euclaise/mathqa_programs huggingface dataset:
Problem: simple interest on a certain sum of money for 3 years at 8 % per annum is half the compound interest on $ 4000 for 2 years at 10 % per annum . the sum placed on simple interest is :
Options: a ) $ 1750 , b ) $ 2250 , c ) $ 1250 , d ) $ 1500 , e ) $ 2000
Rationale: "compound interest = ( 4000 x ( 1 + 10 / 100 ) ^ 2 - 4000 ) = 4000 x 11 / 10 x 11 / 10 - 4000 = 840 therefore the sum is 420 x 100 / ( 3 x 8 ) = 1750 . answer a ) $ 1750"
Answer: a
Python program:
a = 4000 * 10
b = a / 100
c = 4000 * 10
d = c / 100
e = 4000 + d 
f = e * 10
g = f / 100
h = b + g 
i = h / 2
j = i / 3
k = j * 100
l = k / 8
Problem: in one hour , a boat goes 11 km along the stream and 3 km against the stream . the sped of the boat in still water ( in km / hr ) is :
Options: a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 10
Rationale: "solution speed in still water = 1 / 2 ( 11 + 3 ) km / hr = 7 kmph . answer c"
Answer: c
Python program:
a = 11 + 3 
b = a / 2
Problem: if a + b = − 6 , and a = 10 / b , what is the value of a ^ 2 + b ^ 2 ?
Options: a ) 22 , b ) 24 , c ) 16 , d ) 18 , e ) 20
Rationale: a ^ 2 + b ^ 2 should make you think of these formulas : ( a + b ) ( a + b ) = a ^ 2 + b ^ 2 + 2 ab we already know ( a + b ) = - 6 and a * b = 10 ( a + b ) ( a + b ) = ( - 6 ) ( - 6 ) = a ^ 2 + b ^ 2 + 2 * ( 10 ) a ^ 2 + b ^ 2 = 36 - 20 = 16 answer : c
Answer: c
Python program:
a = 6 ** 2
b = 2 * 10
c = a - b
Problem: a professional basketball player just signed a contract that has a 10 % raise in base salary from last year to this year . the contract also has provisions for a performance bonus of up to $ 10000 . if he earns the maximum performance bonus , his new effective salary will be a 10.5 % raise over last year ' s total salary , when he received no performance bonus . assuming he earns the full performance bonus , what will be his new salary ?
Options: a ) 2010000 , b ) 2110000 , c ) 2150000 , d ) 2200000 , e ) 2210000
Rationale: let x = old salary then ( 1 + . 10 ) * x + 10000 = ( 1 + . 105 ) * x i . e . new base salary + 10000 = effective new salary thus 1.1 * x + 10000 = 1.105 * x 10000 = . 005 * x 2000000 = x thus the new effective salary is 1.105 * 2000000 = 2210000 e
Answer: e
Python program:
a = 4 / 2
Problem: how long does a train 110 m long running at the speed of 72 km / hr takes to cross a bridge 175 m length ?
Options: a ) 12.9 sec , b ) 12.1 sec , c ) 17.9 sec , d ) 16.8 sec , e ) 14.25 sec
Rationale: "speed = 72 * 5 / 18 = 20 m / sec total distance covered = 110 + 175 = 285 m . required time = 285 / 20 = 14.25 sec . answer : e"
Answer: e
Python program:
a = 110 + 175 
b = 72 * const_0_2778
c = a / b
Problem: find the length of the wire required to go 15 times round a square field containing 69696 m 2 .
Options: a ) 15840 , b ) 15848 , c ) 15828 , d ) 27892 , e ) 22892
Rationale: "a 2 = 69696 = > a = 264 4 a = 1056 1056 * 15 = 15840 answer : a"
Answer: a
Python program:
a = square_perimeter * (
Problem: 5 n + 2 > 17 and 7 n - 5 < 44 ; n must be between which numbers ?
Options: a ) 1 and 8 , b ) 2 and 6 , c ) 0 and 9 , d ) 3 and 7 , e ) 2 and 9
Rationale: "5 n > 15 - - > n > 3 7 n < 49 - - > n < 7 3 < n < 7 answer : d"
Answer: d
Python program:
a = 2 * 10
b = 44 + 5 
c = b / 7
d = a + c
Problem: find the average of first 6 multiples of 5 ?
Options: a ) 10 , b ) 15 , c ) 12.5 , d ) 13 , e ) 17.5
Rationale: "average = ( 5 + 10 + 15 + 20 + 25 + 30 ) / 6 = 17.5 answer is e"
Answer: e
Python program:
a = 6 + 1 
b = 6 + 1 
c = b + 2 
d = a + c 
e = 5 - 6
f = 5 - 2
g = e + f 
h = d + g 
i = h / 6
Problem: a large box contains 15 small boxes and each small box contains 20 chocolate bars . how many chocolate bars are in the large box ?
Options: a ) a ) 220 , b ) b ) 490 , c ) c ) 380 , d ) d ) 300 , e ) e ) 690
Rationale: "the only thing you have to do is a simple multiply we have : 15 * 20 = 300 correct answer is : d ) 300"
Answer: d
Python program:
a = 15 * 20
Problem: the current of a stream runs at the rate of 4 kmph . a boat goes 10 km and back to the starting point in 2 hours , then find the speed of the boat in still water ?
Options: a ) a ) 7 , b ) b ) 2 , c ) c ) 8.9 , d ) d ) 11.4 , e ) e ) 3
Rationale: "s = 4 m = x ds = x + 4 us = x - 4 10 / ( x + 4 ) + 10 / ( x - 4 ) = 2 x = 11.4 answer : d"
Answer: d
Python program:
a = 4 ** 2
b = a / 2
Problem: a retail appliance store priced a video recorder at 20 percent above the wholesale cost of $ 200 . if a store employee applied the 5 percent employee discount to the retail price to buy the recorder , how much did the employee pay for the recorder ?
Options: a ) $ 198 , b ) $ 228 , c ) $ 220 , d ) $ 230 , e ) $ 240
Rationale: "wholesale cost of video recorder = 200 $ video recorder was priced at 20 percent above 200 = 240 $ % discount given by store employee = 5 emlpoyee paid = . 95 * 240 = 228 $ answer b"
Answer: b
Python program:
a = 200 / 100
b = a * 20
c = 200 + b 
d = 200 / 100
e = d * 20
f = 200 + e 
g = f / 100
h = g * 5
i = c - h
Problem: if a # b = ab – b + b ^ 2 , then 3 # 6 =
Options: a ) 2 , b ) 8 , c ) 15 , d ) 21 , e ) 48
Rationale: "solution - simply substitute 3 and 6 in equation in the place of a and b respectively . 3 # 6 = 3 * 6 - 6 + 6 ^ 2 = 18 - 6 + 36 = 48 . ans e"
Answer: e
Python program:
a = 3 * 6
b = a - 6
c = 6 ** 2
d = b + c
Problem: a man engaged a servant on a condition that he ' ll pay rs 90 and also give him a bag at the end of the yr . he served for 9 months and was given a turban and rs 65 . so the price of turban is
Options: a ) rs 10 , b ) rs 9 , c ) rs 0 , d ) rs 55 , e ) rs 8
Rationale: let the value of turban = rs x for 1 year = 90 + x for 9 months ( i , e 3 / 4 year ) = 65 + x i , e 1 : ( 90 + x ) : : 3 / 4 : ( 65 + x ) i , e ( 90 + x ) / ( 65 + x ) = 1 / ( 3 / 4 ) 270 + 3 x = 260 + 4 x thus x = 10 answer : a
Answer: a
Python program:
a = 90 / 12
b = a * 10
c = b - 65
Problem: if w is the set of all the integers between 29 and 99 , inclusive , that are either multiples of 3 or multiples of 2 or multiples of both , then w contains how many numbers ?
Options: a ) 26 , b ) 32 , c ) 33 , d ) 34 , e ) 47
Rationale: "multiples of 2 from 29 to 99 = multiples of 2 from 1 to 99 - multiples of 2 from 1 to 28 = [ 99 / 2 ] - [ 28 / 2 ] = 49 - 14 = 35 multiples of 3 from 29 to 99 = multiples of 3 from 1 to 99 - multiples of 3 from 1 to 28 = [ 99 / 3 ] - [ 28 / 3 ] = 33 - 9 = 24 multiples of 2 and 3 bothi . e . 6 from 29 to 99 = multiples of 6 from 1 to 99 - multiples of 6 from 1 to 28 = [ 99 / 6 ] - [ 28 / 6 ] = 16 - 4 = 12 these 8 numbers have been counted twice in both the above calculation while calculating multiples of 2 and 3 i . e . total numbers in w = 35 + 24 - 12 = 47 answer option e"
Answer: e
Python program:
a = 99 - 29
b = a / 3
c = math.floor(b)
d = 99 - 29
e = d / 2
f = c + e 
g = 99 - 29
h = 2 * 3
i = g / h
j = math.floor(i)
k = f - j
Problem: for a certain exam , a score of 86 was 7 standard deviations below mean and a score of 90 was 3 standard deviations above mean . what was the mean score for the exam ?
Options: a ) 86.25 , b ) 84 , c ) 85 , d ) 88.8 , e ) 80
Rationale: "mean - 7 sd = 86 mean + 3 sd = 90 by solving above equations we get , sd ( absolute value ) = 0.4 mean = 88.8 ans . d"
Answer: d
Python program:
a = 86 * 3
b = 90 * 7
c = a + b 
d = 7 + 3 
e = c / d
Problem: in a division , a student took 72 as divisor instead of 36 . his answer was 24 . the correct answer is -
Options: a ) 42 , b ) 32 , c ) 48 , d ) 28 , e ) 38
Rationale: "x / 72 = 24 . x = 24 * 72 . so correct answer would be , ( 24 * 72 ) / 36 = 48 . answer : c"
Answer: c
Python program:
a = 72 * 24
b = a / 36
Problem: a scientist used a unique two - color code to identify each of the test subjects involved in a certain study . if the scientist found that choosing from among 5 colors produced enough color codes to identify all but 6 of the test subjects , how many test subjects were in the study ? ( assume that the order of the colors in the codes does not matter . )
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: 5 c 2 = 10 the number of test subjects is 10 + 6 = 16 the answer is c .
Answer: c
Python program:
a = math.factorial(5)
b = 5 - 2
c = math.factorial(b)
d = math.factorial(2)
e = c * d
f = a / e
g = f + 6
Problem: enrollment in city college in 1980 was 85 / 3 percent of enrollment in 1990 . what was the percent increase in the college ’ s enrollment from 1980 to 1990 ?
Options: a ) 100 % , b ) 16 2 / 3 % , c ) 200 % , d ) 253 % , e ) 183 1 / 3 %
Rationale: assume 100 enrollments present in 1990 85 / 3 % of 1990 = enrollments on 1980 enrollments on 1980 = 28.33 % change = ( enrollment in 1990 - enrollment in 1980 ) * 100 / ( enrollment in 1980 ) = ( 100 - 28.33 ) * 100 / 28.333 = 7166.67 / 28.333 = 253 % ans - d
Answer: d
Python program:
a = 85 / 3
b = 100 - a
c = 85 / 3
d = b / c
e = d * 100
Problem: there were two candidates in an election . winner candidate received 54 % of votes and won the election by 288 votes . find the number of votes casted to the winning candidate ?
Options: a ) 776 , b ) 1944 , c ) 2199 , d ) 2157 , e ) 2125
Rationale: "w = 54 % l = 46 % 54 % - 46 % = 8 % 8 % - - - - - - - - 288 54 % - - - - - - - - ? = > 1944 answer : b"
Answer: b
Python program:
a = 100 - 54
b = 54 - a
c = b / 100
d = 288 / c
e = d * 54
f = e / 100
Problem: a person bought 115 glass bowls at a rate of rs . 18 per bowl . he sold 104 of them at rs . 20 and the remaining broke . what is the percentage gain for a ?
Options: a ) 40 , b ) 300 / 11 , c ) 243 / 7 , d ) 279 / 11 , e ) 100 / 207
Rationale: "cp = 115 * 18 = 2070 and sp = 104 * 20 = 2080 gain % = 100 * ( 2080 - 2070 ) / 2070 = 100 / 207 answer : e"
Answer: e
Python program:
a = 104 * 20
b = 115 * 18
c = a - b
d = 115 * 18
e = c / d
f = e * 100
Problem: lisa and robert have taken the same number of photos on their school trip . lisa has taken 3 times as many photos as claire and robert has taken 10 more photos than claire . how many photos has claire taken ?
Options: a ) 5 , b ) 8 , c ) 11 , d ) 12 , e ) 14
Rationale: "l = r l = 3 c r = c + 10 3 c = c + 10 c = 5 the answer is a ."
Answer: a
Python program:
a = 3 - 1
b = 10 / a
Problem: how many even multiples of 45 are there between 449 and 901 ?
Options: a ) 5 , b ) 6 , c ) 9 , d ) 10 , e ) 11
Rationale: 450 = 10 * 45 900 = 20 * 45 the even multiples are 45 multiplied by 10 , 12 , 14 , 16 , 18 , and 20 for a total of 6 . the answer is b .
Answer: b
Python program:
a = 901 - 449
b = 45 * 2
c = a / b
d = c + 1
Problem: 19 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?
Options: a ) 286 , b ) 342 , c ) 422 , d ) 540 , e ) 618
Rationale: "2 * 19 c 2 = 2 * 171 = 342 the answer is b ."
Answer: b
Python program:
a = 19 - 1
b = 19 * a
Problem: rs . 585 is divided amongst a , b , c so that 4 times a ' s share , 6 times b ' s share and 3 times c ' s share are all equal . find c ' s share ?
Options: a ) 260 , b ) 150 , c ) 817 , d ) 716 , e ) 616
Rationale: a + b + c = 585 4 a = 6 b = 3 c = x a : b : c = 1 / 4 : 1 / 6 : 1 / 3 = 3 : 2 : 4 4 / 9 * 585 = rs . 260 answer : a
Answer: a
Python program:
a = 3 / 4
b = 3 / 6
c = a + b 
d = c + 1 
e = 585 / d
Problem: in 10 years , a will be twice as old as b was 10 years ago . if a is now 8 years older than b the present age of b is
Options: a ) 37 , b ) 38 , c ) 39 , d ) 40 , e ) 41
Rationale: "let present age of a be a and b be b a + 10 = 2 * ( b - 10 ) = > 2 b - a = 30 . . . . . . ( i ) a = b + 8 = > 2 b - b - 8 = 30 b = 38 so the present age of b is 38 years answer : b"
Answer: b
Python program:
a = 2 * 10
b = a + 10 
c = b + 8
Problem: a die is rolled twice . what is the probability of getting a sum equal to 12 ?
Options: a ) 1 / 36 , b ) 1 / 9 , c ) 1 / 7 , d ) 1 / 24 , e ) 2 / 36
Rationale: "total number of outcomes possible when a die is rolled = 6 ( ∵ any one face out of the 6 faces ) hence , total number of outcomes possible when a die is rolled twice , n ( s ) = 6 × 6 = 36 e = getting a sum of 12 when the two dice fall = { ( 6 , 6 ) } hence , n ( e ) = 1 p ( e ) = n ( e ) / n ( s ) = 1 / 36 = 1 / 36 answer : option a"
Answer: a
Python program:
a = 1 / 12
Problem: a man can row his boat with the stream at 14 km / h and against the stream in 4 km / h . the man ' s rate is ?
Options: a ) 1 kmph , b ) 3 kmph , c ) 8 kmph , d ) 7 kmph , e ) 5 kmph
Rationale: "ds = 14 us = 4 s = ? s = ( 14 - 4 ) / 2 = 5 kmph answer : e"
Answer: e
Python program:
a = 14 - 4
b = a / 2
Problem: cost is expressed by the formula tb ^ 4 . if b is doubled , the new cost is what percent t of the original cost ?
Options: a ) t = 200 , b ) t = 600 , c ) t = 800 , d ) t = 1600 , e ) t = 50
Rationale: "original cost c 1 = t 1 * b 1 ^ 4 new cost c 2 = t 2 * b 2 ^ 4 . . . . only b is doubled so t 2 = t 1 and b 2 = 2 b 1 c 2 = t 2 * ( 2 b 1 ) ^ 4 = 16 ( t 1 * b 1 ^ 4 ) = 16 c 1 16 times c 1 = > 1600 % of c 1 ans d = 1600"
Answer: d
Python program:
a = 2 ** 4
b = a * 100
Problem: in a certain egg - processing plant , every egg must be inspected , and is either accepted for processing or rejected . for every 96 eggs accepted for processing , 4 eggs are rejected . if , on a particular day , 12 additional eggs were accepted , but the overall number of eggs inspected remained the same , the ratio of those accepted to those rejected would be 99 to 1 . how many q eggs does the plant process per day ?
Options: a ) 100 , b ) 300 , c ) 400 , d ) 3000 , e ) 4000
Rationale: straight pluggin in for me . as usual , i started with c and got the answer . lets ' back calculate and see what we get let us consider eggs processed each day to be 400 so initial ratio of eggs processed and rejected is 96 : 4 or 24 : 1 so out of 400 eggs , there will be 384 eggs processed and 16 rejected . now if the no . of eggs inspected remain and 12 more eggs get accepted that means there q = 384 + 12 = 396 eggs accepted and 4 rejected . . . and the ratio will be 99 : 1 bingo . . . this is what the questions says . . . . its always a good idea to start with c .
Answer: c
Python program:
a = 99 - 96
b = 12 / a
c = b * 100
Problem: on her annual road trip to visit her family in seal beach , california , traci stopped to rest after she traveled 1 ⁄ 2 of the total distance and again after she traveled 1 ⁄ 4 of the distance remaining between her first stop and her destination . she then drove the remaining 400 miles and arrived safely at her destination . what was the total distance , in miles , from traci ’ s starting point to seal beach ?
Options: a ) 250 , b ) 3200 / 3 , c ) 3150 / 3 , d ) 4002 / 3 , e ) 550
Rationale: "let d = total distance traci traveled 1 / 2 = d / 2 i . e . remaining distance = d / 2 she traveled 1 / 4 th of d / 2 = d / 8 thus : d = ( d / 2 ) + ( d / 8 ) + 400 d = 3200 / 3 answer : b"
Answer: b
Python program:
a = 400 * 2
Problem: a certain country had a total annual expenditure of $ 1.2 x 10 ^ 11 last year . if the population of the country was 240 million last year , what was the per capita expenditure ?
Options: a ) $ 500 , b ) $ 1,000 , c ) $ 2,000 , d ) $ 3,000 , e ) $ 5,000
Rationale: "total expenditure / population = per capita expenditure hence , ( 1,2 x 10 ^ 11 ) / 240 000 000 = ( 12 x 10 ^ 10 ) / ( 2,4 x 10 ^ 8 ) = 5 x 10 ^ ( 10 - 8 ) = 5 x 10 ^ 2 = 500 . answer is a ."
Answer: a
Python program:
a = 10 ** 11
b = 1 * 2
c = 4 + 2 
d = 10 ** c
e = 240 * d
f = b / e
Problem: two students appeared at an examination . one of them secured 9 marks more than the other and his marks was 56 % of the sum of their marks . the marks obtained by them are :
Options: a ) 39,30 , b ) 41,32 , c ) 42,33 , d ) 43,34 , e ) 35,36
Rationale: let their marks be ( x + 9 ) and x . then x + 9 = 56 / 100 ( x + 9 + x ) 3 x = 99 x = 33 their marks 42 and 33 answer c
Answer: c
Python program:
a = 9 * 100
b = 56 * 9
c = a - b
d = 56 * 2
e = d - 100
f = c / e
g = f + 9
Problem: aaron will jog from home at 4 miles per hour and then walk back home by the same route at 8 miles per hour . how many miles from home can aaron jog so that he spends a total of 3 hours jogging and walking ?
Options: a ) 2 , b ) 10 , c ) 12 , d ) 8 , e ) 15
Rationale: "xyt / ( x + y ) x = 4 , y = 8 t = 3 4 * 8 * 3 / 4 + 8 = 96 / 12 = 8 answer : d"
Answer: d
Python program:
a = 2 * 0
b = a * 3
c = 4 * 8
d = b / c
Problem: if x is the product of the positive integers from 1 to 8 , inclusive , and if i , k , m , and p are positive integers such that x = 2 ^ i ∗ 3 ^ k ∗ 5 ^ m ∗ 7 ^ p , then i + k + m + p =
Options: a ) 4 , b ) 7 , c ) 8 , d ) 11 , e ) 12
Rationale: "here the idea is to go expressing each factor from one to eight , decomposed into its primes : 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 = 1 * 2 * 3 * ( 2 * 2 ) * 5 + ( 2 * 3 ) * 7 * ( 2 * 2 * 2 ) = 2 ^ 7 * 3 ^ 2 * 5 ^ 1 * 7 ^ 1 then i = 7 k = 2 m = 1 p = 1 i + k + m + p = 11 correct answer d"
Answer: d
Python program:
a = 7 + 2 
b = 5 / 5
c = a + b 
d = 3 / 3
e = c + d
Problem: each side of a rectangular field diminished by 40 % . by how much per cent is the area of the field diminished ?
Options: a ) 32
b ) 64
c ) 25
d ) 16
e ) none
Rationale: solution : let the original length of the rectangle be 20 unit and breadth be 10 unit . then original area = length * breadth = 20 * 10 = 200 square unit . 40 % decrease in each side , then length = ( 20 - 40 % of 20 ) = 12 unit . breadth = ( 10 - 40 % of 10 ) = 6 unit . now , area = 12 * 6 = 72 square unit . decrease in area = 200 - 72 = 128 square unit . % decrease in area = ( 128 / 200 ) * 100 = 64 % mind calculation method : let the original area be 100 square unit . 100 = = = 40 % ↓ ( decrease in length ) = = = > 60 = = = 40 % ↓ = = = ( decrease in breadth ) = = = > 36 . diminished in area = 100 - 36 = 64 % answer : option b
Answer: b
Python program:
a = 100 * 100
b = 100 - 40
c = 100 - 40
d = b * c
e = a - d
f = 100 * 100
g = e / f
h = g * 100
Problem: the average of 10 numbers is calculated as 14 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?
Options: a ) a ) 16 , b ) b ) 15 , c ) c ) 19 , d ) d ) 22 , e ) e ) 24
Rationale: "explanation : 10 * 14 + 36 – 26 = 150 = > 150 / 10 = 15 b )"
Answer: b
Python program:
a = 36 - 26
b = a / 10
c = 14 + b
Problem: there are two groups of students in the sixth grade . there are 20 students in group a , and 80 students in group b . if , on a particular day , 20 % of the students in group a forget their homework , and 15 % of the students in group b forget their homework , then what percentage of the sixth graders forgot their homework ?
Options: a ) 13 % , b ) 14 % , c ) 15 % , d ) 16 % , e ) 17 %
Rationale: "number of students in group a = 20 students who forget homework in group a = 20 % of 20 = 4 students number of students in group b = 80 students who forget homework in group b = 15 % of 80 = 12 students total number of students = 20 + 80 = 100 students who forgot homework = 4 + 12 = 16 students percentage of students who forget homework = 16 / 100 * 100 = 16 % answer : d"
Answer: d
Python program:
a = 20 * 20
b = a / 100
c = 80 * 15
d = c / 100
e = b + d 
f = 20 + 80 
g = e / f
h = g * 100
Problem: the average of 6 quantities is 8 . the average of 4 of them is 5 . what is the avg . of the remaining 2 numbers ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "sum of 8 quantities = total no of quantities x average of them = 6 x 8 = 48 sum of 4 quantities = 4 x 5 = 20 sum of 4 quantities + sum of 2 quantities = sum of 6 quantities 20 + sum of 2 quantities = 48 sum of 2 quantities = 28 average of 2 quantities = sum of 2 quantities / 2 = 28 / 2 = 14 answer : d"
Answer: d
Python program:
a = 6 * 8
b = 4 * 5
c = a - b
d = c / 2
Problem: suresh started a business , investing rs . 18000 . after 3 months and 4 months respectively , rohan and sudhir joined him with capitals of 12000 and 9000 . at the end of the year the total profit was rs . 4048 . what is the difference between rohan ’ s and sudhir ’ s share in the profit ?
Options: a ) s . 345 , b ) s . 350 , c ) s . 352 , d ) s . 362 , e ) s . 368
Rationale: "suresh : rohan : sudhir ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8 = 6 : 3 : 2 the difference between rohan ’ s and sudhir ’ s share = 1 share : . i . e . = rs . 4048 × 1 / 11 = rs . 368 . e"
Answer: e
Python program:
a = 3 * 4
b = a - 3
c = 3 * 4
d = b / c
e = 12000 * d
f = 3 * 4
g = f - 4
h = 3 * 4
i = g / h
j = 9000 * i
k = e - j
l = 3 * 4
m = l - 3
n = 3 * 4
o = m / n
p = 12000 * o
q = 18000 + p 
r = 3 * 4
s = r - 4
t = 3 * 4
u = s / t
v = 9000 * u
w = q + v 
x = 4048 / w
y = k * x
Problem: a man has rs . 10350 in the form of rs . 50 notes and rs . 500 notes . the total number of notes are 90 . find the number of notes of rs . 50 denomination .
Options: a ) 15 , b ) 21 , c ) 17 , d ) 57 , e ) 77
Rationale: total money = rs . 10350 . let 50 rupees note was x . then 500 rupees note = 90 - x now , 50 * x + 500 * ( 90 - x ) = 10350 50 x + 45000 - 500 x = 10350 - 450 x = - 34650 x = 77 . no . of 50 rupees note = 77 . answer : option e
Answer: e
Python program:
a = 500 * 90
b = a - 10350
c = 500 - 50
d = b / c
Problem: during 2003 , a company produced an average of 4,000 products per month . how many products will the company need to produce from 2004 through 2007 in order to increase its monthly average for the period from 2003 through 2007 by 150 % over its 2003 average ?
Options: a ) 435,000 , b ) 440,000 , c ) 450,000 , d ) 480,000 , e ) 432,000
Rationale: "company produced 12 * 4000 = 48,000 products in 2003 . if company produces x products from 2004 to 2007 , then total amount of product produced in 4 years ( 2003 through 2007 ) is x + 48,000 . the gives the average of ( x + 48,000 ) / 4 . this average needs to be 300 % higher than that in 2003 . in math terms , 48,000 + 150 % ( 48,000 ) = 120,000 . so : ( x + 48,000 ) / 4 = 120,000 x + 48,000 = 480,000 x = 432,000 the answer is e ."
Answer: e
Python program:
a = 2007 - 2003
b = a / 2
c = 150 * b
Problem: the average age of an adult class is 40 years . 12 new students with an avg age of 32 years join the class . thereforedecreasing the average by 4 year . find what was theoriginal strength of class ?
Options: a ) 10 , b ) 12 , c ) 16 , d ) 20 , e ) 22
Rationale: "let original strength = y then , 40 y + 12 x 32 = ( y + 12 ) x 36 ⇒ 40 y + 384 = 36 y + 432 ⇒ 4 y = 48 ∴ y = 12 b"
Answer: b
Python program:
a = 40 - 4
b = 12 * a
c = 12 * 32
d = b - c
e = d / 4
Problem: the distance from the x - axis to point p is half the distance from the y - axis to point p . if the coordinates of p are ( x , - 5 ) , how many units is p from the y - axis ?
Options: a ) 2.5 , b ) 5 , c ) 7.5 , d ) 10 , e ) 12
Rationale: "the x - axis is 5 units from the point p . thus the y - axis is 10 units from the point p . the answer is d ."
Answer: d
Python program:
a = 5 * 2
Problem: two numbers are respectively 20 % and 60 % more than a third number . the percentage that is first of the second is ?
Options: a ) 34 % , b ) 68 % , c ) 51 % , d ) 75 % , e ) 83 %
Rationale: "i ii iii 120 160 100 160 - - - - - - - - - - 120 100 - - - - - - - - - - - ? = > 75 % answer : d"
Answer: d
Python program:
a = 20 + 100 
b = 60 + 100 
c = a / b
d = c * 100
e = 100 - d
Problem: we bought a total of 90 books at the store . math books cost $ 4 and history books cost $ 5 . the total price was $ 397 . how many math books did we buy ?
Options: a ) 47 , b ) 53 , c ) 56 , d ) 61 , e ) 64
Rationale: "let m be the number of math books and let h be the number of history books . m + h = 90 . h = 90 - m . 4 m + 5 h = 397 . 4 m + 5 ( 90 - m ) = 397 . - m + 450 = 397 . m = 450 - 397 = 53 . the answer is b ."
Answer: b
Python program:
a = 90 * 4
b = 397 - a
c = 90 - b
Problem: two employees a and b are paid a total of rs . 580 per week by their employer . if a is paid 150 percent of the sum paid to b , how much is b paid per week ?
Options: a ) s . 130 , b ) s . 140 , c ) s . 150 , d ) s . 232 , e ) s . 280
Rationale: "let the amount paid to a per week = x and the amount paid to b per week = y then x + y = 580 but x = 150 % of y = 150 y / 100 = 15 y / 10 ∴ 15 y / 10 + y = 580 ⇒ y [ 15 / 10 + 1 ] = 580 ⇒ 25 y / 10 = 580 ⇒ 25 y = 5800 ⇒ y = 5800 / 25 = rs . 232 d )"
Answer: d
Python program:
a = 150 / 100
b = a + 1 
c = 580 / b