euclaise/mathqa_programs huggingface dataset:
Problem: a snail , climbing a 20 feet high wall , climbs up 4 feet on the first day but slides down 2 feet on the second . it climbs 4 feet on the third day and slides down again 2 feet on the fourth day . if this pattern continues , how many days will it take the snail to reach the top of the wall ?
Options: a ) 12 , b ) 16 , c ) 17 , d ) 20 , e ) 21
Rationale: "total transaction in two days = 4 - 2 = 2 feet in 16 days it will climb 16 feet on the 17 th day , the snail will climb 4 feet , thus reaching the top therefore , total no of days required = 17 answer : c"
Answer: c
Python program:
a = 20 - 4
Problem: if n is the smallest integer such that 432 times n is the square of an integer , what is the value of n ?
Options: a ) 2
b ) 3
c ) 6
d ) 12
e ) 24
Rationale: the prime factorization of a square has to have even powers of all its prime factors . if the original number has a factor , say of 7 , then when it ’ s squared , the square will have a factor of 7 ^ 2 . another way to say that is : any positive integer all of whose prime factors have even powers must be a perfect square of some other integer . look at the prime factorization of 432 432 = ( 2 ^ 4 ) * ( 3 ^ 3 ) the factor of 2 already has an even power — - that ’ s all set . the factor of 3 currently has an odd power . if n = 3 , then 432 * n would have an even power of 2 and an even power of 3 ; therefore , it would be a perfect square . thus , n = 3 is a choice that makes 432 * n a perfect square . answer : b .
Answer: b
Python program:
a = 432 / 2
b = a / 2
c = b / 2
d = c / 2
e = d / 3
f = e / 3
Problem: the average of the marks of 12 students in a class is 36 . if the marks of each student are doubled , find the new average ?
Options: a ) 72 , b ) 23 , c ) 29 , d ) 26 , e ) 13
Rationale: "sum of the marks for the 12 students = 12 * 36 = 432 . the marks of each student are doubled , the sum also will be doubled . the new sum = 432 * 2 = 864 . so , the new average = 864 / 12 = 72 . answer : a"
Answer: a
Python program:
a = 36 * 2
Problem: a trader sells 85 meters of cloth for rs . 8925 at the profit of rs . 20 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) 21 , b ) 28 , c ) 90 , d ) 85 , e ) 11
Rationale: "explanation : sp of 1 m of cloth = 8925 / 85 = rs . 105 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 105 - rs . 20 = rs . 85 . answer : d"
Answer: d
Python program:
a = 8925 / 85
b = a - 20
Problem: if the simple interest on $ 1500 increase by $ 20 , when the time increase by 2 years . find the rate percent per annum .
Options: a ) 0.6 % , b ) 0.5 % , c ) 0.1 % , d ) 0.2 % , e ) 0.7 %
Rationale: applying the above formula , we have 20 = 1500 * r * 2 / 100 r = 20 * 100 / 1500 * 2 = 0.7 % . answer is e
Answer: e
Python program:
a = 20 / 2
b = a / 1500
c = b * 100
Problem: a man sells an article at a profit of 25 % . if he had bought it at 20 % less and sold it for rs . 8.40 less , he would have gained 30 % . find the cost of the article .
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: "let c . p = 100 gain = 25 % s . p = 125 supposed c . p = 80 gain = 30 % s . p = ( 130 * 80 ) / 100 = 104 diff = ( 125 - 104 ) = 21 diff 21 when c . p = 100 then diff 8.40 when c . p = ( 100 * 8.40 ) / 21 = 40 answer : b"
Answer: b
Python program:
a = 8 * 40
b = 25 + 100 
c = 30 + 100 
d = 100 - 20
e = c * d
f = e / 100
g = b - f
h = a / g
Problem: the sum of two numbers is 29 and the difference of their squares is 145 . the difference between the number is
Options: a ) 13 , b ) 5 , c ) 8 , d ) 11 , e ) 12
Rationale: "explanation : let the numbers be x and y . we know that , ( x − y ) = x 2 − y 2 / ( x + y ) = 145 / 29 = 5 correct option : b"
Answer: b
Python program:
a = 29 ** 2
b = 145 - a
c = b / 2
Problem: the cube root of what integer power of 2 is closest to 50 ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20
Rationale: integer powers of 2 = 2 , 2 ^ 2 , 2 ^ 3 , 2 ^ 4 , 2 ^ 5 , 2 ^ 6 , 2 ^ 7 etc . let , cube root of x is closest to 50 i . e . x is closest to cube of 50 = 50 * 50 * 50 = 125000 but x must be equivalent to an integer power of 2 2 ^ 10 = 1024 2 ^ 7 = 128 i . e . 2 ^ 17 = 128 * 1024 = 128000 ( approx . ) i . e . 2 ^ 18 = 256 * 1024 = 256000 ( approx . ) i . e . 2 ^ 16 = 64 * 1024 = 64000 ( approx . ) i . e . 2 ^ 17 which is closest to 125000 i . e . integer power of 2 must be 7 answer : option b
Answer: b
Python program:
a = 50 / 2
b = 4 + 4 
c = a - b
Problem: a watch was sold at a loss of 10 % . if it was sold for rs . 190 more , there would have been a gain of 4 % . what is the cost price ?
Options: a ) s . 1000 , b ) s . 1009 , c ) s . 1007 , d ) s . 1357.1 , e ) s . 1002
Rationale: "explanation : 90 % 104 % - - - - - - - - 14 % - - - - 190 100 % - - - - ? = > rs . 1357.1 answer : d"
Answer: d
Python program:
a = 190 * 100
b = 100 + 4 
c = 100 - 10
d = b - c
e = a / d
Problem: if 3 ^ x * 4 ^ y = 19683 and x – y = 9 , then x = ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: since 19,683 is an odd number , it is not a multiple of 4 . this means that y must equal zero . since x - y = 9 and y = 0 , then x = 9 . the answer is b .
Answer: b
Python program:
a = 3 ** 9
b = a / 19683
c = math.log(b)
d = 3 * 4
e = math.log(d)
f = c / e
g = 9 - f
Problem: in triangle pqr , the angle q = 90 degree , pq = 2 cm , qr = 8 cm . x is a variable point on pq . the line through x parallel to qr , intersects pr at y and the line through y , parallel to pq , intersects qr at z . find the least possible length of xz
Options: a ) 1.6 cm , b ) 2.4 cm , c ) 4.8 cm , d ) 2.16 cm , e ) 3.2 cm
Rationale: "look at the diagram below : now , in case when qy is perpendicular to pr , two right triangles pqr and pqy are similar : qy : qp = qr : pr - - > qy : 2 = 8 : 10 - - > qy = 1.6 . answer : a ."
Answer: a
Python program:
a = 2 * 8
b = a / 10
Problem: 5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 210 only . men â € ™ s wages are ?
Options: a ) 6 rs , b ) 2 rs , c ) 4 rs , d ) 9 rs , e ) 14 rs
Rationale: "5 m = xw = 8 b 5 m + xw + 8 b - - - - - 210 rs . 5 m + 5 m + 5 m - - - - - 210 rs . 15 m - - - - - - 210 rs . = > 1 m = 14 rs . answer : e"
Answer: e
Python program:
a = 3 * 5
b = 210 / a
Problem: in may mrs lee ' s earnings were 60 percent of the lee family ' s total income . in june mrs lee earned 10 percent more than in may . if the rest of the family ' s income was the same both months , then , in june , mrs lee ' s earnings were approximately what percent of the lee family ' s total income ?
Options: a ) 62 % , b ) 68 % , c ) 72 % , d ) 76 % , e ) 80 %
Rationale: "let in may lee family ' s total income = 100 in may mrs lee ' s income = 60 in may rest of the family ' s income = 40 in june mrs lees income = 60 * 110 / 100 = 66 in june total income = 66 + 40 = 106 % of mrs lee ' s income = 66 / 106 = 62.26 ( a )"
Answer: a
Python program:
a = 100 + 10 
b = 100 + 10 
c = b + 100 
d = a / c
e = d * 100
Problem: express a speed of 60 kmph in meters per second ?
Options: a ) 10 mps , b ) 16.67 mps , c ) 97.67 mps , d ) 17.67 mps , e ) 18 mps
Rationale: "60 * 5 / 18 = 16.67 mps answer : b"
Answer: b
Python program:
a = const_0_2778 * 60
Problem: a person decided to build a house in 100 days . he employed 100 men in the beginning and 100 more after 50 days and completed the construction in stipulated time . if he had not employed the additional men , how many days behind schedule would it have been finished ?
Options: a ) 40 , b ) 80 , c ) 50 , d ) 60 , e ) 50
Rationale: 200 men do the rest of the work in 100 - 50 = 50 days 100 men can do the rest of the work in 50 * 200 / 100 = 100 days required number of days = 100 - 50 = 50 days answer is c
Answer: c
Python program:
a = 100 - 50
Problem: how many multiples of 6 are there between 30 and 140 , 30 and 140 inclusive ?
Options: a ) 18 , b ) 16 , c ) 17 , d ) 19 , e ) 15
Rationale: "6 multiples are . . . 30 , 36,42 , 48,54 , 60,66 , 72,78 , 84,90 , 96,102 , 108,114 , 120,126 , 132,138 , . . . , . . . , the answer is = 19 answer is d"
Answer: d
Python program:
a = 140 - 30
b = a / 6
c = b + 1
Problem: how many seconds will a 400 metre long train take to cross a man running with a speed of 6 km / hr in the direction of the moving train if the speed of the train is 46 km / hr ?
Options: a ) 25 , b ) 30 , c ) 40 , d ) 45 , e ) 36
Rationale: "explanation : speed of train relatively to man = ( 46 - 6 ) km / hr = 40 km / hr = ( 40 x 5 / 18 ) m / sec = 11.11 m / sec time taken to pass the man = ( 400 / 11.11 ) sec = 36 sec . answer : e"
Answer: e
Python program:
a = 46 - 6
b = const_0_2778 * a
c = 400 / b
Problem: if x + y = 24 , x - y = 40 , for integers of x and y , x = ?
Options: a ) 20 , b ) 23 , c ) 25 , d ) 32 , e ) 42
Rationale: "x + y = 24 x - y = 40 2 x = 64 x = 32 answer is d"
Answer: d
Python program:
a = 24 + 40 
b = a / 2
Problem: a car traveling at a certain constant speed takes 12 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?
Options: a ) 60 , b ) 72 , c ) 72.5 , d ) 73 , e ) 73.5
Rationale: "many approaches are possible , one of them : let the distance be 1 kilometer . time to cover this distance at 75 kilometers per hour is 1 / 75 hours = 3,600 / 75 seconds = 48 seconds ; time to cover this distance at regular speed is 48 + 12 = 60 seconds = 60 / 3,600 hours = 1 / 60 hours ; so , we get that to cover 1 kilometer 1 / 60 hours is needed - - > regular speed 60 kilometers per hour ( rate is a reciprocal of time or rate = distance / time ) . answer : a"
Answer: a
Python program:
a = 1 / 75
b = 3600 * a
c = b + 12 
d = c / 3600
e = 1 / d
Problem: if 222 = 6 333 = 12 444 = 20 then , 555 = ? ?
Options: a ) 30 , b ) 35 , c ) 40 , d ) 45 , e ) 50
Rationale: 222 = 2 * 2 + 2 = 6 333 = 3 * 3 + 3 = 12 444 = 4 * 4 + 4 = 20 555 = 5 * 5 + 5 = 30 answer : a
Answer: a
Python program:
a = 2 + 3 
b = a * 6
Problem: if n = 6 ^ 11 – 6 , what is the units digit of n ?
Options: a ) 0 , b ) 1 , c ) 4 , d ) 6 , e ) 8
Rationale: always divide the power ( incase 11 ) by 4 and use the remainder as the new power . the question now becomes 6 ^ 3 - 6 . now 6 ^ 3 has last digit 6 . , we subtract 6 from 6 = 0 is the answer . option a
Answer: a
Python program:
a = math.log(6)
b = 6 ** 11
c = math.log(b)
d = a / c
Problem: a certain industrial loom weaves 0.128 meters of cloth every second . approximately how many seconds will it take for the loom to weave 25 meters of cloth ?
Options: a ) 205 , b ) 200 , c ) 180 , d ) 195 , e ) 175
Rationale: "explanation : let the required number of seconds be x more cloth , more time , ( direct proportion ) hence we can write as ( cloth ) 0.128 : 25 : : 1 : x ⇒ 0.128 x = 25 ⇒ x = 25 / 0.128 = 25000 / 128 = 3125 / 16 ≈ 195 answer : option d"
Answer: d
Python program:
a = 25 / 0
Problem: a man goes from a to b at a speed of 14 kmph and comes back to a at a speed of 10 kmph . find his average speed for the entire journey ?
Options: a ) 11.6 kmph , b ) 12.9 kmph , c ) 12.8 kmph , d ) 11.9 kmph , e ) 12.6 kmph
Rationale: "distance from a and b be ' d ' average speed = total distance / total time average speed = ( 2 d ) / [ ( d / 14 ) + ( d / 10 ] = ( 2 d ) / [ 12 d / 70 ) = > 11.6 kmph . answer : a"
Answer: a
Python program:
a = 14 + 10 
b = a / 2
Problem: p software has coding line 5 % more than n , n software has coding line 4 / 20 more than m . m software has 80 lines of coding . find p lines .
Options: a ) 101 , b ) 107 , c ) 108 , d ) 109 , e ) 110
Rationale: "m s / w has 80 line of code n s / w has = 80 + 80 * 4 / 20 = 96 line of code p s / w 5 % more n ' code 96 + 4.8 = 100.8 or 101 line of code answer : a"
Answer: a
Python program:
a = 80 / 20
b = 80 + a
Problem: if f ( x ) = 5 - 2 x , then f - 1 ( - 3 ) = ?
Options: a ) 1 , b ) 8 , c ) 6 , d ) 4 , e ) 3
Rationale: find f - 1 ( x ) and then find f - 1 ( - 3 ) y = 5 - 2 x , given x = 5 - 2 y , interchange x and y 2 y = 5 - x , y = log 2 ( 5 - x ) , solve for y f - 1 ( x ) = log 2 ( 5 - x ) , inverse function f - 1 ( - 3 ) = log 2 ( 5 + 3 ) = log 2 ( 23 ) = 3 correct answer e
Answer: e
Python program:
a = 3 - 1
b = a / 2
c = b * 2
d = 5 - c
Problem: the weight of every type a widget is the same , the weight of every type b widget is the same , and the weight of every type c widget is the same . if the weight of 7 type a widgets is equal to the weight of 2 type b widgets , and the weight of 4 type b widgets is equal to the weight of 7 type c widgets . what is the ratio of the total weight of 1 type a widget and 1 type b widget , to the total weight of 1 type b widget and 1 type c widget ?
Options: a ) 3 : 5 , b ) 5 : 7 , c ) 7 : 9 , d ) 9 : 11 , e ) 11 : 13
Rationale: "4 b = 7 c and so b = 7 c / 4 7 a = 2 b and so a = 2 b / 7 = c / 2 a + b = c / 2 + 7 c / 4 = 9 c / 4 b + c = 7 c / 4 + c = 11 c / 4 the ratio of a + b : b + c = 9 : 11 the answer is d ."
Answer: d
Python program:
a = 7 / 2
b = 1 + a 
c = 7 / 2
d = 4 / 2
e = c + d 
f = b / e
Problem: ( 500 + 200 ) × 4 × ( 3 + 2 ) = ?
Options: a ) 2902 , b ) 14000 , c ) 8402 , d ) 16800 , e ) none of these
Rationale: "( 500 + 200 ) × 4 × ( 3 + 2 ) = ? or , ? = 700 × 4 × 5 = 14000 answer b"
Answer: b
Python program:
a = 500 + 200 
b = a / 4
Problem: how many seconds will a 700 meter long train moving with a speed of 63 km / hr take to cross a man walking with a speed of 3 km / hr in the direction of the train ?
Options: a ) 48 , b ) 36 , c ) 42 , d ) 11 , e ) 18
Rationale: "explanation : here distance d = 700 mts speed s = 63 - 3 = 60 kmph = 60 x 5 / 18 m / s time t = = 42 sec . answer : c"
Answer: c
Python program:
a = 63 - 3
b = a * const_0_2778
c = 700 / b
Problem: joan and karl each bought a telescopes and the sum of their purchases was $ 400 . if twice of what joan paid was $ 74 more than what karl paid , what did joan pay for her telescope ?
Options: a ) $ 150 , b ) $ 152 , c ) $ 154 , d ) $ 156 , e ) $ 158
Rationale: j + k = 400 so k = 400 - j 2 j = k + 74 2 j = ( 400 - j ) + 74 3 j = 474 j = 158 the answer is e .
Answer: e
Python program:
a = 400 * 2
b = a - 74
c = b / 3
d = 400 - c
Problem: how many odd prime numbers are there less than 150 ?
Options: a ) 24 , b ) 34 , c ) 44 , d ) 54 , e ) 64
Rationale: "odd prime number less than 150 : 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , 59 , 61 , 67 , 71 , 73 , 79 , 83 , 89 , 97 , 101 , 103 , 107 , 109 , 113 , 127 , 131 , 137 , 139 , 149 there is 34 the odd prime number answer is b"
Answer: b
Python program:
a = 150 - 100
b = a + 4
Problem: a can do a piece of work in 8 days . he works at it for 4 days and then b finishes it in 6 days . in how many days can a and b together finish the work ?
Options: a ) 4.1 days , b ) 4.8 days , c ) 3.8 days , d ) 2.8 days , e ) 4.5 days
Rationale: 4 / 8 + 6 / x = 1 = > x = 12 1 / 8 + 1 / 12 = 5 / 24 = > 4.8 days answer : b
Answer: b
Python program:
a = 1 / 8
b = 6 * 2
c = 1 / b
d = a + c 
e = 1/(d)
Problem: a boat moves upstream at the rate of 1 km in 20 minutes and down stream 1 km in 12 minutes . then the speed of the current is :
Options: a ) 1 kmph , b ) 2 kmph , c ) 3 kmph , d ) 2.5 kmph , e ) 3.5 kmph
Rationale: rate upstream = ( 1 / 20 * 60 ) = 3 kmph rate dowm stream = 1 / 12 * 60 = 5 kmph rate of the current = ½ ( 5 - 3 ) = 1 kmph answer : a
Answer: a
Python program:
a = 1 / 12
b = a * const_60
c = 1 / 20
d = c * const_60
e = b - d
f = e / 2
Problem: a parking garage rents parking spaces for $ 10 per week or $ 40 per month . how much does a person save in a year by renting by the month rather than by the week ?
Options: a ) $ 40 , b ) $ 160 , c ) $ 220 , d ) $ 240 , e ) $ 260
Rationale: "10 $ per week ! an year has 52 weeks . annual charges per year = 52 * 10 = 520 $ 30 $ per month ! an year has 12 months . annual charges per year = 12 * 40 = 480 $ 520 - 480 = 40 ans a"
Answer: a
Python program:
a = 3 + 2 
b = 10 * a
c = b + 2 
d = c * 10
e = 40 * 12
f = d - e
Problem: what sum of money will produce rs . 70 as simple interest in 4 years at 4 1 / 2 percent ?
Options: a ) 263 , b ) 500 , c ) 388.9 , d ) 368 , e ) 339
Rationale: "70 = ( p * 4 * 9 / 2 ) / 100 p = 388.9 answer : c"
Answer: c
Python program:
a = 1 / 2
b = 4 + a 
c = 4 * b
d = c / 100
e = 70 / d
Problem: in a dairy farm , 34 cows eat 34 bags of husk in 34 days . in how many days one cow will eat one bag of husk ?
Options: a ) 34 days , b ) 40 days , c ) 46 days , d ) 50 days , e ) none of these
Rationale: "explanation : less cows , more days ( indirect proportion ) less bags , less days ( direct proportion ) [ cows 1 34 bags 34 1 ] : : 34 : x = > x ∗ 34 ∗ 1 = 34 ∗ 1 ∗ 34 = > x = 34 option a"
Answer: a
Python program:
a = 34 / 34
b = a * 34
Problem: if the sides of a triangle are 28 cm , 24 cm and 15 cm , what is its area ?
Options: a ) 180 cm 2 , b ) 112 cm 2 , c ) 776 cm 2 , d ) 666 cm 2 , e ) 886 cm 2
Rationale: "the triangle with sides 28 cm , 24 cm and 15 cm is right angled , where the hypotenuse is 28 cm . area of the triangle = 1 / 2 * 24 * 15 = 180 cm 2 answer : a"
Answer: a
Python program:
a = 24 * 15
b = a / 2
Problem: if y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer , then y must be
Options: a ) 2 , b ) 5 , c ) 6 , d ) 7 , e ) 14
Rationale: "3150 * y = a ^ 2 3 * 1050 * y = a ^ 2 3 * 5 * 210 * y = a ^ 2 3 * 5 * 7 * 3 * 2 * 5 * y = a ^ 2 2 * 3 ^ 2 * 5 ^ 2 * 7 * y = a ^ 2 concept : the factors of squared integer should occur in pair . so , the only numbers left are 2 * 7 hence 14 ; answer : e"
Answer: e
Python program:
a = 2 + 3 
b = a * 2
Problem: 10 play kabadi , 20 play kho kho only , 5 play both gmaes . then how many in total ?
Options: a ) 30 , b ) 35 , c ) 38 , d ) 40 , e ) 45
Rationale: "10 play kabadi = > n ( a ) = 10 , 5 play both gmaes . = > n ( anb ) = 5 20 play kho kho only , = > n ( b ) = n ( b only ) + n ( anb ) = 20 + 5 = 25 total = > n ( aub ) = n ( a ) + n ( b ) - n ( anb ) = 10 + 25 - 5 = 30 answer : a"
Answer: a
Python program:
a = 20 + 5 
b = 10 + a 
c = b - 5
Problem: if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 210 games will be played during the tournament . what is the number of participants ?
Options: a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "let n be the number of participants . the number of games is nc 2 = n * ( n - 1 ) / 2 = 210 n * ( n - 1 ) = 420 = 21 * 20 ( trial and error ) the answer is d ."
Answer: d
Python program:
a = 210 * 2
b = a * 4
c = b + 1 
d = math.sqrt(c)
e = d + 1 
f = e / 2
Problem: the length of a rectangular floor is more than its breadth by 500 % . if rs . 324 is required to paint the floor at the rate of rs . 6 per sq m , then what would be the length of the floor ?
Options: a ) 24.6 m . , b ) 23.4 m . , c ) 22.5 m . , d ) 23.8 m . , e ) 25.5 m .
Rationale: "let the length and the breadth of the floor be l m and b m respectively . l = b + 500 % of b = l + 5 b = 6 b area of the floor = 324 / 6 = 54 sq m l b = 54 i . e . , l * l / 6 = 108 l 2 = 648 = > l = 25.5 m . answer : e"
Answer: e
Python program:
a = 324 / 6
b = a / 3
c = math.sqrt(b)
d = c * 3
Problem: sandy is younger than molly by 14 years . if the ratio of their ages is 7 : 9 , how old is sandy ?
Options: a ) 42 , b ) 49 , c ) 56 , d ) 63 , e ) 70
Rationale: "let sandy ' s age be 7 x and let molly ' s age be 9 x . 9 x - 7 x = 14 x = 7 sandy is 49 years old . the answer is b ."
Answer: b
Python program:
a = 9 - 7
b = 7 / a
c = b * 14
Problem: find the product of the localvalue and absolutevalue of 1 in 20168 ?
Options: a ) 100 , b ) 110 , c ) 151 , d ) 120 , e ) 140
Rationale: "local value of 1 = 1 x 100 = 100 place value of 1 = 1 there fore = 1 x 100 = 100 a"
Answer: a
Python program:
a = 1 * 1000
b = a * 1
Problem: if a ( a - 6 ) = 7 and b ( b - 6 ) = 7 , where a ≠ b , then a + b =
Options: a ) − 48 , b ) − 2 , c ) 6 , d ) 9 , e ) 48
Rationale: "i . e . if a = - 1 then b = 7 or if a = 7 then b = - 1 but in each case a + b = - 1 + 7 = 6 answer : option c"
Answer: c
Python program:
a = 6 + 7 
b = 6 - 7
c = a + b 
d = c - 1
e = d - 1
f = e - 1
g = f - 1
Problem: a train 605 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
Options: a ) 51 , b ) 64 , c ) 11 , d ) 22 , e ) 33
Rationale: "speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 605 * 3 / 55 ] sec = 33 sec answer : e"
Answer: e
Python program:
a = 605 / 1000
b = 60 + 6 
c = a / b
d = 3600 * c
Problem: the average of 13 numbers is 60 . average of the first 6 of them is 57 and that of the last 8 is 61 . find the 8 th number ?
Options: a ) 46 , b ) 48 , c ) 50 , d ) 52 , e ) 54
Rationale: "sum of all the 13 numbers = 13 * 60 = 780 sum of the first 6 of them = 6 * 57 = 342 sum of the last 8 of them = 8 * 61 = 488 so , the 8 th number = 342 + 488 - 780 = 50 . answer : c"
Answer: c
Python program:
a = 8 * 61
b = 13 * 60
c = 57 * 6
d = b - c
e = a - d
Problem: is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 22 , then how old is b ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 22 5 x = 20 = > x = 4 hence , b ' s age = 2 x = 8 years . answer : b"
Answer: b
Python program:
a = 22 - 2
b = 3 + 2 
c = a / b
d = c * 2
Problem: in a fuel station the service costs $ 2.20 per vehicle and every liter of fuel costs $ 0.70 . assuming that you fill up 3 mini - vans and 2 trucks , what will be the total cost , if a mini - van ' s tank is 65 liters and a truck ' s tank is 120 % bigger and they are all empty ?
Options: a ) $ 341.50 , b ) $ 344.60 , c ) $ 347.70 , d ) $ 350.80 , e ) $ 353.90
Rationale: "the service cost of 3 vans and 2 trucks is 5 * 2.20 $ 11.00 the fuel in 3 vans is 3 * 65 = 195 liters the fuel in 2 trucks is 2 * 65 * 2.2 = 286 liters the total fuel ( vans + trucks ) = 481 liters the total fuel cost is 481 * 0.7 = $ 336.70 the total cost is $ 336.70 + $ 11.00 = $ 347.70 the answer is c ."
Answer: c
Python program:
a = 120 * 65
b = a / 100
c = b + 65 
d = c * 2
e = d * 0
f = 3 * 65
g = f * 0
h = e + g 
i = 3 + 2 
j = 2 * 20
k = h + j
Problem: four bells commence tolling together and toll at intervals of 2 , 3 , 4 and 5 seconds respectively . in 10 minutes , how many times do they toll together ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "lcm of 2 , 3 , 4 , and 5 is 60 . so , after each 60 seconds , they would toll together . hence , in 10 minutes , they would toll 10 * 60 seconds / 60 seconds = 10 times but then the question says they commence tolling together . so , they basically also toll at thebeginning ( 0 second ) . so , total tolls together = 10 + 1 = 11 answer : b"
Answer: b
Python program:
a = 2 + 3 
b = a * 2
c = b * 3
d = 2 * c
e = d * 2
f = e / 10
g = 10 / f
Problem: an article is bought for rs . 600 and sold for rs . 550 , find the loss percent ?
Options: a ) 8.33 % , b ) 16 7 / 3 % , c ) 16 2 / 8 % , d ) 16 2 / 3 % , e ) 76 2 / 3 %
Rationale: "600 - - - - 50 100 - - - - ? = > 8.33 % answer : a"
Answer: a
Python program:
a = 550 * 100
b = a / 600
c = 100 - b
Problem: it takes printer a 4 more minutes more than printer b to print 40 pages . working together , the two printers can print 50 pages in 6 minutes . how long will it take printer a to print 120 pages ?
Options: a ) 12 , b ) 18 , c ) 20 , d ) 24 , e ) 36
Rationale: "if it takes 4 more minutes for a to print 40 pages than it takes b , it takes 5 more minutes for a to print 50 pages than it takes b . thus if b is the number of minutes than b takes to print 50 pages , we can write : 1 / b + 1 / ( b + 5 ) = 1 / 6 ( since in 1 minute , they print 1 / 6 th of the 50 page job ) 6 ( 2 b + 5 ) = b ( b + 5 ) b ^ 2 - 7 b - 30 = 0 ( b - 10 ) ( b + 3 ) = 0 b = 10 thus it takes a 15 minutes to print 50 pages and 15 * 120 / 50 = 36 minutes to print 120 pages ( answer e )"
Answer: e
Python program:
a = 4 * 2
b = a + 4 
c = 120 * b
d = c / 40