euclaise/mathqa_programs huggingface dataset:
Problem: a satellite is composed of 24 modular units , each of which is equipped with a set of sensors , some of which have been upgraded . each unit contains the same number of non - upgraded sensors . if the number of non - upgraded sensors on one unit is 1 / 3 the total number of upgraded sensors on the entire satellite , what fraction of the sensors on the satellite have been upgraded ?
Options: a ) 5 / 6 , b ) 1 / 5 , c ) 1 / 6 , d ) 1 / 9 , e ) 1 / 24
Rationale: let x be the number of upgraded sensors on the satellite . the number of non - upgraded sensors per unit is x / 3 . the number of non - upgraded sensors on the whole satellite is 24 ( x / 3 ) = 8 x . the fraction of sensors which have been upgraded is x / ( x + 8 x ) = x / 9 x = 1 / 9 the answer is d .
Answer: d
Python program:
a = 1 / 3
b = a * 24
c = 24 * b
d = 24 + c 
e = 24 / d
Problem: tom drives from town a to town b , driving at a constant speed of 60 miles per hour . from town b tom immediately continues to town c . the distance between a and b is twice the distance between b and c . if the average speed of the whole journey was 36 mph , then what is tom ' s speed driving from b to c in miles per hour ?
Options: a ) 12 , b ) 20 , c ) 24 , d ) 30 , e ) 36
Rationale: let ' s assume that it takes 4 hours to go from point a to b . then the distance between them becomes 240 which makes distance between b and c 120 . ( 240 + 120 ) / ( 4 + x ) gives us the average speed which is 36 . you find x = 6 . so the question simplifies itself to 120 / 6 = 20 hence the answer is b
Answer: b
Python program:
a = 3 / 36
b = 2 / 60
c = a - b
d = 1 / c
Problem: the average ( arithmetic mean ) of 22 , 33 , and 53 is 8 less than the average of 30 , 56 , and x . what is x ?
Options: a ) 42 , b ) 44 , c ) 46 , d ) 48 , e ) 50
Rationale: "the average of 22 , 33 , and 53 is 108 / 3 = 36 . the average of 30 , 56 and x is 44 . then 30 + 56 + x = 132 . x = 46 . the answer is c ."
Answer: c
Python program:
a = 22 + 33 
b = a + 53 
c = 8 * 3
d = c + 30 
e = d + 56 
f = b - e
Problem: how many 3 - digit numbers are completely divisible 6 ?
Options: a ) 100 , b ) 150 , c ) 200 , d ) 250 , e ) 300
Rationale: "3 - digit number divisible by 6 are : 102 , 108 , 114 , . . . , 996 this is an a . p . in which a = 102 , d = 6 and l = 996 let the number of terms be n . then tn = 996 . a + ( n - 1 ) d = 996 102 + ( n - 1 ) x 6 = 996 6 x ( n - 1 ) = 894 ( n - 1 ) = 149 n = 150 number of terms = 150 . b )"
Answer: b
Python program:
a = 100 * 3
b = a + 100
Problem: 1 , 6 , 16 , 31 , 51 , ( . . . . )
Options: a ) 61 , b ) 66 , c ) 76 , d ) 86 , e ) 83
Rationale: "explanation : the pattern is 5 , 10 , 15 , 20 , 25 , etc hence 25 = 66 answer : b"
Answer: b
Python program:
a = negate - (
Problem: in a public show 60 % of the seats were filled . if there were 600 seats in the hall , how many seats were vacant ?
Options: a ) 100 , b ) 110 , c ) 120 , d ) 140 , e ) 240
Rationale: "75 % of 600 = 60 / 100 × 600 = 360 therefore , the number of vacant seats = 600 - 360 = 240 . answer : e"
Answer: e
Python program:
a = 100 - 60
b = 600 * a
c = b / 100
Problem: what is the decimal equivalent of ( 1 / 10 ) ^ 2 ?
Options: a ) 0.0016 , b ) 0.0625 , c ) 0.16 , d ) 0.25 , e ) 0.01
Rationale: "( 1 / 10 ) ² = ( 1 / 10 ) ( 1 / 10 ) = 1 / 100 approach # 1 : use long division to divide 100 into 1 to get 1 / 100 = 0.01 e"
Answer: e
Python program:
a = 1 / 10
b = a ** 2
Problem: for a bake sale , simon baked 2 n more pies than theresa . theresa baked half as many pies as roger , who baked 1313 n pies . no other pies were baked for the sale . what fraction of the total pies for sale did roger bake ?
Options: a ) 1 / 16 , b ) 1 / 8 , c ) 3 / 16 , d ) 3 / 8 , e ) 13 / 16
Rationale: s : simon t : theresa r : roger let theresa baked a . as per question , we have s = a + 2 n r = 2 a = n / 3 or a = n / 6 now , total = a + ( a + 2 n ) + 2 a = 8 n / 3 fraction , ( n / 3 ) / ( 8 n / 3 ) = 1 / 8 answer : b
Answer: b
Python program:
a = 1 / 3
b = 1 / 3
c = b * 2
d = c * 2
e = d * 2
f = a / e
Problem: sarah is driving to the airport . after driving at 50 miles per hour for one hour , she realizes that if she continues at that same average rate she will be an hour late for her flight . she then travels 100 miles per hour for the rest of the trip , and arrives 30 minutes before her flight departs . how many miles did she drive in all ?
Options: a ) 140 , b ) 175 , c ) 200 , d ) 245 , e ) 280
Rationale: "after driving at 50 miles per hourfor one hour , this distance left to cover is d - 50 . say this distance is x miles . now , we know that the difference in time between covering this distance at 50 miles per hour and 100 miles per hour is 1 + 1 / 2 = 3 / 2 hours . so , we have that x / 50 - x / 100 = 3 / 2 - - > 2 x / 100 - x / 100 = 3 / 2 - - > x / 100 = 3 / 2 - - > x = 150 total distance = x + 50 = 200 miles . answer : c ."
Answer: c
Python program:
a = 50 - 30
b = 30 - a
Problem: two trains a and b are 225 m and 150 m long and are moving at one another at 54 km / hr and 36 km / hr respectively . arun is sitting on coach b 1 of train a . calculate the time taken by arun to completely cross train b .
Options: a ) 10 s , b ) 15 s , c ) 4 s , d ) 8 s , e ) 12 s
Rationale: "detailed solution speed of a = 54 ∗ 1000 / 60 ∗ 60 = 15 m / s speed of b = 36 ∗ 1000 / 60 ∗ 60 = 10 m / s relative speed = s 1 + s 2 = 15 + 10 m / s = 25 m / s the length that needs to be crossed = length of train b = 150 m . therefore time taken = 150 / 25 = 6 s . what is the time taken for trains to completely cross each other ? the length that needs to be crossed = 225 + 150 = 375 m . time taken = 375 / 25 = 15 s . correct answer b ."
Answer: b
Python program:
a = 225 + 150 
b = 54 * 1000
c = b / 3600
d = 36 * 1000
e = d / 3600
f = c + e 
g = a / f
Problem: a gardener grows cabbages in her garden that is in the shape of a square . each cabbage takes 1 square feet of area in her garden . this year , she has increased her output by 199 cabbages as compared to last year . the shape of the area used for growing the cabbages has remained a square in both these years . how many cabbages did she produce this year ?
Options: a ) 10,000 , b ) 11,025 , c ) 14,400 , d ) 12,696 , e ) can not be determined
Rationale: "let the side for growing cabbages this year be x ft . thus the area is x ^ 2 . let the side for growing cabbages last year be y ft . thus , the area was y ^ 2 . the area would have increased by 199 sq ft as each cabbage takes 1 sq ft space . x ^ 2 - y ^ 2 = 199 ( x + y ) ( x - y ) = 199 199 is a prime number and thus it will be ( 100 + 99 ) * ( 100 - 99 ) . thus x = 100 and y = 99 x ^ 2 = 100 ^ 2 = 10,000 the answer is a ."
Answer: a
Python program:
a = 199 / 2
b = const_0_25 + const_0_25 
c = a + b 
d = c ** 2
Problem: if x , y , and z are positive integers and x = 4 y = 7 z , then the least possible value of x - y - z is
Options: a ) 33 , b ) 17 , c ) 49 , d ) 16 , e ) 23
Rationale: x - y - z = x - x / 4 - x / 7 = ( 28 - 7 - 4 ) x / 28 = 17 x / 28 17 is not divisible by 28 ( it ' s a prime # ) , so for least value , x = 28 answer - b
Answer: b
Python program:
a = 4 * 7
b = a - 7
c = b - 4
Problem: one hour after yolanda started walking from x to y , a distance of 80 miles , bob started walking along the same road from y to x . if yolanda â s walking rate was 8 miles per hour and bob â s was 9 miles per hour , how many miles had bob walked when they met ?
Options: a ) 38.07 , b ) 40 , c ) 42 , d ) 39 , e ) 40.07
Rationale: "let t be the number of hours that bob had walked when he met yolanda . then , when they met , bob had walked 4 t miles and yolanda had walked 8 ( t + 1 ) miles . these distances must sum to 80 miles , so 9 t + 8 ( t + 1 ) = 80 , which may be solved for t as follows 9 t + 8 ( t + 1 ) = 80 9 t + 8 t + 8 = 80 17 t = 72 t = 4.23 ( hours ) therefore , bob had walked 9 t = 9 ( 4.23 ) = 38.07 miles when they met . the best answer is a ."
Answer: a
Python program:
a = 80 - 8
b = 8 + 9 
c = a / b
d = c * 9
Problem: a boat can travel with a speed of 13 km / hr in still water . if the speed of the stream is 5 km / hr . find the time taken by the boat to go 68 km downstream ?
Options: a ) 2 hours , b ) 3 hours , c ) 3 hours 48 minutes , d ) 5 hours , e ) none
Rationale: "solution speed downstream = ( 13 + 5 ) km / hr = 18 km / hr . time taken to travel 68 km downstream = ( 68 / 18 ) hrs = 3 hrs 48 minutes . answer c"
Answer: c
Python program:
a = 13 + 5 
b = 68 / a
Problem: the speed of a train is 94 kmph . what is the distance covered by it in 12 minutes ?
Options: a ) 15 kmph , b ) 11 kmph , c ) 88 kmph , d ) 19 kmph , e ) 12 kmph
Rationale: "94 * 12 / 60 = 18.8 kmph answer : d"
Answer: d
Python program:
a = 12 / const_60
b = a * 94
Problem: if 5 machines can produce 20 units in 10 hours , how long would it take 20 machines to produce 180 units ?
Options: a ) 50 hours , b ) 40 hours , c ) 22.5 hours , d ) 12 hours , e ) 8 hours
Rationale: "here , we ' re told that 5 machines can produce 20 units in 10 hours . . . . that means that each machine works for 10 hours apiece . since there are 5 machines ( and we ' re meant to assume that each machine does the same amount of work ) , then the 5 machines equally created the 20 units . 20 units / 5 machines = 4 units are made by each machine every 10 hours now that we know how long it takes each machine to make 4 units , we can break this down further if we choose to . . . 10 hours / 4 units = 2.5 hours per unit when 1 machine is working . the prompt asks us how long would it take 20 machines to produce 180 units . if 20 machines each work for 2.5 hours , then we ' ll have 20 units . since 180 units is ' 9 times ' 20 , we need ' 9 times ' more time . ( 2.5 hours ) ( 9 times ) = 22.5 hours final answer : [ reveal ] spoiler : c"
Answer: c
Python program:
a = 20 / 10
b = a / 5
c = b * 20
d = 180 / c
Problem: a worker ' s daily wage is increased by 50 % and the new wage is $ 51 per day . what was the worker ' s daily wage before the increase ?
Options: a ) $ 28 , b ) $ 32 , c ) $ 34 , d ) $ 35 , e ) $ 40
Rationale: "let x be the daily wage before the increase . 1.5 x = $ 51 x = $ 34 the answer is c ."
Answer: c
Python program:
a = 50 / 100
b = 1 + a 
c = 51 / b
Problem: in an election , candidate douglas won 60 percent of the total vote in counties x and y . he won 72 percent of the vote in county x . if the ratio of people who voted in county x to county y is 2 : 1 , what percent of the vote did candidate douglas win in county y ?
Options: a ) 18 % , b ) 30 % , c ) 36 % , d ) 48 % , e ) 54 %
Rationale: "given voters in ratio 2 : 1 let x has 200 votersy has 100 voters for x 72 % voted means 72 * 200 = 144 votes combined for xy has 300 voters and voted 60 % so total votes = 180 balance votes = 180 - 144 = 36 as y has 100 voters so 36 votes means 36 % of votes required ans c"
Answer: c
Python program:
a = 60 / 100
b = 72 / 100
c = 2 / 3
d = b * c
e = a - d
f = 1 / 3
g = e / f
h = g * 100
Problem: a ferry can transport 50 tons of vehicles . automobiles range in weight from 1600 to 3200 pounds . what is the greatest number of automobiles that can be loaded onto the ferry ?
Options: a ) 23 , b ) 41 , c ) 48 , d ) 62 , e ) 86
Rationale: to get maximum vehicles we must take into consideration the minimum weight i . e 1600 pounds here since , 1 ton = 2000 pounds 50 tons will be 100,000 pounds from the answer choices : let max number of vehicles be 62 total weight will be = 62 * 1600 = 99200 pounds , which is lesser than the maximum weight allowed . ans : d
Answer: d
Python program:
a = 2 * 1000
b = 1600 / a
c = 50 / b
Problem: how much time does a train 150 metres long running at 54 km / hr take to pass a pole ?
Options: a ) 7.9 s , b ) 2.5 s , c ) 7.5 s , d ) 7.6 s , e ) 10 s
Rationale: "explanation : 54 km / hr = 54 * 5 / 18 = 15 m / s speed = distance / time ; v = d / t 15 = 150 / t t = 10 s answer : e"
Answer: e
Python program:
a = 150 / 1000
b = a / 54
c = b * 3600
Problem: the cash realised on selling a 14 % stock is rs . 104.25 , brokerage being 1 / 4 % is
Options: a ) 123 , b ) 106 , c ) 100 , d ) 156 , e ) 104
Rationale: "explanation : cash realised = rs . ( 104.25 - 0.25 ) = rs . 104 . answer : e"
Answer: e
Python program:
a = 1 / 4
b = 104 - 25
Problem: by selling 12 pencils for a rupee a man loses 12 % . how many for a rupee should he sell in order to gain 18 % ?
Options: a ) 12 , b ) 9 , c ) 10 , d ) 89 , e ) 81
Rationale: "88 % - - - 12 112 % - - - ? 88 / 112 * 12 = 9 answer : a"
Answer: a
Python program:
a = 100 + 18 
b = 100 - 12
c = 1 / b
d = a * c
e = 1 / d
f = e * 12
Problem: ages of two persons differ by 4 years . if 3 years ago , the elder one was 3 times as old the younger one , find their present age
Options: a ) 5,9 , b ) 14,18 , c ) 16,20 , d ) 18,22 , e ) 19,23
Rationale: "explanation : let the age of the younger person be x , then the elder person ' s age is ( x + 4 ) = > 3 ( x - 3 ) = ( x + 4 - 3 ) [ 3 years before ] = > 3 x - 9 = x + 1 = > x = 5 . so the elder person ' s age is x + 4 = 9 answer : option a"
Answer: a
Python program:
a = 3 * 3
b = a + 4 
c = b - 3
d = 3 - 1
e = c / d
f = e - 1
Problem: a type of extra - large suv averages 12.2 miles per gallon ( mpg ) on the highway , but only 7.6 mpg in the city . what is the maximum distance , in miles , that this suv could be driven on 23 gallons of gasoline ?
Options: a ) 190 , b ) 284.6 , c ) 300 , d ) 280 , e ) 312
Rationale: "so 12.2 * 23 = 280 . . imo option d is correct answer . ."
Answer: d
Python program:
a = 12 * 2
Problem: if 12 men or 20 women can do a piece of work in 54 days , then in how many days can 9 men and 21 women together do the work ?
Options: a ) 10 days , b ) 30 days , c ) 20 days , d ) 80 days , e ) 40 days
Rationale: "b 30 days given that 12 m = 20 w = > 3 m = 5 w 9 men + 21 women = 15 women + 21 women = 36 women 20 women can do the work in 54 days . so , 36 women can do it in ( 20 * 54 ) / 36 = 30 days ."
Answer: b
Python program:
a = 12 * 54
b = 9 / a
c = 20 * 54
d = 21 / c
e = b + d 
f = 1/(e)
Problem: a man sold 20 articles for $ 60 and gained 20 % . how many articles should he sell for $ 70 to incur a loss 20 % ?
Options: a ) 45 , b ) 35 , c ) 40 , d ) 50 , e ) 48
Rationale: "production cost per article : $ 60 * ( 100 % - 20 % ) / 20 = $ 2.40 required production costs for a loss of 20 % : $ 70 * ( 100 % + 20 % ) = $ 84 number of articles to be sold for $ 84 to incur a 20 % loss : $ 84 / $ 2.40 = 35 thus , solution b is correct ."
Answer: b
Python program:
a = original_price_before_loss / (
Problem: solution p is 20 percent lemonade and 80 percent carbonated water by volume ; solution q is 45 percent lemonade and 55 percent carbonated water by volume . if a mixture of pq contains 60 percent carbonated water , what percent of the volume of the mixture is p ?
Options: a ) 20 % , b ) 30 % , c ) 40 % , d ) 50 % , e ) 60 %
Rationale: "60 % is 20 % - points below 80 % and 5 % - points above 55 % . so the ratio of solution p to solution q is 1 : 4 . mixture p is 1 / 5 = 20 % of the volume of mixture pq . the answer is a ."
Answer: a
Python program:
a = 60 / 100
b = 55 / 100
c = a - b
d = 60 / 100
e = 55 / 100
f = d - e
g = 80 / 100
h = 60 / 100
i = g - h
j = f + i 
k = c / j
l = k * 100
Problem: how many integers from 0 to 50 inclusive have a remainder of 3 when divided by 11 ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "the numbers should be of the form 11 c + 3 . the minimum is 3 when c = 0 . the maximum is 47 when c = 4 . there are 5 such numbers . the answer is a ."
Answer: a
Python program:
a = 50 / 10
Problem: find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number .
Options: a ) 3 , b ) 5 , c ) 7 , d ) 12 , e ) 15
Rationale: "sol . let the number be x . then , x + 17 = 60 / x ⇔ x 2 + 17 x - 60 = 0 ⇔ ( x + 20 ) ( x - 3 ) = 0 ⇔ x = 3 . answer a"
Answer: a
Python program:
a = math.gcd(60, 17)
b = 2 + a
Problem: a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 80 as remainder . find the no . is ?
Options: a ) 220880 , b ) 145778 , c ) 220081 , d ) 220080 , e ) 220030
Rationale: ( 555 + 445 ) * 2 * 110 + 80 = 220000 + 80 = 220080 d
Answer: d
Python program:
a = 555 + 445 
b = a * 2
c = 555 - 445
d = b * c
e = d + 80
Problem: the sum of two number is 120 and their difference is 30 . find the numbers .
Options: a ) 9525 , b ) 5565 , c ) 7545 , d ) 6555 , e ) 8535
Rationale: let the two number be x and y . x + y = 120 . . . . . . . ( 1 ) x - y = 30 . . . . . . . . . ( 2 ) = > 2 x = 150 = > x = 75 . x - y = 30 = > y = 45 . the two numbers are 7545 ans : c
Answer: c
Python program:
a = 120 * 30
b = a * 2
Problem: the prices of tea and coffee per kg were the same in june . in july the price of coffee shot up by 10 % and that of tea dropped by 20 % . if in july , a mixture containing equal quantities of tea and coffee costs 50 / kg . how much did a kg of coffee cost in june ?
Options: a ) 50 , b ) 45 , c ) 52.63 , d ) 40 , e ) 35
Rationale: "let the price of tea and coffee be x per kg in june . price of tea in july = 1.1 x price of coffee in july = 0.8 x . in july the price of 1 / 2 kg ( 500 gm ) of tea and 1 / 2 kg ( 500 gm ) of coffee ( equal quantities ) = 50 1.1 x ( 1 / 2 ) + 0.8 x ( 1 / 2 ) = 50 = > x = 52.63 c"
Answer: c
Python program:
a = 20 / 100
b = 1 - a
c = 10 / 100
d = c + 1 
e = b * d
f = 50 / e
Problem: a dishonest person wants to make a profit on the selling of milk . he would like to mix water ( costing nothing ) with milk costing 33 $ per litre so as to make a profit of 30 % on cost when he sells the resulting milk and water mixture for 36 $ . in what ratio should he mix the water and milk ?
Options: a ) 1 : 20 , b ) 1 : 10 , c ) 1 : 120 , d ) 23 : 4 , e ) 23 : 120
Rationale: "first of all , let ' s consider 1 liter of the stuff he is going to sell - - - naive customers think it ' s pure milk , but we know it ' s some milk - water mixture . he is going to sell this liter of milk - water for $ 36 . this $ 36 should be a 30 % increase over cost . here , we need to think about percentage increases as multipliers . using multipliers ( cost ) * 1.30 = $ 36 cost = 36 / 1.3 = 360 / 12 = $ 27.69 if he wants a 30 % increase over cost on the sale of one liter of his milk - water , the cost has to be $ 27.69 . well , a liter of milk costs $ 33 , so if he is going to use just $ 30 of milk in his mixture , that ' s 27.69 / 33 = 120 / 143 of a liter . if milk is 120 / 143 of the liter , then water is 23 / 143 of the liter , and the ratio of water to milk is 23 : 120 . answer choice ( e )"
Answer: e
Python program:
a = 100 + 30 
b = a / 100
c = 36 / b
d = 33 - c
e = 100 + 30 
f = e / 100
g = 36 / f
h = d / g
Problem: a train 110 m long is running at 50 kmph . in how much time will it pass a platform 210 m long ?
Options: a ) 14.15 seconds , b ) 15.24 seconds , c ) 16.28 seconds , d ) 13.30 seconds , e ) 10.24 seconds
Rationale: distance travelled = 110 + 210 m = 320 m speed = 50 * 5 / 8 = 125 / 4 m time = 320 * 4 / 125 = 10.24 seconds answer : e .
Answer: e
Python program:
a = 110 + 210 
b = 50 * const_0_2778
c = a / b
Problem: a man buys an article for $ 100 . and sells it for $ 115 . find the gain percent ?
Options: a ) 10 % , b ) 15 % , c ) 25 % , d ) 20 % , e ) 30 %
Rationale: "c . p . = $ 100 s . p . = $ 115 gain = $ 15 gain % = 15 / 100 * 100 = 25 % answer is b"
Answer: b
Python program:
a = 100 / 100
b = 115 / a
c = b - 100
Problem: there was a cycle race going on . 1 / 5 th of the those in front of a person and 5 / 6 th of those behind him gives the total number of participants . how many people took part in the race ?
Options: a ) 31 , b ) 39 , c ) 30 , d ) 33 , e ) 34
Rationale: explanation : let total participants be ( x + 1 ) then = > ( 1 / 5 ) * x + ( 5 / 6 ) * x = x + 1 = > 31 x / 30 = x + 1 = > x = 30 so total participants ( x + 1 ) = 31 hence ( a ) is the correct answer . answer : a
Answer: a
Python program:
a = 5 * 6
b = a + 1
Problem: at what rate percent on simple interest will rs . 1750 amount to rs . 2000 in 2 years ?
Options: a ) 4 % , b ) 7.14 % , c ) 2 6 / 7 % , d ) 5 % , e ) 6 %
Rationale: "explanation : 250 = ( 1750 x 2 xr ) / 100 r = 7.14 % answer : option b"
Answer: b
Python program:
a = 2000 - 1750
b = a / 1750
c = b / 2
d = c * 100
Problem: what is the least number which when divided by 5 , 6 , 7 and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder ?
Options: a ) 1108 , b ) 1683 , c ) 2007 , d ) 3363 , e ) 1436
Rationale: "lcm of 5 , 6 , 7 and 8 = 840 hence the number can be written in the form ( 840 k + 3 ) which is divisible by 9 . if k = 1 , number = ( 840 × 1 ) + 3 = 843 which is not divisible by 9 . if k = 2 , number = ( 840 × 2 ) + 3 = 1683 which is divisible by 9 . hence 1683 is the least number which when divided by 5 , 6 , 7 and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder . answer : b"
Answer: b
Python program:
a = math.lcm(5, 6)
b = math.lcm(7, 8)
c = math.lcm(a, b)
d = c + 3
Problem: what is the difference between the largest number and the least number written with the digits 7 , 3 , 1 , 4 ?
Options: a ) 6084 , b ) 6184 , c ) 5084 , d ) 6048 , e ) 6049
Rationale: "1347 7431 - - - - - - - - - - - - 6084 answer : a"
Answer: a
Python program:
a = 7 * 100
b = a * 10
c = 4 * 100
d = b + c 
e = 3 * 10
f = d + e 
g = f + 1 
h = 3 * 100
i = 1000 + h 
j = 4 * 10
k = i + j 
l = k + 7 
m = g - l
Problem: if a light flashes every 30 seconds , how many times will it flash in 1 / 2 of an hour ?
Options: a ) 30 , b ) 42 , c ) 61 , d ) 59 , e ) 45
Rationale: "there are 60 minutes in an hour . in 1 / 2 of an hour there are ( 60 * 1 / 2 ) minutes = 30 minutes . in 1 / 2 of an hour there are ( 60 * 30 ) seconds = 1800 seconds . light flashed for every 30 seconds . in 1800 seconds 1800 / 30 = 60 times . the count start after the first flash , the light will flashes 61 times in 1 / 2 of an hour . answer : c"
Answer: c
Python program:
a = 3600 / 4
b = a * 3
c = b / 30
Problem: what is the smallest positive integer k such that the product of 720 x k is a perfect square ?
Options: a ) 5 , b ) 9 , c ) 15 , d ) 25 , e ) 63
Rationale: "a perfect square , is just an integer that can be written as the square of some other integer . for example 16 = 4 ^ 2 , is a perfect square . now , 720 = 3 ^ 2 * 4 ^ 2 * 5 , so if k = 5 then 720 k = ( 3 * 4 * 5 ) ^ 2 , which is a perfect square ( basically the least positive value of k must complete only the power of 7 to even power as powers of other primes are already even ) . answer : a ."
Answer: a
Python program:
a = 3 + 4
Problem: the ratio of two numbers is 2 : 3 and their h . c . f . is 6 . their l . c . m . is
Options: a ) 48 , b ) 22 , c ) 36 , d ) 27 , e ) 67
Rationale: explanation : let the numbers be 2 x and 3 x . then , their h . c . f . = x . so , x = 6 . so , the numbers 12 and 18 l . c . m . of 12 and 18 = 36 option c
Answer: c
Python program:
a = 2 * 3
b = 6 * a
Problem: the speed at which a girl can row a boat in still water is 90 kmph . if she rows downstream , where the speed of current is 18 kmph , what time will he take to cover 330 metres ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "speed of the boat downstream = 90 + 18 = 108 kmph = 108 * 5 / 18 = 30 m / s hence time taken to cover 330 m = 330 / 30 = 11 seconds . answer : a"
Answer: a
Python program:
a = 330 * const_3_6
b = 90 + 18 
c = a / b
Problem: one hour after matthew started waking from q to y , a distance of 45 km , johnny started walking along the same road from y to q . matthew ' s walking rate was 3 km per hour and johnny ' s was 4 km per hour , how many km had johnny walked when they met ?
Options: a ) 24 , b ) 23 , c ) 22 , d ) 21 , e ) 19.5
Rationale: just an alternative method . . . after the first hour the distance q is 42 km ( 45 - 3 ) . now the problem can be treated as if bothof them started at the same time . since the speeds are in the ratio 3 : 4 , the distances will also be in the same ratio . splitting 42 in that ratio we get 18 : 24 . so answer is 24 . hence a .
Answer: a
Python program:
a = 45 - 3
b = 3 + 4 
c = a / b
d = c * 4