euclaise/mathqa_programs huggingface dataset:
Problem: a train leaves delhi at 9 a . m . at a speed of 30 kmph . another train leaves at 3 p . m . at a speed of 40 kmph on the same day and in the same direction . how far from delhi , will the two trains meet ?
Options: a ) 229 , b ) 288 , c ) 600 , d ) 720 , e ) 121
Rationale: "d = 30 * 6 = 180 rs = 40 – 30 = 10 t = 180 / 10 = 18 d = 40 * 18 = 720 km answer : d"
Answer: d
Python program:
a = 3 + 3 
b = 30 * a
c = 40 - 30
d = b / c
e = d * 40
Problem: when a merchant imported a certain item , she paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1,000 . if the amount of the import tax that the merchant paid was $ 112.70 , what was the total value of the item ?
Options: a ) $ 2420 , b ) $ 2610 , c ) $ 2860 , d ) $ 3050 , e ) $ 3270
Rationale: "let x be the value of the item . 0.07 * ( x - 1000 ) = 112.70 x = 2610 the answer is b ."
Answer: b
Python program:
a = 7 / 100
b = 112 / 70
c = 1 + 0
Problem: compound x contains elements a and b at an approximate ratio , by weight , of 2 : 10 . approximately how many grams of element b are there in 300 grams of compound x ?
Options: a ) 54 , b ) 162 , c ) 250 , d ) 270 , e ) 322
Rationale: "total number of fractions = 2 + 10 = 12 element b constitutes = 10 out of 12 parts of x so in 300 gms of x have 300 * 10 / 12 = 250 gms of b and 300 - 250 = 50 gms of a . cross check : - a / b = 50 / 250 = 2 / 10 ( as given ) ans c"
Answer: c
Python program:
a = 300 * 10
b = 2 + 10 
c = a / b
Problem: find the cost of fencing around a circular field of diameter 26 m at the rate of rs . 1.50 a meter ?
Options: a ) 122.55 , b ) 132 , c ) 156 , d ) 158 , e ) 267
Rationale: "2 * 22 / 7 * 13 = 81.7 81.7 * 1 1 / 2 = rs . 122.55 answer : a"
Answer: a
Python program:
a = 26 / 2
b = circumface * (
Problem: a can give b a start of 50 metres or 10 seconds in a kilometer race . how long does a take to complete the race ?
Options: a ) 200 seconds , b ) 140 seconds , c ) 220 seconds , d ) 190 seconds , e ) none
Rationale: solution : a can give b a start of 50 metres or 10 seconds in a 1000 m race . that is , b takes 10 seconds to run 50 metres . therefore , b will take ( 10 / 50 ) * 1000 = 200 seconds to run 1000 metres . a who can give b a start of 10 seconds will take 10 seconds lesser to run the 1000 m . hence , the time taken by a = 190 seconds . answer d
Answer: d
Python program:
a = 10 / 50
b = a * 1000
c = b - 10
Problem: last year sandy saved 6 % of her annual salary . this year , she made 10 % more money than last year , and she saved 10 % of her salary . the amount saved this year was what percent of the amount she saved last year ?
Options: a ) 133 % , b ) 145 % , c ) 158 % , d ) 170 % , e ) 183 %
Rationale: "let last year ' s salary be x . last year , sandy save 0.06 x this year , sandy saved 0.1 * 1.1 x = 0.11 x 0.11 x / 0.06 x = 11 / 6 = 1.83 = 183 % the answer is e ."
Answer: e
Python program:
a = 10 / 100
b = 100 + 10 
c = a * b
d = 6 * 100
e = d / 100
f = c / e
g = f * 100
Problem: if 10 litres of an oil of rs . 50 per litres be mixed with 5 litres of another oil of rs . 68 per litre then what is the rate of mixed oil per litre ?
Options: a ) rs . 49.17 , b ) rs . 51.03 , c ) rs . 56 , d ) rs . 55.33 , e ) none of the above
Rationale: "50 * 10 = 500 68 * 5 = 340 840 / 15 = 56 answer : c"
Answer: c
Python program:
a = 10 * 50
b = 5 * 68
c = a + b 
d = 10 + 5 
e = c / d
Problem: a broker invested her own money in the stock market . during the first year , she increased her stock market wealth by 90 percent . in the second year , largely as a result of a slump in the stock market , she suffered a 50 percent decrease in the value of her stock investments . what was the net increase or decrease on her overall stock investment wealth by the end of the second year ?
Options: a ) − 5 % , b ) 5 % , c ) 15 % , d ) 20 % , e ) 80 %
Rationale: "the actual answer is obtained by multiplying 140 % by 70 % and subtracting 100 % from this total . that is : 190 % × 50 % = 95 % ; 95 % − 100 % = - 5 % . answer : a"
Answer: a
Python program:
a = 90 / 100
b = 1 + a 
c = 50 / 100
d = 1 - c
e = b * d
f = e - 1
g = f * 100
Problem: what least number should be added to 1056 , so that the sum is completely divisible by 23
Options: a ) 4 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: "explanation : ( 1056 / 23 ) gives remainder 21 21 + 2 = 23 , so we need to add 2 answer : option c"
Answer: c
Python program:
a = 23 - reminder
Problem: the average temperature for tuesday , wednesday and thursday was 52 ° c . the average temperature for wednesday , thursday and friday was 54 ° c . if the temperature on friday be 53 ° c , what was the temperature on tuesday ?
Options: a ) 39 ° c , b ) 44 ° c , c ) 37 ° c , d ) 47 ° c , e ) none of these
Rationale: explanation : t + w + t = 52 × 3 = 156 ° c w + t + f = 54 × 3 = 162 ° c also , temperature on friday = 53 ° c temperature on tuesday = 156 + 53 - 162 = 47 ° c answer : option d
Answer: d
Python program:
a = 52 * 3
b = 54 * 3
c = b - 53
d = a - c
Problem: the smallest number which when diminished by 6 , is divisible by 12 , 16 , 18 , 21 and 28 is
Options: a ) 1008 , b ) 1014 , c ) 1022 , d ) 1032 , e ) 1043
Rationale: "required number = ( l . c . m of 12 , 16 , 18 , 21,28 ) + 6 = 1008 + 6 = 1014 answer : b"
Answer: b
Python program:
a = 3 ** 2
b = 2 ** 0
c = a * b
d = 3 + 4 
e = c * d
f = e + 6
Problem: the true discount on a bill due 9 months hence at 16 % per annum is rs . 240 . the amount of the bill is
Options: a ) 2200 , b ) 2240 , c ) 1600 , d ) 1354 , e ) none of these
Rationale: "explanation : let p . w . be rs . x . then , s . i . on rs . x at 16 % for 9 months = rs . 240 . x ã — 16 ã — ( 9 / 12 ) ã — ( 1 / 100 ) = 240 or x = 2000 . p . w . = rs . 2000 . sum due = p . w . + t . d . = rs . ( 2000 240 ) = rs . 2240 . answer : b"
Answer: b
Python program:
a = 4 * 3
b = 9 / a
c = b * 16
d = c / 100
e = 240 / d
f = e + 240
Problem: instead of multiplying a number by 3 , the number is divided by 5 . what is the percentage of error obtained ?
Options: a ) 92.33 % , b ) 91.33 % , c ) 95.33 % , d ) 93.33 % , e ) 94.33 %
Rationale: "let the number be x the right number is 3 x the wrong number is x / 5 error is ( 3 x - x / 5 ) = 14 x / 5 percentage of error is ( ( 14 x / 5 ) / 3 x ) * 100 = 93.33 % answer : d"
Answer: d
Python program:
a = 5 / 5
b = 3 * 5
c = a / b
d = c * 100
e = 100 - d
Problem: a man sold 18 toys for rs . 23100 , gaining thereby the cost price of 3 toy find the cost price of a toy
Options: a ) s . 600 , b ) s . 800 , c ) s . 500 , d ) s . 900 , e ) s . 1100
Rationale: "let the cost of one toy = x . then , cost of 18 toys = 18 x . gain = 3 x . sp of 18 toys = rs . 23100 . gain = sp â € “ cp 3 x = 23100 â € “ 18 x 21 x = 23100 x = rs . 1100 . answer : option e"
Answer: e
Python program:
a = 18 + 3 
b = 23100 / a
Problem: if ( a – b ) is 17 more than ( c + d ) and ( a + b ) is 3 less than ( c – d ) , then ( a – c ) is :
Options: a ) 6 , b ) 2 , c ) 3 , d ) 7 , e ) 5
Rationale: "( a – b ) – ( c + d ) = 17 and ( c – d ) – ( a + b ) = 3 = > ( a – c ) – ( b + d ) = 17 and ( c – a ) – ( b + d ) = 3 = > ( b + d ) = ( a – c ) – 17 and ( b + d ) = ( c – a ) – 3 = > ( a – c ) – 17 = ( c – a ) – 3 = > 2 ( a – c ) = 14 = > ( a – c ) = 7 answer : d"
Answer: d
Python program:
a = 17 / 3
Problem: in an objective competitive exam , a correct answer score 4 marks and on a wrong answer 2 marks are negatively added . a student scores 420 marks from 150 question . how many answers were correct ?
Options: a ) 150 , b ) 155 , c ) 140 , d ) 120 , e ) 165
Rationale: let x be the correct answer and y be the wrong answer so the total number of questions is ( x + y ) = 150 . . . . . ( 1 ) = > 4 x - 2 y = 420 . . . . . ( 2 ) by solving ( 1 ) & ( 2 ) , we get = > 6 x = 720 hence x = 120 therefore , number of correct answers are 120 . answer d
Answer: d
Python program:
a = 150 * 2
b = a + 420 
c = 4 + 2 
d = b / c
Problem: running at their respective constant rates , machine x takes 2 days longer to produce w widgets than machine y . at these rates , if the two machines together produce 5 / 4 w widgets in 3 days , how many days would it take machine x alone to produce 4 w widgets ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 24 , e ) 12
Rationale: "let y produce w widgets in y days hence , in 1 day y will produce w / y widgets . also , x will produce w widgets in y + 2 days ( given , x takes two more days ) hence , in 1 day x will produce w / y + 2 widgets . hence together x and y in 1 day will produce { w / y + w / y + 2 } widgets . together x and y in 3 days will produce = 3 * [ { w / y + w / y + 2 } ] widgets . it is given that in 3 days together they produce ( 5 / 4 ) w widgets . equating , 3 * [ { w / y + w / y + 2 } ] = ( 5 / 4 ) w take out w common and move 3 to denominator of rhs w { 1 / y + 1 / ( y + 2 ) } = ( 5 / 12 ) w canceling w from both sides { 1 / y + 1 / ( y + 2 ) } = 5 / 12 2 y + 2 / y ( y + 2 ) = 5 / 12 24 y + 24 = 5 y ^ 2 + 10 y 5 y ^ 2 - 14 y - 24 = 0 5 y ^ 2 - 20 y + 6 y - 24 = 0 5 y ( y - 4 ) + 6 ( y - 4 ) = 0 ( 5 y + 6 ) + ( y - 4 ) = 0 y = - 6 / 5 or y = 4 discarding y = - 6 / 5 as no of days can not be negative y = 4 hence it takes y , 4 days to produce w widgets . therefore , it will take x ( 4 + 2 ) = 6 days to produce w widgets . hence it will take x 4 * 6 = 24 days to produce 4 w widgets . answer : d"
Answer: d
Python program:
a = 3 * 4
b = a * 2
c = 3 * 4
d = b - c
e = d / 2
Problem: a car traveled 75 % of the way from town a to town b at an average speed of 50 miles per hour . the car travels at an average speed of s miles per hour for the remaining part of the trip . the average speed for the entire trip was 50 miles per hour . what is s ?
Options: a ) 10 , b ) 20 , c ) 25 , d ) 30 , e ) 50
Rationale: "total distance = 100 miles ( easier to work with % ) 75 % of the distance = 75 miles 25 % of the distance = 25 miles 1 st part of the trip → 75 / 50 = 1.5 2 nd part of the trip → 25 / s = t total trip → ( 75 + 25 ) / 50 = 1.5 + t » 100 / 50 = 1.5 + t » 2 = 1.5 + t » t = 0.5 back to 2 nd part of the trip formula : 25 / s = 0.5 » s = 50 ans e"
Answer: e
Python program:
a = 50 + 50 
b = a - 75
c = 50 + 50 
d = c / 50
e = 75 / 50
f = d - e
g = b / f
Problem: excluding stoppages , the average speed of a bus is 60 km / hr and including stoppages , the average speed of the bus is 30 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 22 , b ) 30 , c ) 77 , d ) 20 , e ) 99
Rationale: "in 1 hr , the bus covers 60 km without stoppages and 30 km with stoppages . stoppage time = time take to travel ( 60 - 30 ) km i . e 30 km at 60 km / hr . stoppage time = 30 / 60 hrs = 30 min . answer : b"
Answer: b
Python program:
a = 1 * const_60
b = 30 / 60
c = b * const_60
d = a - c
Problem: if a + b + c = 13 , then find the ab + bc + ca :
Options: a ) 22 , b ) 99 , c ) 50 , d ) 29 , e ) 11
Rationale: answer : c ) 50
Answer: c
Python program:
a = 13 + 2 
b = math.factorial(a)
c = math.factorial(13)
d = b / c
e = d / 2
Problem: indu gave bindu rs . 6250 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?
Options: a ) 5 , b ) 2 , c ) 10 , d ) 5 , e ) 1
Rationale: 6250 = d ( 100 / 4 ) 2 d = 10 answer : c
Answer: c
Python program:
a = 4 / 100
b = 1 + a 
c = b ** 2
d = 6250 * c
e = d - 6250
f = 4 / 100
g = 6250 * f
h = g * 2
i = e - h
Problem: if log 102 = 0.3010 , what is the value of log 101600 ?
Options: a ) 3.208 , b ) 3.202 , c ) 3.209 , d ) 3.204 , e ) 3.2112
Rationale: explanation : log 101600 = log 10 ( 16 × 100 ) = log 10 ( 16 ) + log 10 ( 100 ) = log 10 ( 24 ) + log 10 ( 102 ) = 4 log 10 ( 2 ) + 2 = ( 4 × 0.3010 ) + 2 = 1.204 + 2 = 3.204 answer : option d
Answer: d
Python program:
a = 4 * 0
b = math.log(100)
c = math.log(10)
d = b / c
e = a + d
Problem: a man can row his boat with the stream at 16 km / h and against the stream in 12 km / h . the man ' s rate is ?
Options: a ) 8 kmph , b ) 9 kmph , c ) 2 kmph , d ) 4 kmph , e ) 1 kmph
Rationale: "ds = 16 us = 14 s = ? s = ( 16 - 2 ) / 2 = 2 kmph answer : c"
Answer: c
Python program:
a = 16 - 12
b = a / 2
Problem: if 125 % of j is equal to 25 % of k , 150 % of k is equal to 50 % of l , and 175 % of l is equal to 75 % of m , then 20 % of m is equal to what percent of 200 % of j ?
Options: a ) 0.35 , b ) 3.5 , c ) 35 , d ) 350 , e ) 3500
Rationale: first of all , let us write the information in form of equations and numbers 125 j = 5 k or 5 j = k ( i ) 150 k = 50 l or 3 k = l ( ii ) 175 l = 75 m or 7 l = 3 m ( iii ) we need to find a relation between j and m from ( i ) and ( ii ) , 15 j = l multiplying this by 7 , 105 j = 7 l = 3 m hence , 35 j = m now , we are asked : 20 % of m is equal to what percent of 200 % of j assume j = 1 , hence m = 35 20 % of m = 7 and 200 % of j = 2 20 % of m = 3.5 ( 200 % of j ) = ( 350 / 100 ) * ( 200 % of j ) hence 20 % of m = 350 % of 200 % of j . option d
Answer: d
Python program:
a = 125 * 150
b = a * 175
c = 25 * 50
d = c * 75
e = b / d
f = e * 20
g = f / 200
h = g * 100
Problem: a library has an average of 570 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :
Options: a ) 250 , b ) 276 , c ) 280 , d ) 295 , e ) none
Rationale: "since the month begins with sunday , to there will be five sundays in the month average required = ( 570 x 5 + 240 x 25 ) / 30 ) = 295 answer : option d"
Answer: d
Python program:
a = 3 + 4 
b = 30 / a
c = math.floor(b)
d = c + 1 
e = d * 570
f = 3 + 4 
g = 30 / f
h = math.floor(g)
i = h + 1 
j = 30 - i
k = j * 240
l = e + k 
m = l / 30
Problem: in a room filled with 7 people , 1 people have exactly 1 sibling in the room and 6 people have exactly 2 siblings in the room . if two individuals are selected from the room at random , what is the probability that those two individuals are not siblings ?
Options: a ) 5 / 21 , b ) 3 / 7 , c ) 4 / 21 , d ) 5 / 7 , e ) 16 / 21
Rationale: "there are suppose a b c d e f g members in the room 4 people who have exactly one sibling . . . . a b c d . . . . ( a is bs ∘ sssibl ∈ g ∘ ssand ∘ ssviceversa ) ∘ ss ( c ∘ ssis ∘ ssds ∘ sssibl ∈ g ∘ ssand ∘ ssviceversa ) ∘ ss ( c ∘ ssis ∘ ssdssibl ∈ gandviceversa ) ( cisds sibling and viceversa ) ( c is ds sibling and viceversa ) . . . now remaning efg are 6 people who have exactly 2 siblings . . . . ( e has f and g as his / her sibling and so on . . ) there are now 3 different set of siblings ( a and b ) ( c and d ) ; ( efg ) now first selecting 2 people out of 7 is 7 c 2 = 21 first sibling pair - - - - ( a and b ) - - selecting 2 people - - 2 c 2 = 1 second sibling pair ( c and d ) - - selecting 2 people - - 2 c 2 = 1 third sibling pair ( e f g ) - - selecting 2 out of 6 - - 6 c 2 = 15 total = 1 + 1 + 15 = 17 but , a / c to formula p ( success ) - 1 - p ( fail ) here , p ( failure ) is selecting 2 people who are siblings = 17 / 21 ( 21 is 7 c 2 ) = 1 - 17 / 21 = 4 / 21 ans c"
Answer: c
Python program:
a = 1 / 7
b = 7 - 2
c = 7 - 1
d = b / c
e = a * d
f = 1 / 7
g = 7 - 1
h = 7 - 1
i = g / h
j = f * i
k = e + j
Problem: the roof of an apartment building is rectangular and its length is 4 times longer than its width . if the area of the roof is 676 feet squared , what is the difference between the length and the width of the roof ?
Options: a ) 39 . , b ) 40 . , c ) 42 . , d ) 44 . , e ) 46 .
Rationale: "let the width = x x * 4 x = 676 x ^ 2 = 169 x = 13 length = 4 * 13 = 52 difference = 52 - 13 = 39 a is the answer"
Answer: a
Python program:
a = 676 / 4
b = math.sqrt(a)
c = b * 4
d = 676 / 4
e = math.sqrt(d)
f = c - e
Problem: the area of a rectangular plot is 360 square metres . if the length is 25 % less than the breadth , what is the breadth of the plot ?
Options: a ) 32 m
b ) 12 m
c ) 20 m
d ) 22 m
e ) 25 m
Rationale: length = 75 % of breadth . length × breadth = 360 m 2 ⇒ 75 % of breadth × breadth = 360 m 2 ⇒ 75 / 100 × breadth × breadth = 360 m 2 ⇒ breadth × breadth = 480 m 2 ⇒ breadth = 22 m answer : d
Answer: d
Python program:
a = 25 / 100
b = 1 - a
c = 360 / b
d = math.sqrt(c)
Problem: a 60 cm long wire is to be cut into two pieces so that one piece will be 2 / 5 th of the other , how many centimeters will the shorter piece be ?
Options: a ) a ) 73 , b ) b ) 20 , c ) c ) 83 , d ) d ) 17.1 , e ) e ) 52
Rationale: "explanation : 1 : 2 / 5 = 5 : 2 2 / 7 * 60 = 20 answer : option d"
Answer: d
Python program:
a = 2 / 5
b = a + 1 
c = 60 / b
d = 60 - c
Problem: one week , a certain truck rental lot had a total of 24 trucks , all of which were on the lot monday morning . if 50 % of the trucks that were rented out during the week were returned to the lot on or before saturday morning of that week , and if there were at least 12 trucks on the lot that saturday morning , what is the greatest number of different trucks that could have been rented out during the week ?
Options: a ) 24 , b ) 16 , c ) 12 , d ) 8 , e ) 4
Rationale: n - not rented trucks ; r - rented trucks n + r = 24 n + r / 2 = 12 r = 24 a
Answer: a
Python program:
a = 50 / 100
b = 24 * a
c = 12 + b
Problem: if two projectiles are launched at the same moment from 1455 km apart and travel directly towards each other at 470 km per hour and 500 km per hour respectively , how many minutes will it take for them to meet ?
Options: a ) 90 , b ) 85 , c ) 80 , d ) 75 , e ) 70
Rationale: "the projectiles travel a total of 970 km per hour . the time to meet is 1455 / 970 = 1.5 hours = 90 minutes the answer is a ."
Answer: a
Python program:
a = 470 + 500 
b = 1455 / a
c = b * const_60
Problem: if the least common addition of two prime numbers x and y is 36 , where x < y , then the value of 4 x + y is
Options: a ) 32 , b ) 45 , c ) 59 , d ) 73 , e ) 87
Rationale: ( x + y ) = 36 and both x an y are prime . the only values of x and y can be 17 and 19 ( x = 17 and y = 19 ) 4 x + y = 4 * 17 + 19 = 87 correct option : e
Answer: e
Python program:
a = 36 * 2
b = 36 / 4
c = a + b 
d = 3 + 3 
e = c + d
Problem: a man can do a job in 10 days . his father takes 20 days and his son finishes it in 25 days . how long will they take to complete the job if they all work together ?
Options: a ) 6.3 , b ) 6.9 , c ) 5.3 , d ) 6.1 , e ) 6.2
Rationale: "1 day work of the three persons = ( 1 / 10 + 1 / 20 + 1 / 25 ) = 19 / 100 so , all three together will complete the work in 100 / 19 = 5.3 days . answer : c"
Answer: c
Python program:
a = 1 / 25
b = 1 / 10
c = 1 / 20
d = b + c 
e = a + d 
f = 1 / e
Problem: a train 2500 m long can cross an electric pole in 50 sec and then find the speed of the train ?
Options: a ) 178 , b ) 180 , c ) 182 , d ) 184 , e ) 186
Rationale: "length = speed * time speed = l / t s = 2500 / 50 s = 50 m / sec speed = 50 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 180 kmph answer : b"
Answer: b
Python program:
a = 2500 / 1000
b = 50 / 3600
c = a / b
Problem: a semicircle has a radius of 14 . what is the approximate perimeter of the semicircle ?
Options: a ) 72 , b ) 76 , c ) 80 , d ) 84 , e ) 88
Rationale: "the perimeter of a circle is 2 * pi * r . the perimeter of a semicircle is 2 * pi * r / 2 + 2 r = pi * r + 2 r the perimeter is pi * 14 + 2 * 14 which is about 72 . the answer is a ."
Answer: a
Python program:
a = circumface / (
b = a + 2
Problem: the average of 25 results is 24 . the average of first 12 of those is 14 and the average of last 12 is 17 . what is the 13 th result ?
Options: a ) 740 , b ) 228 , c ) 690 , d ) 780 , e ) 458
Rationale: "solution : sum of 1 st 12 results = 12 * 14 sum of last 12 results = 12 * 17 13 th result = x ( let ) now , 12 * 14 + 12 * 17 + x = 25 * 24 or , x = 228 . answer : option b"
Answer: b
Python program:
a = 25 * 24
b = 12 * 17
c = a - b
d = 12 * 14
e = c - d
Problem: a starts business with rs . 4500 and after 7 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b â € ™ s contribution in the capital ?
Options: a ) 24887 , b ) 20778 , c ) 16200 , d ) 9000 , e ) 2811
Rationale: "explanation : a invested rs . 3500 for 12 months . let b joined with investment x . and he invested for 12 - 7 = 5 months . so there profit ratio = ( 4500 ã — 12 ) : ( 5 x ) = 2 : 3 â ‡ ’ x = 16200 answer : c"
Answer: c
Python program:
a = 4500 * 12
b = a * 3
c = 12 - 7
d = c * 2
e = b / d
Problem: the average of 6 no . ' s is 3.95 . the average of 2 of them is 3.4 , while the average of theother 2 is 3.85 . what is the average of the remaining 2 no ' s ?
Options: a ) 2.3 , b ) 2.5 , c ) 3.5 , d ) 3.6 , e ) 4.6
Rationale: "sum of the remaining two numbers = ( 3.95 * 6 ) - [ ( 3.4 * 2 ) + ( 3.85 * 2 ) ] = 23.70 - ( 6.8 + 7.7 ) = 23.70 - 14.5 = 9.20 . required average = ( 9.2 / 2 ) = 4.6 . e"
Answer: e
Python program:
a = 6 * 3
b = 2 * 3
c = 2 * 3
d = b + c 
e = a - d
f = e / 2
Problem: some persons can do a piece of work in 12 days . two times the number of such persons will do half of that work in
Options: a ) 9 , b ) 8 , c ) 4 , d ) 3 , e ) 1
Rationale: "explanation : let x men can do the in 12 days and the required number of days be z more men , less days [ indirect proportion ] less work , less days [ direct proportion ] answer : d ) 3 days"
Answer: d
Python program:
a = 1 / 2
b = 12 * a
c = 1 / 2
d = b * c
Problem: find the number of zero ’ s in 173 ! ( 173 factorial ) ?
Options: a ) 38 , b ) 39 , c ) 40 , d ) 41 , e ) 42
Rationale: no of zeroes in 173 ! is 173 / 5 = 34 ( quotient ) 34 / 5 = 6 ( quotient ) 6 / 5 = 1 ( quotient ) 34 + 6 + 1 = 41 ans 41 zeroes answer : d
Answer: d
Python program:
a = 1 + 4 
b = 173 / a
c = math.floor(b)
d = 1 + 4 
e = d ** 2
f = 173 / e
g = math.floor(f)
h = c + g 
i = 1 + 4 
j = i ** 3
k = 173 / j
l = math.floor(k)
m = h + l
Problem: 270 ã · ? ã — 15 + 270 = 405
Options: a ) 24 , b ) 25 , c ) 30 , d ) 39 , e ) 43
Rationale: "explanation : 270 ã · ? ã — 15 = 405 - 270 = 135 ( 270 ã — 15 ) / ? = 135 ? = ( 270 ã — 15 ) / 135 = 30 answer : option c"
Answer: c
Python program:
a = 405 - 270
b = a + 15 
c = b * 2
d = c / 10
e = 405 - 270
f = e + 15 
g = f * 2
h = g / 10
i = h / 10
j = d + i 
k = j + 1
Problem: what is the sum of the odd integers from 55 to 65 , inclusive ?
Options: a ) 495 , b ) 360 , c ) 555 , d ) 600 , e ) 605
Rationale: "the mean is 60 . sum = mean ( # of elements ) there are 6 odd numbers between 55 - 65 inclusive . 6 * 60 = 360 b"
Answer: b
Python program:
a = 55 * 65
b = a / 4
Problem: when a person aged 39 is added to a group of n people , the average age increases by 2 . when a person aged 15 is added instead , the average age decreases by 1 . what is the value of e ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: a simple and elegant solution . as addition of 39 , shifts mean by 2 , and addition of 15 , shifts mean by 1 to the other side , we have the mean lying between 3915 , and in a ratio of 2 : 1 39 - 15 = 24 24 divide by 3 is 8 . meaning mean of the n terms is 15 + 8 = 39 - 16 = 23 now , from first statement , when a person aged 39 is added to a group of n people , the average age increases by 2 . e * 23 + 39 = 25 * ( e + 1 ) e = 7 ans . ( a )
Answer: a
Python program:
a = 39 - 15
b = 2 + 1 
c = a / b
d = c - 1
Problem: the present age of a father is 3 years more than 3 times the age of his son . 3 years hence , father as age will be 8 years more than twice the age of the son . find the present age of the father .
Options: a ) 88 , b ) 77 , c ) 33 , d ) 44 , e ) 27
Rationale: explanation : let the present age be ' x ' years . then father ' s present age is 3 x + 3 years . three years hence ( 3 x + 3 ) + 3 = 2 ( x + 3 ) + 8 x = 8 hence father ' s present age = 3 x + 3 = [ ( 3 x 8 ) + 3 ] = 27 years . answer : e
Answer: e
Python program:
a = 3 * 8
b = a + 3
Problem: the “ length of integer x ” refers to the number of prime factors , not necessarily distinct , that x has . ( if x = 60 , the length of x would be 4 because 60 = 2 × 2 × 3 × 5 . ) what is the greatest possible length of integer z if z < 2500 ?
Options: a ) 7 , b ) 9 , c ) 11 , d ) 13 , e ) 15
Rationale: "to maximize the length of z , we should minimize its prime base . the smallest prime is 2 and since 2 ^ 11 = 2048 < 2500 , then the greatest possible length of integer z is 11 . the answer is c ."
Answer: c
Python program:
a = 2 ** 10
b = math.log(a)