euclaise/mathqa_programs huggingface dataset:
Problem: if n is the smallest integer such that 144 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: "144 can written as = 2 * 2 * 2 * 2 * 3 * 3 - - > 2 ^ 4 * 3 ^ 2 - - - ( 1 ) so for 144 * n to be a square of an integer , the integer should have even powers to the prime numbers it composed of . here 2 already has even power - > so n has to be 3 to make the power of 2 in ( 1 ) even option a is correct"
Answer: a
Python program:
a = 144 / 2
b = a / 2
c = b / 2
d = c / 2
e = d / 3
f = e / 3
Problem: claire has a total of 86 pets consisting of gerbils and hamsters only . one - quarter of the gerbils are male , and one - third of the hamsters are male . if there are 25 males altogether , how many gerbils does claire have ?
Options: a ) 39 , b ) 50 , c ) 60 , d ) 54 , e ) 60
Rationale: "g + h = 86 . . . 1 ; g / 4 + h / 3 = 25 . . . . 2 or 3 g + 4 h = 25 * 12 = 300 g = 86 - h or 3 ( 86 - h ) + 4 h = 300 h = 300 - 258 = 42 then g = 96 - 42 = 54 d"
Answer: d
Python program:
a = 86 - 25
b = a + 1
Problem: jackie has two solutions that are 4 percent sulfuric acid and 12 percent sulfuric acid by volume , respectively . if these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid , approximately how many liters of the 12 percent solution will be required ?
Options: a ) 18 , b ) 20 , c ) 24 , d ) 33.75 , e ) 42
Rationale: "let a = amount of 4 % acid and b = amount of 12 % acid . now , the equation translates to , 0.04 a + . 12 b = . 05 ( a + b ) but a + b = 60 therefore . 04 a + . 12 b = . 05 ( 60 ) = > 4 a + 12 b = 300 but b = 60 - a therefore 4 a + 12 ( 60 - a ) = 300 = > 16 a = 420 hence a = 26.25 . b = 60 - 26.25 = 33.75 answer : d"
Answer: d
Python program:
a = 60 / 10
b = 3 * a
Problem: how much space , in cubic units , is left vacant when maximum number of 4 x 4 x 4 cubes are fitted in a rectangular box measuring 10 x 12 x 16 ?
Options: a ) 0
b ) 36
c ) 180
d ) 216
e ) 384
Rationale: no of cubes that can be accommodated in box = ( 10 * 12 * 16 ) / ( 4 * 4 * 4 ) 12 * 16 in numerator can be perfectly divided by 4 * 4 in denominator . side with length 10 ca n ' t be perfectly divided by 4 and hence is the limiting factor . closet multiple of 4 less that 10 is 8 . so vacant area in cube = = 12 * 16 * ( 10 - 8 ) = 12 * 16 * 2 = 384 answer : e
Answer: e
Python program:
a = 4 * 2
b = 10 - a
c = 12 * 16
d = b * c
Problem: it is currently 8 : 34 pm . at what time in the morning was it exactly 39,668 minutes ago ?
Options: a ) 7 : 22 , b ) 7 : 24 , c ) 7 : 26 , d ) 7 : 28 , e ) 7 : 30
Rationale: divide 39,668 by 60 to convert to minutes : 39,668 / 60 = 661 r 8 . that is 661 hours , 8 minutes . all of the answer choices are during the same hour before : 34 , so we can assume the 661 hours takes the time back into the 7 am hour to 7 : 34 am . going back 8 more minutes yields the time 7 : 26 am . c
Answer: c
Python program:
a = 34 - 3
b = 8 / a
Problem: a palindrome is a number that reads the same forward and backward . for example . 2442 and 111 are palindromes . if 5 - digit palindromes are formed using one or more of the digits , 1 , 2 , 3 , how many such palindromes are possible ?
Options: a ) 12 , b ) 15 , c ) 18 , d ) 24 , e ) 27
Rationale: xyzyx x can be 1 , 2 , or 3 , thus 3 options . y can be 1 , 2 , or 3 , thus 3 options . z can be 1 , 2 , or 3 , thus 3 options . total 3 ^ 3 = 27 . answer : e .
Answer: e
Python program:
a = 3 * 3
b = a * 3
Problem: a train 125 m long passes a man , running at 20 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ?
Options: a ) 36 , b ) 50 , c ) 28 , d ) 26 , e ) 65
Rationale: "speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) * ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 20 ) km / hr . x - 20 = 45 = = > x = 65 km / hr answer : e"
Answer: e
Python program:
a = 20 * const_0_2778
b = a * 20
c = 125 - b
d = c / 20
e = d / const_0_2778
Problem: if 20 % of ( x - y ) = 14 % of ( x + y ) , then what percent of x is y ?
Options: a ) 50.5 % , b ) 44.4 % , c ) 22.2 % , d ) 17.6 % , e ) 25 %
Rationale: "20 % of ( x - y ) = 14 % of ( x + y ) 20 / 100 ( x - y ) = 14 / 100 ( x + y ) 6 x = 34 y required percentage = y / x * 100 = 6 y / 34 y * 100 = 17.64 % answer is d"
Answer: d
Python program:
a = 20 - 14
b = 20 + 14 
c = a / b
d = c * 100
Problem: if rs . 510 be divided among a , b , c in such a way that a gets 2 / 3 of what b gets and b gets 1 / 4 of what c gets , then their shares are respectively :
Options: a ) rs . 260 , b ) rs . 360 , c ) rs . 350 , d ) rs . 364 , e ) rs . 362
Rationale: "( a = 2 / 3 b and b = 1 / 4 c ) = a / b = 2 / 3 and b / c = 1 / 4 a : b = 2 : 3 and b : c = 1 : 4 = 3 : 12 a : b : c = 2 : 3 : 12 a ; s share = 510 * 2 / 17 = rs . 60 b ' s share = 510 * 3 / 17 = rs . 90 c ' s share = 510 * 12 / 17 = rs . 360 . answer : b"
Answer: b
Python program:
a = 2 / 3
b = 1 / 4
c = a * b
d = 1 / 4
e = c + d 
f = e + 1 
g = 510 / f
Problem: what is the dividend . divisor 15 , the quotient is 9 and the remainder is 5 ?
Options: a ) a ) 140 , b ) b ) 134 , c ) c ) 148 , d ) d ) 158 , e ) e ) 160
Rationale: "d = d * q + r d = 15 * 9 + 5 d = 135 + 5 d = 140 answer a"
Answer: a
Python program:
a = 15 * 9
b = a + 5
Problem: an order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2 . subsequently , the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter . find the ratio of the areas of the carpets in both the cases .
Options: a ) 4 : 3 , b ) 8 : 7 , c ) 4 : 1 , d ) 6 : 5 , e ) none of these
Rationale: "explanation : let the length and breadth of the carpet in the first case be 3 x units and 2 x units respectively . let the dimensions of the carpet in the second case be 7 y , 3 y units respectively . from the data , . 2 ( 3 x + 2 x ) = 2 ( 7 y + 3 y ) = > 5 x = 10 y = > x = 2 y required ratio of the areas of the carpet in both the cases = 3 x * 2 x : 7 y : 3 y = 6 x 2 : 21 y 2 = 6 * ( 2 y ) 2 : 21 y 2 = 6 * 4 y 2 : 21 y 2 = 8 : 7 answer is b"
Answer: b
Python program:
a = 3 * 2
b = a * 4
c = 7 * 3
d = b / c
Problem: stacy and heather are 10 miles apart and walk towards each other along the same route . stacy walks at constant rate that is 1 mile per hour fast than heather ' s constant rate of 5 miles / hour . if heather starts her journey 24 minutes after stacy , how far from the original destination has heather walked when the two meet ? .
Options: a ) 6.0 mile , b ) 3.0 mile , c ) 4.0 mile , d ) 3.45 mile , e ) 12 mile
Rationale: "ss - stacy ' s speed = 6 m / hr sh - heather ' s speed = 5 m / hr in 24 minutes stacy will cover = ( 24 / 60 ) * 6 = 2.4 miles now since both are walking in opposite directions , add their speeds - 6 + 5 = 11 m / hr and distance to cover is 10 - 2.4 = 7.6 time taken = distance / speed = 7.6 / 11 = 0.69 hrs heather will cover = 5 * 0.69 = 3.45 miles . answer d"
Answer: d
Python program:
a = 1 + 5 
b = a / const_60
c = 24 * b
d = 10 - c
e = 1 + 5 
f = 5 + e 
g = d / f
h = g * 5
Problem: a man can row upstream at 26 kmph and downstream at 40 kmph , and then find the speed of the man in still water ?
Options: a ) 22 , b ) 37 , c ) 30 , d ) 33 , e ) 18
Rationale: "us = 26 ds = 40 m = ( 40 + 26 ) / 2 = 33 answer : d"
Answer: d
Python program:
a = 26 + 40 
b = a / 2
Problem: if n is an integer from 1 to 96 ( inclusive ) , what is the probability for n * ( n + 1 ) * ( n + 2 ) being divisible by 8 ?
Options: a ) 25 % , b ) 50 % , c ) 62.5 % , d ) 72.5 % , e ) 75 %
Rationale: ( a ) 25 % , to be divisible by 8 the number needs to have 3 2 s in it . only a multiple of 4 can provide that . number of numbers divisible by 4 = 96 / 4 = 24 . so p ( 8 ) = 24 / 96 = 25 % .
Answer: a
Python program:
a = 96 + 2 
b = 1 + 1 
c = a + b 
d = 1 + 1 
e = c * d
f = e / 8
Problem: by selling an article for $ 90 , a person gains $ 15 . what is the gain % ?
Options: a ) 25 % , b ) 30 % , c ) 50 % , d ) 20 % , e ) 10 %
Rationale: "s . p . = $ 90 gain = $ 15 c . p . = 90 - 15 = 75 gain % = 15 / 75 * 100 = 20 % answer is d"
Answer: d
Python program:
a = 15 * 100
b = 90 - 15
c = a / b
Problem: on multiplying a number b by 153 , the result obtained was 102325 . however , it is found that both the 2 ' s are wrong . find the correct result .
Options: a ) 104345 , b ) 107375 , c ) 108385 , d ) 109395 , e ) 105355
Rationale: the only thing you actually know about the correct number b is that it is divisible by 153 and has 5 as a factor . you should immediately try to find the factors of 153 and look for them in the options . 153 = 9 * 17 divisibility by 9 is easy to check . only ( d ) satisfies .
Answer: d
Python program:
a = 153 * 2
b = a * 10
c = 102325 + b
Problem: if a computer program generates 3 - digit odd numbers using the numbers 9 , 7 , 0 , 8 , and 1 , and the digits can be repeated , what is the probability that the number formed from the program is a multiple of 3 ?
Options: a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 7
Rationale: a
Answer: a
Python program:
a = 9 + 10 
b = 2 * 3
c = b * 10
d = a / c
Problem: how many pounds of salt at 70 cents / lb must be mixed with 45 lbs of salt that costs 40 cents / lb so that a merchant will get 20 % profit by selling the mixture at 48 cents / lb ?
Options: a ) 5 , b ) 9 , c ) 40 , d ) 50 , e ) 25
Rationale: "selling price is 48 cents / lb for a 20 % profit , cost price should be 40 cents / lb ( cp * 6 / 5 = 48 ) basically , you need to mix 40 cents / lb ( salt 1 ) with 70 cents / lb ( salt 2 ) to get a mixture costing 45 cents / lb ( salt avg ) weight of salt 1 / weight of salt 2 = ( salt 2 - saltavg ) / ( saltavg - salt 1 ) = ( 70 - 45 ) / ( 45 - 40 ) = 5 / 1 we know that weight of salt 1 is 45 lbs . weight of salt 2 must be 9 lbs . answer ( b )"
Answer: b
Python program:
a = 48 * 45
b = 100 + 20 
c = b / 100
d = 40 * 45
e = c * d
f = a - e
g = 100 + 20 
h = g / 100
i = 70 * h
j = i - 48
k = f / j
Problem: the length of a side of a hexagon is 5 inches . what is the perimeter ?
Options: a ) 116 , b ) 25 , c ) 30 , d ) 24 , e ) 15
Rationale: "hexagon . it means 6 equal sides . p = 5 + 5 + 5 + 5 + 5 + 5 = 10 + 10 + 10 = 30 inches answer c"
Answer: c
Python program:
a = 3 * 2
b = 5 * a
Problem: one fourth of a solution that was 12 % salt by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight . the second solution was what percent salt by weight ?
Options: a ) 28 % , b ) 34 % , c ) 22 % , d ) 18 % , e ) 8.5 %
Rationale: consider total solution to be 100 liters and in this case you ' ll have : 75 * 0.12 + 25 * x = 100 * 0.16 - - > x = 0.28 . answer : a .
Answer: a
Python program:
a = 16 / 100
b = a * 4
c = 12 / 100
d = c * 4
e = 12 / 100
f = d - e
g = b - f
h = g * 100
Problem: a house wife saved $ 4 in buying an item on sale . if she spent $ 28 for the item , approximately how much percent she saved in the transaction ?
Options: a ) 8 % , b ) 13 % , c ) 10 % , d ) 11 % , e ) 12 %
Rationale: "actual price = 28 + 4 = $ 32 saving = 4 / 32 * 100 = 13 % approximately answer is b"
Answer: b
Python program:
a = 28 + 4 
b = 4 / a
c = b * 100
Problem: a can do a work in 3 days . b can do the same work in 6 days . both a & b together will finish the work and they got $ 1000 from that work . find their shares ?
Options: a ) 600,400 , b ) 500,500 , c ) 300,700 , d ) 800,200 , e ) 200,400
Rationale: "ratio of their works a : b = 3 : 6 ratio of their wages a : b = 1 : 2 a ' s share = ( 1 / 5 ) 1000 = 200 b ' s share = ( 2 / 5 ) 1000 = 400 correct option is e"
Answer: e
Python program:
a = 3 * 6
b = 3 + 6 
c = a / b
Problem: two friends deepak and rajeev have agreed to meet at a definite spot on a particular day between 9 pm and 10 pm . the first person to come waits for some time and leaves . if the other one does not turn up by that time . if deepak comes first , he waits for 45 minutes and if rajeev comes first , he waits for 15 minutes . what is the probability of meeting between deepak and rajeev if their arrival times are independent of eachother and each person arrives during the indicated period at random ?
Options: a ) 3 / 4 , b ) 11 / 16 , c ) 7 / 8 , d ) 3 / 16 , e ) 5 / 16
Rationale: deepak : 45 / 60 = 3 / 4 rajeev : 15 / 60 = 1 / 4 as these are independent events total probability = ( 3 / 4 ) * ( 1 / 4 ) = 3 / 16 answer : d
Answer: d
Python program:
a = 45 / const_60
b = 15 / const_60
c = a * b
Problem: claire has a total of 90 pets consisting of gerbils and hamsters only . one - quarter of the gerbils are male , and one - third of the hamsters are male . if there are 25 males altogether , how many gerbils does claire have ?
Options: a ) 39 , b ) 50 , c ) 66 , d ) 57 , e ) 60
Rationale: g + h = 90 . . . 1 ; g / 4 + h / 3 = 25 . . . . 2 or 3 g + 4 h = 25 * 12 = 300 g = 90 - h or 3 ( 90 - h ) + 4 h = 300 h = 300 - 270 = 30 then g = 96 - 30 = 66 c
Answer: c
Python program:
a = 90 - 25
b = a + 1
Problem: what is the units digit of 2222 ^ ( 333 ) * 3333 ^ ( 444 ) ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "each of the other explanations to this question has properly explained that you need to break down the calculation into pieces and figure out the repeatingpatternof the units digits . here ' s another way to organize the information . we ' re given [ ( 2222 ) ^ 333 ] [ ( 3333 ) ^ 222 ] we can ' combine ' some of the pieces and rewrite this product as . . . . ( [ ( 2222 ) ( 3333 ) ] ^ 222 ) [ ( 2222 ) ^ 111 ] ( 2222 ) ( 3333 ) = a big number that ends in a 6 taking a number that ends in a 6 and raising it to a power creates a nice pattern : 6 ^ 1 = 6 6 ^ 2 = 36 6 ^ 3 = 216 etc . thus , we know that ( [ ( 2222 ) ( 3333 ) ] ^ 222 ) will be a gigantic number that ends in a 6 . 2 ^ 111 requires us to figure out thecycleof the units digit . . . 2 ^ 1 = 2 2 ^ 2 = 4 2 ^ 3 = 8 2 ^ 4 = 16 2 ^ 5 = 32 2 ^ 6 = 64 2 ^ 7 = 128 2 ^ 8 = 256 so , every 4 powers , the pattern of the units digits repeats ( 2 , 4 , 8 , 6 . . . . . 2 , 4 , 8 , 6 . . . . ) . 111 = 27 sets of 4 with a remainder of 3 . . . . this means that 2 ^ 111 = a big number that ends in an 8 so we have to multiply a big number that ends in a 6 and a big number that ends in an 8 . ( 6 ) ( 8 ) = 48 , so the final product will be a gigantic number that ends in an 4 . final answer : c"
Answer: c
Python program:
a = 4 + 3 
b = a + 2
Problem: a shopkeeper labeled the price of his articles so as to earn a profit of 30 % on the cost price . he then sold the articles by offering a discount of 10 % on the labeled price . what is the actual percent profit earned in the deal ?
Options: a ) 18 % , b ) 20 % , c ) 17 % , d ) 18 % , e ) none of these
Rationale: explanation : let the cp of the article = rs . 100 . then labeled price = rs . 130 . sp = rs . 130 - 10 % of 130 = rs . 130 - 13 = rs . 117 . gain = rs . 117 – rs . 100 = rs . 17 therefore , gain / profit percent = 17 % . answer : option c
Answer: c
Python program:
a = 100 + 30 
b = 100 + 30 
c = 10 / 100
d = b * c
e = a - d
f = e - 100
Problem: what is the area inscribed by the lines y = 10 , x = 1 , y = 3 x + 1 on an xy - coordinate plane ?
Options: a ) a ) 1 , b ) b ) 2 , c ) c ) 3 , d ) d ) 6 , e ) e ) 12
Rationale: "first , let ' s graph the lines y = 10 and x = 1 at this point , we need to find the points where the line y = 3 x + 1 intersects the other two lines . for the vertical line , we know that x = 1 , so we ' ll plug x = 1 into the equation y = 3 x + 1 to get y = 3 ( 1 ) + 1 = 4 perfect , when x = 1 , y = 5 , so one point of intersection is ( 1,4 ) for the horizontal line , we know that y = 10 , so we ' ll plug y = 10 into the equation y = 3 x + 1 to get 10 = 3 x + 1 . solve to get : x = 3 so , when y = 10 , x = 3 , so one point of intersection is ( 3,10 ) now add these points to our graph and sketch the line y = 3 x + 1 at this point , we can see that we have the following triangle . the base has length 2 and the height is 6 area = ( 1 / 2 ) ( base ) ( height ) = ( 1 / 2 ) ( 2 ) ( 6 ) = 6 answer : d"
Answer: d
Python program:
a = 3 - 10
b = a - 10
c = 10 * const_0_25
d = 3 - 10
e = d - 10
f = c * e
g = b * f
Problem: what is rate of interest if principal . amount be 400 , simple interest 100 and time 2 year .
Options: a ) 10 , b ) 12.5 , c ) 25 , d ) 12 , e ) 14.5
Rationale: "s . i = ( p * r * t ) / 100 100 = 800 r / 100 r = 100 / 8 = 12.5 % answer b"
Answer: b
Python program:
a = 400 * 2
b = 100 / a
c = b * 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 4 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 ) 4 / 7
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 4 * x his total tip for the 7 months = 6 * ( average tip for the months other than august ) + 4 x = 10 x august tips as a fraction of total tips = 4 x / 10 x = 2 / 5 . so b"
Answer: b
Python program:
a = 4 * 1
b = 4 * 1
c = 4 * 1
d = b + c 
e = a / d
Problem: a train covers a distance of 12 km in 10 minutes . if it takes 7 seconds to pass a telegraph post , then the length of the train is
Options: a ) 100 m , b ) 120 m , c ) 140 m , d ) 160 m , e ) 170 cm
Rationale: "explanation : speed = 12 / 10 x 60 km / hr = 72 x 5 / 18 m / sec = 20 m / sec . length of the train = ( speed x time ) = ( 20 x 7 ) m = 140 m answer : option c"
Answer: c
Python program:
a = 12 / 10
b = a - 7
c = 12 / b
Problem: the ratio of the volumes of two cubes is 6859 : 1331 . what is the ratio of their total surface areas ?
Options: a ) 1 : 21 , b ) 12 : 7 , c ) 1 : 15 , d ) 21 : 17 , e ) 13 : 13
Rationale: "ratio of the sides = ³ √ 6859 : ³ √ 1331 = 19 : 11 ratio of surface areas = 192 : 112 = 12 : 7 answer : b"
Answer: b
Python program:
a = 6859 / 1331
b = 1 / 3
c = a ** b
Problem: if a lends rs . 3500 to b at 10 % per annum and b lends the same sum to c at 14 % per annum then the gain of b in a period of 3 years is ?
Options: a ) 400 , b ) 410 , c ) 460 , d ) 420 , e ) 430
Rationale: "( 3500 * 4 * 3 ) / 100 = > 420 answer : d"
Answer: d
Python program:
a = 3500 * 14
b = a * 3
c = b / 100
d = 3500 * 10
e = d * 3
f = e / 100
g = c - f
Problem: a take twice as much time as b or thrice as much time to finish a piece of work . working together , they can finish the work in 6 days . b can do the work alone in ?
Options: a ) 19 , b ) 36 , c ) 11 , d ) 19 , e ) 114
Rationale: "suppose a , b and c take x , x / 2 and x / 3 respectively to finish the work . then , ( 1 / x + 2 / x + 3 / x ) = 1 / 6 6 / x = 1 / 6 = > x = 36 so , b takes 18 hours to finish the work . answer : b"
Answer: b
Python program:
a = 1 + 2 
b = a + 3 
c = b * 6
Problem: a train running at a speed of 36 km / h passes an electric pole in 14 seconds . in how many seconds will the whole train pass a 350 - meter long platform ?
Options: a ) 43 , b ) 45 , c ) 47 , d ) 49 , e ) 51
Rationale: "let the length of the train be x meters . when a train crosses an electric pole , the distance covered is its own length x . speed = 36 km / h = 36000 m / 3600 s = 10 m / s x = 14 * 10 = 140 m . the time taken to pass the platform = ( 140 + 350 ) / 10 = 49 seconds the answer is d ."
Answer: d
Python program:
a = 36 * const_0_2778
b = a * 14
c = b + 350 
d = 36 * const_0_2778
e = c / d
Problem: mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 110 mangoes .
Options: a ) 367 , b ) 380 , c ) 400 , d ) 406 , e ) 412
Rationale: "mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 120 mangoes . method 1 : let price per mango = x . let number of mangoes be n . then , nx = 360 . now price = 0.9 x ; number of mangoes = n + 12 . total amount = 0.9 x * ( n + 12 ) = 360 . nx = 0.9 nx + 10.8 x = > 0.1 nx = 10.8 x = > n = 108 = > x = 360 / 108 = 3.33 original price of 110 mangoes = 110 * 3.33 = 367 . answer a"
Answer: a
Python program:
a = 1 / 10
b = 1 - a
c = 360 / b
d = c - 360
e = d / 12
f = e * 110
Problem: there are two numbers . if 20 % of the first number is added to the second number , then the second number increases to its 5 - fourth . what is the ratio of the first number to the second number ?
Options: a ) 2 : 9 , b ) 3 : 8 , c ) 8 : 5 , d ) 5 : 4 , e ) 7 : 3
Rationale: let the two numbers be x and y . ( 2 / 10 ) * x + y = ( 5 / 4 ) * y ( 2 / 10 ) * x = ( 1 / 4 ) * y x / y = 10 / 8 = 5 / 4 the answer is d .
Answer: d
Python program:
a = 20 / 5
b = 5 / a
Problem: a train is 560 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length ?
Options: a ) 56 seconds , b ) 18 seconds , c ) 40 seconds , d ) 19 seconds , e ) 45 seconds
Rationale: "speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 560 + 140 = 700 meter time = distance / speed = 700 * ( 2 / 25 ) = 56 seconds answer : a"
Answer: a
Python program:
a = 560 + 140 
b = 45 * 1000
c = b / 3600
d = a / c
Problem: the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 1600 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?
Options: a ) 140 , b ) 99 , c ) 88 , d ) 160 , e ) 12
Rationale: "given that the area of the square = 1600 sq . units = > side of square = √ 1600 = 40 units the radius of the circle = side of the square = 40 units length of the rectangle = 2 / 5 * 40 = 16 units given that breadth = 10 units area of the rectangle = lb = 16 * 10 = 160 sq . units answer : d"
Answer: d
Python program:
a = math.sqrt(1600)
b = 10 / 2
c = a / b
d = 2 * c
e = 10 * d
Problem: the average age of 28 students in a group is 11 years . when teacher ’ s age is included to it , the average increases by one . what is the teacher ’ s age in years ?
Options: a ) 36 , b ) 38 , c ) 40 , d ) can not be determined , e ) none of these
Rationale: "age of the teacher = ( 29 × 12 – 28 × 11 ) years = 40 years . answer c"
Answer: c
Python program:
a = 28 + 1
Problem: a man can row his boat with the stream at 10 km / h and against the stream in 6 km / h . the man ' s rate is ?
Options: a ) 2 kmph , b ) 7 kmph , c ) 98 kmph , d ) 6 kmph , e ) 4 kmph
Rationale: "ds = 10 us = 6 s = ? s = ( 10 - 6 ) / 2 = 2 kmph answer : a"
Answer: a
Python program:
a = 10 - 6
b = a / 2
Problem: if the product of 12 integers is negative , at most how many of the integers can be negative ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 11
Rationale: "the product of 12 integers is negative thus an odd number of integers need to be negative to have a negative product we are asked at most how many are required . so , the highest odd integer before 6 , i . e . 11 correct option : e"
Answer: e
Python program:
a = 12 - 1
Problem: a number is said to be prime saturated if the product of all the different positive prime factors of d is less than the square root of d . what is the greatest two digit prime saturated integer ?
Options: a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95
Rationale: "clearly d a number is said to be prime saturated if the product of all the different positive prime factors of d is less than the square root of d . 96 has more number of smaller prime factor thats the clue ! ! = d"
Answer: d
Python program:
a = 2 * 3
b = 100 - 10
c = a + b