euclaise/mathqa_programs huggingface dataset:
Problem: 60 litres of diesel is required to travel 600 km using a 800 cc engine . if the volume of diesel required to cover a distance varies directly as the capacity of the engine , then how many litres of diesel is required to travel 800 km using 1200 cc engine ?
Options: a ) 80 litres , b ) 90 litres , c ) 120 litres , d ) 170 litres , e ) none of these
Rationale: explanatory answer to cover a distance of 800 kms using a 800 cc engine , the amount of diesel required = 800 / 600 * 60 = 80 litres . however , the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity . i . e . , for instance , if the capacity of engine doubles , the diesel requirement will double too . therefore , with a 1200 cc engine , quantity of diesel required = 1200 / 800 * 80 = 120 litres . answer c
Answer: c
Python program:
a = 800 * 600
b = 60 / a
c = 800 * b
d = 1200 * c
Problem: what is the remainder when 8 ^ 714 is divided by 5 ?
Options: a ) 2 , b ) 3 , c ) 1 , d ) 0 , e ) 4
Rationale: "8 ^ 0 = 1 8 ^ 1 = 8 8 ^ 2 = 64 8 ^ 3 = 512 8 ^ 4 = 4096 8 ^ 5 = . . . . . 8 and so on after ignoring the first last - digit of 8 ^ 0 = 1 , in a recurring last - digit pattern of 8,4 , 2,6 , 8,4 , 2,6 . . . . 715 / 4 = 178 ( with a remainder 2 ) so the last number is a 4 . so when 8 ^ 714 is divided by 5 the remainder is 4 , ans = e"
Answer: e
Python program:
a = 5 / 2
b = 8 * 8
c = a - b
Problem: 20.20 / 2000 is equal to :
Options: a ) 1.01252677 , b ) 0.013466667 , c ) 0.125266677 , d ) 0.126256677 , e ) 0.12725776
Rationale: "20.20 / 2000 = 2525 / 200000 = 0.013466667 answer : b"
Answer: b
Python program:
a = 20 / 20
Problem: a bus trip of 450 miles would have taken 1 hour less if the average speed s for the trip had been greater by 5 miles per hour . what was the average speed s , in miles per hour , for the trip ?
Options: a ) 10 , b ) 40 , c ) 45 , d ) 50 , e ) 55
Rationale: "( s + 5 ) ( t - 1 ) = 450 s * t = 450 solving both the equations , we get : s = 45 or - 50 since speed should be positive , s = 45 hence , option c"
Answer: c
Python program:
a = 450 * 5
b = a * 4
c = 5 ** 2
d = b + c 
e = math.sqrt(d)
f = e - 5
g = f / 2
Problem: an equal number of desks and bookcases are to be placed along a library wall that is 15 meters long . each desk is 2 meters long , and each bookshelf is 1.5 meters long . if the maximum possible number of desks and bookcases are to be placed along the wall , then the space along the wall that is left over will be how many meters w long ?
Options: a ) 0.5 , b ) 1 , c ) 1.5 , d ) 2 , e ) 3
Rationale: let x be the number of desks and bookcases that are placed along the library wall . 2 x + 1.5 x < 15 3.5 x < 15 since x is a non negative integer , the largest number x can be is 4 . when x is 4 , the desks and bookcases take up 3.5 * 4 = 14 m , leaving 1 m of empty space . thus , i believe the answer is b ) 1
Answer: b
Python program:
a = 4 * 2
b = 4 * 1
c = a + b 
d = 15 - c
Problem: i flew my tiny seaplane to visit my mother . on the flight up , i flew at 110 mph . on the way home , i flew 72 mph . what was my average speed for the trip ?
Options: a ) 198 mph , b ) 91 mph , c ) 88 mph , d ) 100 mph , e ) 99 mph
Rationale: "( 110 mph + 72 mph ) / 2 = 91 mph correct answer is : b"
Answer: b
Python program:
a = 110 + 72 
b = a / 2
Problem: a starts business with rs . 35000 and after 5 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b ’ s contribution in the capital ?
Options: a ) 22378 , b ) 279889 , c ) 2788 , d ) 9000 , e ) 2882
Rationale: explanation : ratio in which profit is to be divided = 2 : 3 assume that b ' s contribution to the capital = b ⇒ 3500 × 12 : b × 7 = 2 : 3 ⇒ 3500 × 12 / 7 b = 2 / 3 ⇒ b = ( 3500 × 12 × 3 ) / ( 2 × 7 ) = 500 × 6 × 3 = 9000 answer : d
Answer: d
Python program:
a = 35000 * 12
b = a * 3
c = 12 - 5
d = c * 2
e = b / d
f = e / 10
Problem: if 45 - [ 28 - { 37 - ( 15 - * ) } ] = 55 , then * is equal to :
Options: a ) - 29 , b ) - 19 , c ) 16 , d ) 29 , e ) 39
Rationale: 45 - [ 28 - { 37 - ( 15 - * ) } ] = 55 = > 45 - [ 28 - { 37 - 15 + * } ] = 55 45 - [ 28 - 37 + 15 - * ] = 55 = > 45 [ 43 - 37 - * ] = 55 45 - [ 6 - * ] = 55 = > 45 - 6 + * = 55 39 + * = 55 = > * = 55 - 39 = 16 answer : c
Answer: c
Python program:
a = 28 - 37
b = a + 15 
c = 45 - b
d = 55 - c
Problem: find the fraction which has the same ratio to 2 / 5 that 3 / 8 has to 1 / 5
Options: a ) 1 / 15 , b ) 3 / 4 , c ) 5 / 8 , d ) 9 / 6 , e ) 8 / 7
Rationale: "p : 2 / 5 = 3 / 8 : 1 / 5 as the product of the means is equal to the product of the extremes . p * 1 / 5 = 2 / 5 * 3 / 8 p * 1 / 5 = 6 / 40 p = 3 / 4 = > p = 3 / 4 answer : b"
Answer: b
Python program:
a = 3 / 8
b = 1 / 5
c = a / b
d = 2 / 5
e = c * d
Problem: in a class of 27 students in an examination in maths 5 students scored 95 marks each , 3 get zero each and the average of the rest was 45 . what is the average of the whole class ?
Options: a ) a ) 47 , b ) b ) 45.6 , c ) c ) 44 , d ) d ) 48 , e ) e ) 49.3
Rationale: explanation : total marks obtained by a class of 25 students = 5 * 95 + 3 * 0 + 19 * 45 = 1330 average marks of whole class = 1330 / 27 = 49.3 answer : option e
Answer: e
Python program:
a = 3 + 5 
b = 27 - a
c = 45 * b
d = 95 * 5
e = c + d 
f = e / 27
Problem: a man sitting in a train which is traveling at 56 kmph observes that a goods train , traveling in opposite direction , takes 15 seconds to pass him . if the goods train is 410 m long , find its speed
Options: a ) 52 kmph , b ) 56 kmph , c ) 58 kmph , d ) 42 kmph , e ) 72 kmph
Rationale: "explanation : relative speed = 410 / 15 m / sec = ( ( 410 / 15 ) × ( 18 / 5 ) ) kmph = 98 kmph . speed of goods train = ( 98 - 56 ) kmph = 42 kmph answer : option d"
Answer: d
Python program:
a = 410 / 15
b = a * const_3_6
c = b - 56
Problem: a trader marked the selling price of an article at 12 % above the cost price . at the time of selling , he allows certain discount and suffers a loss of 1 % . he allowed a discount of :
Options: a ) 10 % , b ) 10.5 % , c ) 11 % , d ) 12.5 % , e ) 9.8
Rationale: "sol . let c . p . = rs . 100 . then , marked price = rs . 110 , s . p . = rs . 99 . ∴ discount % = [ 11 / 112 * 100 ] % = 9.8 % answer e"
Answer: e
Python program:
a = 2 + 3 
b = a * 2
c = b + 1 
d = 100 + 12 
e = c / d
f = 100 * e
Problem: in a river flowing at 2 km / hr , a boat travels 64 km upstream and then returns downstream to the starting point . if its speed in still water be 6 km / hr , find the total journey time .
Options: a ) 10 hours , b ) 12 hours , c ) 14 hours , d ) 24 hours , e ) none of these
Rationale: "explanation : speed of the boat = 6 km / hr speed downstream = ( 6 + 2 ) = 8 km / hr speed upstream = ( 6 - 2 ) = 4 km / hr distance travelled downstream = distance travelled upstream = 64 km total time taken = time taken downstream + time taken upstream = ( 64 / 8 ) + ( 64 / 4 ) = = 24 hr . answer : option d"
Answer: d
Python program:
a = 6 - 2
b = 64 / a
c = 6 + 2 
d = 64 / c
e = b + d
Problem: ( 128.5 x 32 ) + ( 13.8 x 30 ) = ? x 25
Options: a ) 524.48 , b ) 556.02 , c ) 574.36 , d ) 181.04 , e ) 595.46
Rationale: "explanation : ? = ( 128.5 x 32 ) + ( 13.8 x 30 ) / 25 = 4112 + 414 / 25 = 181.04 answer : option d"
Answer: d
Python program:
a = 4 + 1 
b = a ** 4
c = 128 * 5
Problem: if ( m - 8 ) is a factor of m ^ 2 - pm - 24 , then p =
Options: a ) 3 , b ) 5 , c ) 6 , d ) 11 , e ) 16
Rationale: "( m - 8 ) ( m - a ) = m ^ 2 - pm - 24 a = - 3 p = 8 + a = 5 = b"
Answer: b
Python program:
a = 24 / 8
b = 8 - a
Problem: you and your friend spent a total of $ 15 for lunch . your friend spent $ 1 more than you . how much did your friend spend on their lunch ?
Options: a ) $ 9 , b ) $ 8 , c ) $ 4 , d ) $ 6 , e ) $ 5
Rationale: "my lunch = l , my friends lunch = l + 1 ( l ) + ( l + 1 ) = 15 l + l + 1 - 1 = 15 - 1 2 l = 14 l = 7 my friends lunch l + 1 = 7 + 1 = $ 8 , the answer is b"
Answer: b
Python program:
a = 15 - 1
b = a / 2
c = b + 1
Problem: how many multiples of 4 are there between 8 and 160 ?
Options: a ) 28 , b ) 37 , c ) 32 , d ) 35 , e ) 39
Rationale: "it should be mentioned whether 8 and 160 are inclusive . if 8 and 160 are inclusive , then the answer is ( 160 - 8 ) / 4 + 1 = 39 . if 8 and 160 are not inclusive , then the answer is ( 156 - 12 ) / 4 + 1 = 37 . since oa is b , then we have not inclusive case ."
Answer: b
Python program:
a = 160 - 8
b = a / 4
c = b + 1
Problem: √ 7 percent of 7 √ 7 =
Options: a ) 0.55 , b ) 0.96 , c ) 0.1 , d ) 0.45 , e ) 0.6
Rationale: "the other solutions are great , but here ' s one more approach . first , we scan the answer choices to see that they are quite spread apart . this means we can also use someapproximation all test - takers must memorize the following approximations : √ 2 ≈ 1.4 √ 3 ≈ 1.7 √ 5 ≈ 2.2 √ 6 ≈ 2.4 √ 7 ≈ 2.6 so , √ 7 percent of 7 √ 7 ≈ 2.6 percent of ( 7 ) ( 2.6 ) ≈ ( 2.6 / 100 ) ( 18.2 ) ≈ 47.32 / 100 ≈ 0.47 check the answer choices to see that d is the only answer that ' s close . answer : d"
Answer: d
Python program:
a = math.sqrt(7)
b = math.sqrt(7)
c = a * b
d = c * 7
e = d / 100
Problem: harold works at a resort from the beginning of march to the end of september . during the month of august this past year , he made 7 times the average ( arithmetic mean ) of his monthly totals in tips for the other months . his total tips for august were what fraction of his total tips for all of the months he worked ?
Options: a ) 1 / 3 , b ) 2 / 5 , c ) 3 / 7 , d ) 1 / 2 , e ) 7 / 13
Rationale: "the time from beginning of march to the end of september is 7 months . if x is the average monthly tip for all months other than august then his august month tip will be 7 * x his total tip for the 7 months = 6 * ( average tip for the months other than august ) + 7 x = 13 x august tips as a fraction of total tips = 7 x / 13 x = 7 / 13 . so e"
Answer: e
Python program:
a = 7 * 1
b = 7 * 1
c = 7 * 1
d = b + c 
e = a / d
Problem: maxwell leaves his home and walks toward brad ' s house . one hour later , brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 54 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h . what is the total time it takes maxwell before he meets up with brad ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "total distance = 54 kms maxwell speed = 4 kms / hr maxwell travelled for 1 hour before brad started , therefore maxwell traveled for 4 kms in 1 hour . time taken = total distance / relative speed total distance after brad started = 50 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken to meet brad after brad started = 50 / 10 = 5 hrs distance traveled by maxwell = maxwell ' s speed * time taken = 4 * 5 = 20 + 4 = 24 kms . . . therefore total time taken by maxwell to meet brad = distance travelled by maxwell / maxwell ' s speed = 24 / 4 = 6 hrs . . . answer d alternatively . . . total time taken by maxwell to meet brad = maxwell started 1 hour earlier to brad + total time taken to meet brad after brad started = 1 + 5 = 6 hrs . . . answer d"
Answer: d
Python program:
a = 54 + 6 
b = 4 + 6 
c = a / b
Problem: tom read a book containing 480 pages by reading the same number of pages each day . if he would have finished the book 5 days extra by reading 10 pages a day less , how many days did tom spend reading the book ?
Options: a ) 13 , b ) 15 , c ) 14 , d ) 13.19 , e ) 16
Rationale: "actually u can set up 2 equation p - - stands for the pages d - - stands for the days 1 ) p * d = 480 ( we want to find the days , sop = 480 / d ) 2 ) ( p - 10 ) ( d + 5 ) = 480 = > pd + 5 p - 10 d - 50 = 480 as the 1 ) stated u can put 1 ) into 2 ) = > 480 + 5 p - 10 d - 50 = 480 = > 5 p - 10 d = 50 put the bold one into it = > 5 * 480 / d - 10 d = 50 the we get the final equation 2400 / d - 10 d = 50 = > d ^ 2 + 5 d - 240 = 0 ( d - 15 ) ( d + 10 ) = 0 so d = 13.19 days . ans : d"
Answer: d
Python program:
a = 10 * 5
b = a * 4
c = 10 ** 2
d = b + c 
e = math.sqrt(d)
f = e - 10
g = f / 2
Problem: what are the total number of divisors of 600 ( including 1 and 600 ) ?
Options: a ) 4 , b ) 24 , c ) 40 , d ) 16 , e ) 20
Rationale: write the prime factorization . 600 = ( 2 ^ 3 ) ( 3 ^ 1 ) ( 5 ^ 2 ) the number of divisors ( including 1 and the number itself ) is the product of one plus the exponents . ( 3 + 1 ) ( 1 + 1 ) ( 2 + 1 ) = 24 answer : b
Answer: b
Python program:
a = const_0_25 * 100
b = 600 / a
Problem: the overall ages of kumar , hathim and rahul is 93 years . 1 decade ago , the ratio of their ages was 2 : 3 : 4 . what is the current age of rahul ?
Options: a ) 38 , b ) 37 , c ) 34 , d ) 35 , e ) 33
Rationale: a 38 if the ages of kumar , hathim and rahul 1 decade ago be 2 a , 3 a and 4 a years correspondingly then , ( 2 a + 10 ) + ( 3 a + 10 ) + ( 4 a + 10 ) = 93 9 a = 93 - 30 9 a = 63 a = 7 rahul ’ s current age = ( 4 a + 10 ) = 38 years .
Answer: a
Python program:
a = 93 / 3
b = 93 / 3
c = b / 2
d = a + c 
e = d - 10
Problem: a gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same . if there are 2 rows or 7 rows or 9 rows , then no tree will be left . find the least number of trees required
Options: a ) 22 , b ) 60 , c ) 126 , d ) 76 , e ) 21
Rationale: "explanation : the least number of trees that are required = lcm ( 2 , 7 , 9 ) = 126 answer : c"
Answer: c
Python program:
a = 9 * 7
b = a * 2
c = b / 2
Problem: set # 1 = { a , b } set # 2 = { k , l , m , n , o , p } there are these two sets of letters , and you are going to pick exactly one letter from each set . what is the probability of picking at least one vowel ?
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 7 / 12 , d ) 2 / 3 , e ) 5 / 6
Rationale: so not a vowel in set - 1 : 1 / 2 and not a vowel in ser - 2 : 5 / 6 now , 1 / 2 ∗ 5 / 6 = 5 / 12 this is for not a vowel . then for at least one vowel will be = 1 − 5 / 12 = 7 / 12 answer will be c .
Answer: c
Python program:
a = 1 / 2
b = 4 + 1 
c = 4 + 1 
d = c + 1 
e = b / d
f = a * e
g = 1 - f
Problem: in a rectangular coordinate system , what is the area of a rectangle whose vertices have the coordinates ( - 7 , 1 ) , ( 1 , 1 ) , ( 1 , - 6 ) and ( - 7 , - 6 ) ?
Options: a ) 112 , b ) 64 , c ) 42 , d ) 24 , e ) 56
Rationale: "length of side 1 = 7 + 1 = 8 length of side 2 = 6 + 1 = 7 area of rectangle = 7 * 8 = 56 e is the answer"
Answer: e
Python program:
a = 7 + 1 
b = 1 + 6 
c = a * b
Problem: in digging a pond 20 m * 12 m * 5 m the volumes of the soil extracted will be ?
Options: a ) 3387 , b ) 1000 , c ) 1200 , d ) 2787 , e ) 1121
Rationale: "20 * 12 * 5 = 1200 answer : c"
Answer: c
Python program:
a = 20 * 12
b = a * 5
Problem: how many times digit 7 is used while writing numbers from 1 to 300 ?
Options: a ) 28 , b ) 42 , c ) 41 , d ) 35 , e ) 49
Rationale: "in 1 to 100 their are 14 seven ' s in 100 to 200 their are 14 seven ' s in 200 to 300 their are 14 seven ' s so total answer is 42 seven ' s correct option : b"
Answer: b
Python program:
a = 300 - 1
b = a / 10
c = 10 + 1 
d = 10 + 1 
e = c * d
f = b + e 
g = 7 * 2
h = f + g
Problem: define a = the sum of digits of the number 7 ^ 100 and b = the sum of the digits of a . what is the sum of the digits of b ?
Options: a ) 7 , b ) 16 , c ) 10 , d ) 11 , e ) can not be determined
Rationale: following approach will take you only couple of sec . \ ( 7 ^ { 100 } = ( 7 ^ { 50 } ) ^ 2 \ ) the sum of digits ( digital root ) of a perfect square can only be 1 , 4 , 7 or 9 . for example \ ( 7 ^ 2 = 49 \ ) = > dr = 4 + 9 = 13 = > 1 + 3 = 4 and etc . checking available options . answer a .
Answer: a
Python program:
a = 2 + 4 
b = 1 + a
Problem: an optometrist charges $ 150 per pair for soft contact lenses and $ 85 per pair for hard contact lenses . last week she sold 5 more pairs of soft lenses than hard lenses . if her total sales for pairs of contact lenses last week were $ 1,925 , what was the total number of pairs of contact lenses that she sold ?
Options: a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 19
Rationale: "( x + 5 ) * 150 + x * 85 = 1925 = > x = 5 total lens = 5 + ( 5 + 5 ) = 15 answer c"
Answer: c
Python program:
a = 4 * 100
b = 5 * 10
c = a + b 
d = c + 5 
e = d + 1000 
f = 150 * 5
g = e - f
h = 150 + 85 
i = g / h
j = i * 2
k = j + 5
Problem: how many zeros does 1000 ! end with ?
Options: a ) 20 o , b ) 24 o , c ) 249 , d ) 30 o , e ) 325
Rationale: "according to above 1000 ! has 1000 / 5 + 1000 / 25 + 1000 / 125 + 1000 / 625 = 200 + 40 + 8 + 1 = 249 trailing zeros . answer : c"
Answer: c
Python program:
a = 4 + 1 
b = 1000 / a
c = 4 + 1 
d = 1000 - c
e = 4 + 1 
f = e ** 2
g = d / f
h = b + g 
i = 4 + 1 
j = 1000 - i
k = 4 + 1 
l = k ** 3
m = j / l
n = h + m
Problem: train e and f , 455 miles apart , are traveling toward each other at constant rates and in the same time zone . if train e left at 4 pm traveling at a speed of 60 miles per hour , and train f left at 5 : 45 pm and traveling at 45 miles per hour , then at what time would they pass each other ?
Options: a ) 9.03 pm , b ) 9.05 pm , c ) 9.07 pm , d ) 9.08 pm , e ) 9.10 pm
Rationale: first , since e has a headstart then in that 1 hr 45 min or 1.75 hrs he travels 105 miles then remaining distance to be traveled will be 455 - 105 = 350 miles now , using relative rates ( 105 ) ( t ) = 350 this gives 10 / 3 hours now 5.45 pm + 10 / 3 hours gives us 9.05 pm hence answer is b
Answer: b
Python program:
a = 455 / 60
b = 455 / 45
c = a + b 
d = c / 2
Problem: in the xy - plane , the point ( 1 , 3 ) is the center of a circle . the point ( - 2 , 3 ) lies inside the circle and the point ( 1 , - 2 ) lies outside the circle . if the radius r of the circle is an integer , then r =
Options: a ) 6 , b ) 5 , c ) 4 , d ) 3 , e ) 2
Rationale: "an easy way to solve this question will be just to mark the points on the coordinate plane . you ' ll see that the distance between the center ( 1 , 3 ) and the point inside the circle ( - 2 , 3 ) is 3 units ( both points are on y = 3 line so the distance will simply be 1 - ( - 2 ) = 3 ) so the radius must be more than 3 units . the distance between the center ( 1,3 ) and the point outside the circle ( 1 , - 2 ) is 5 units ( both points are on x = 1 line so the distance will simply be 3 - ( - 2 ) = 5 ) so the radius must be less than 5 units , which implies 3 < r < 5 , thus as r is an integer then r = 4 . answer : c ."
Answer: c
Python program:
a = 2 + 0 
b = a + 3
Problem: the ratio by weight , measured in pounds , of books to clothes to electronics in a suitcase initially stands at 7 : 5 : 3 . someone removes 5 pounds of clothing from the suitcase , thereby doubling the ratio of books to clothes . how many pounds do the electronics in the suitcase weigh ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "the weights of the items in the suitcase are 7 k , 5 k , and 3 k . if removing 5 pounds of clothes doubles the ratio of books to clothes , then 5 pounds represents half the weight of the clothes . 2.5 k = 5 pounds and then k = 2 pounds . the electronics weigh 3 ( 2 ) = 6 pounds . the answer is d ."
Answer: d
Python program:
a = 7 + 5 
b = a + 3 
c = b * 5
d = negate / (
e = 7 + 5 
f = e + 3 
g = f * 2
h = 7 + 5 
i = h + 3 
j = i * 5
k = g - j
l = 3 * d
Problem: when 2 / 9 of the votes on a certain resolution have been counted , 3 / 4 of those counted are in favor of the resolution . what fraction w of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution ?
Options: a ) 11 / 14 , b ) 13 / 18 , c ) 4 / 7 , d ) 3 / 7 , e ) 3 / 14
Rationale: "if we use variable for total votes there will be too many fractions to manipulate with , so pick some smart # : let set total # of votes is 18 . 2 / 9 of the votes on a certain resolution have been counted - - > 4 counted and 18 - 4 = 14 votes left to be counted ; 3 / 4 of those counted are in favor of the resolution - - > 3 in favor and 1 against ; ratio of those who voted against to those who voted for to be 2 to 1 there should be total of 18 * 2 / 3 = 12 people who voted against , so in the remaining 14 votes there should be 12 - 1 = 11 people who voted against . thus w = 11 / 14 of the remaining votes must be against . answer : a ."
Answer: a
Python program:
a = 1 + 2 
b = 2 / a
c = 2 / 9
d = 2 / 9
e = 3 / 4
f = d * e
g = c - f
h = b - g
i = 9 - 2
j = i / 9
k = h / j
Problem: the total age of a and b is 17 years more than the total age of b and c . c is how many years younger than a ?
Options: a ) 12 , b ) 27 , c ) 21 , d ) 17 , e ) 11
Rationale: "( a + b ) - ( b + c ) = 17 a - c = 17 . c is younger than a by 17 years . answer : d"
Answer: d
Python program:
a = 17 * 1
Problem: a total of $ 20,000 was invested in two certificates of deposit at simple annual interest rates of 3 percent and 6 percent , respectively . if the total interest on the two certificates was $ 1,440 at the end of one year , what fractional part of the $ 20.000 was invested at the higher rate ?
Options: a ) 3 / 8 , b ) 21 / 25 , c ) 1 / 2 , d ) 3 / 5 , e ) 3 / 4
Rationale: "x * 3 / 100 * 1 + ( 20000 - x ) * 8 / 100 * 1 = 1440 3 x - 8 x = 144000 - 160000 = > - 5 x = - 16000 = > x = 32000 so 16800 / 20000 = 21 / 25 answer - b"
Answer: b
Python program:
a = 1 + 4 
b = 2 * a
c = 100 * b
d = 4 * 100
e = c + d 
f = 1 + 4 
g = 2 * f
h = 4 * g
i = e + h 
j = i / 20
k = j / 6
l = k + 6 
m = l - 3
n = m / 20
Problem: if a = ( 10 ^ 10 ) - 47 , what is the sum of all the digit of a ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 80
Rationale: start small and check for any pattern : 10 ^ 2 - 47 = 53 - > number of digits = power of 10 ; number of 9 s = ( power of 10 ) - 2 ; 53 is the last 2 digits 10 ^ 3 - 47 = 953 - > number of digits = power of 10 ; number of 9 s = ( power of 10 ) - 2 ; 53 is the last 2 digits . . . extrapolate 10 ^ 10 - 47 - > number of digits = 10 ; number of 9 s = 8 ; 53 will be the last 2 digits sum , a = 9 * 8 + 5 + 3 = 80 . answer ( e ) .
Answer: e
Python program:
a = 10 * 10
b = a + const_60 
c = b / 2
Problem: two sets of 7 consecutive positive integers have exactly one integer in common . the sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set ?
Options: a ) 24 , b ) 17 , c ) 28 , d ) 42 , e ) it can not be determined from the information given .
Rationale: a = ( 1 , 2,3 , 4,5 , 6,7 ) , sum of this = 28 b = ( 7 , 8,9 , 10,11 , 12,13 ) , sum of this = 70 the differenct between 70 - 28 = 42 hence , 42 is the answer i . e . d
Answer: d
Python program:
a = 7 * 10
b = 4 * 7
c = a - b