % of m is equal to what percent of 200 % of j ?
Options: a ) 0.35 , b ) 3.5 , c ) 350 , d ) 35 , e ) 3500
Rationale: "imo answer should be 350 . . . consider j = 10 , then k = 50 , l = 150 and m = 350 . . . . 20 % of 350 , comes out to be 70 . . . . 200 % of 10 is 20 . . . . ( 70 * 100 ) / 20 = 350 . . . . ans : c"
Answer: c
Python program:
a = 100 * 150
b = a * 125
c = 25 * 50
d = c * 75
e = b / d
f = e * 20
g = f / 200
h = g * 100
Problem: a room of 5 m 44 cm long and 3 m 74 cm broad is to be paved with squre tiles . find the least number of squre tiles required to cover the floor .
Options: a ) 233 , b ) 877 , c ) 279 , d ) 176 , e ) 291
Rationale: "explanation : area of the room = 544 * 374 sq cm size of largest square tile = h . c . f of 544 cm and 374 cm = 34 cm area of 1 tile = 34 * 34 sq cm no . of tiles required = ( 544 * 374 ) / ( 34 * 34 ) = 176 answer : d ) 176"
Answer: d
Python program:
a = 5 * 100
b = a + 44 
c = 3 * 100
d = c + 74 
e = b * d
f = 5 * 100
g = f + 44 
h = 2 ** 4
i = g / h
j = i ** 2
k = e / j
Problem: 5 % of men have unlisted phone numbers and 4 % of women have unlisted phone numbers . population ratio of men : women in the city of gpuzzles is 4 : 3 . if we select randomly 100 people from the phone directory , can you tell us how many people selected will definitely have unlisted phone numbers ?
Options: a ) 0 % , b ) 1 % , c ) 2 % , d ) 3 % , e ) 4 %
Rationale: solution : 0 % explanation : in the number is in the phone directory , it means the number is listed and therefore if we pick any number from phone directory than number is surely listed . answer a
Answer: a
Python program:
a = const_0_25 * 100
b = 4 / 100
c = a * b
d = 3 / 4
e = d * 100
f = 5 / 100
g = e * f
h = c + g
Problem: how many different values of positive integer x , for which | x + 7 | < x , are there ?
Options: a ) 0 , b ) 2 , c ) 3 , d ) 8 , e ) 16
Rationale: "answer a i opted to put the random value option . i used 0 , 7 , - 7 and the the extreme of 30 and - 30 . . i was able to solve it in 1 : 09 b"
Answer: b
Python program:
a = 7 + 7
Problem: you buy a piece of land with an area of â ˆ š 100 , how long is one side of the land plot ?
Options: a ) 28 , b ) 29 , c ) 10 , d ) 31 , e ) 32
Rationale: "try filling the numbers into the answer y x y = find the closest to 100 . answer c"
Answer: c
Python program:
a = math.sqrt(100)
Problem: find the cost of fencing around a circular field of diameter 14 m at the rate of rs . 2.50 a meter ?
Options: a ) 288 , b ) 110 , c ) 772 , d ) 592 , e ) 261
Rationale: "2 * 22 / 7 * 7 = 44 44 * 2.5 = rs . 110 answer : b"
Answer: b
Python program:
a = 14 / 2
b = circumface * (
Problem: a farmer used 1,034 acres of land for beans , wheat , and corn in the ratio of 5 : 2 : 4 , respectively . how many y acres were used for corn ?
Options: a ) 188 , b ) 258 , c ) 376 , d ) 470 , e ) 517
Rationale: "consider 5 x acres of land used for bean consider 2 x acres of land used for wheat consider 4 x acres of land used for corn total given is 1034 acres 11 x = 1034 x = 94 land used for corn y = 4 * 94 = 376 correct option - c"
Answer: c
Python program:
a = 1000 * 1
b = 10 * 3
c = b + 4 
d = a + c 
e = 5 + 2 
f = e + 4 
g = d / f
h = g * 4
Problem: 10 play kabadi , 15 play kho kho only , 5 play both gmaes . then how many in total ?
Options: a ) 25 , b ) 35 , c ) 38 , d ) 40 , e ) 45
Rationale: "10 play kabadi = > n ( a ) = 10 , 5 play both gmaes . = > n ( anb ) = 5 15 play kho kho only , = > n ( b ) = n ( b only ) + n ( anb ) = 15 + 5 = 20 total = > n ( aub ) = n ( a ) + n ( b ) - n ( anb ) = 10 + 20 - 5 = 25 answer : a"
Answer: a
Python program:
a = 15 + 5 
b = 10 + a 
c = b - 5
Problem: a tailor trims 7 feet from opposite edges of a square piece of cloth , and 5 feet from the other two edges . if 45 square feet of cloth remain , what was the length of a side of the original piece of cloth ?
Options: a ) 13 , b ) 15 , c ) 17 , d ) 19 , e ) 21
Rationale: "let the original side of the square be x . ( x - 14 ) * ( x - 10 ) = 45 = 5 * 9 x = 19 the answer is d ."
Answer: d
Python program:
a = 2 * 7
b = 2 * 3
c = a + b 
d = 2 * 5
e = 2 * 7
f = d * e
g = 45 - f
h = 7 * g
i = 2 * 7
j = 2 * 5
k = i + j 
l = k ** 2
m = h + l 
n = math.sqrt(m)
o = c + n 
p = o / 2
Problem: $ 500 will become $ 1000 in 5 years find the rate of interest ?
Options: a ) 10 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 50 %
Rationale: si = simple interest = a - p = 1000 - 500 = $ 500 r = 100 si / pt = 100 * 500 / 500 * 5 = 20 % answer is b
Answer: b
Python program:
a = 1000 - 500
b = 5 / 100
c = 500 * b
d = a / c
Problem: ( ( - 1.9 ) ( 0.6 ) – ( 2.6 ) ( 1.2 ) ) / 3.0 = ?
Options: a ) - 0.71 , b ) 1.0 , c ) 1.07 , d ) - 1.42 , e ) 2.71
Rationale: "dove straight into calculation ( ( - 1.9 ) ( 0.6 ) – ( 2.6 ) ( 1.2 ) ) / 3.0 = - 1.42 answer d"
Answer: d
Python program:
a = 1 * 9
b = negate - (
c = 2 * 6
d = b / c
Problem: the number 523 rbc is divisible by 7 , 89 . then what is the value of r * b * c
Options: a ) 504 , b ) 532 , c ) 210 , d ) 180 , e ) 280
Rationale: lcm of 7 , 8 and 9 is 504 , thus 523 rbc must be divisible by 504 . 523 rbc = 523000 + rbc 523000 divided by 504 gives a remainder of 352 . hence , 352 + rbc = k * 504 . k = 1 rbc = 152 - - > r * b * c = 10 k = 2 rbc = 656 - - > r * b * c = 180 as rbc is three digit number k can not be more than 2 . two answers ? well only one is listed in answer choices , so d . answer : d .
Answer: d
Python program:
a = 3 * 2
b = 2 + 3 
c = a * b
d = 3 * 2
e = c * d
Problem: a man buys rs . 20 shares paying 9 % dividend . the man wants to have an interest of 12 % on his money . what is the market value of each share ?
Options: a ) rs . 12 , b ) rs . 18 , c ) rs . 15 , d ) rs . 21 , e ) rs . 25
Rationale: "explanation : face value of each share = rs . 20 dividend per share = 9 % of 20 = 9 × 20 / 100 = 9 / 5 he needs to have an interest of 12 % on his money ie , money paid for a share 9 × 12 / 100 = 9 / 5 money paid for a share = 9 / 5 × 100 / 12 = 15 ie , market value of the share = rs . 15 answer : option c"
Answer: c
Python program:
a = 100 / 12
b = 9 / 100
c = b * 20
d = a * c
Problem: what is the smallest no . which must be added to 27452 so as to obtain a sum which is divisible by 9 ?
Options: a ) 7 , b ) 2 , c ) 9 , d ) 4 , e ) 6
Rationale: "for 27452 , 2 + 7 + 4 + 5 + 2 = 20 . 7 must be added to 27452 to make it divisible by 9 . now , 2 + 7 + 4 + 5 + 9 = 27 = > 27 is a multiple of 9 and hence 27452 is also divisible by 9 a"
Answer: a
Python program:
a = 27452 * 9
b = a / 27452
Problem: find the average of first 4 multiples of 5 ?
Options: a ) 10 , b ) 15 , c ) 12.5 , d ) 13 , e ) 21
Rationale: "average = ( 5 + 10 + 15 + 20 ) / 4 = 12.5 answer is c"
Answer: c
Python program:
a = 4 + 1 
b = 4 + 1 
c = b + 2 
d = a + c 
e = 5 - 4
f = 5 - 2
g = e + f 
h = d + g 
i = h / 4
Problem: the sale price sarees listed for rs . 400 after successive discount is 10 % and 8 % is ?
Options: a ) 338 , b ) 277 , c ) 331.2 , d ) 882 , e ) 212
Rationale: "400 * ( 90 / 100 ) * ( 92 / 100 ) = 331.2 answer : c"
Answer: c
Python program:
a = 400 * 10
b = a / 100
c = 400 - b
d = 400 * 10
e = d / 100
f = 400 - e
g = f * 8
h = g / 100
i = c - h