euclaise/mathqa_programs huggingface dataset:
Problem: how many positive integers less than 256 are multiple of 4 but not multiples of 6 ?
Options: a ) 20 , b ) 31 , c ) 42 , d ) 43 , e ) 64
Rationale: from here , it might be easier to go up in bounds of 60 , so we know that 61 - 120 gives 10 more numbers . 121 - 180 and 181 - 240 as well . this brings us up to 240 with 40 numbers . a cursory glance at the answer choices should confirm that it must be 42 , as all the other choices are very far away . the numbers 244 and 248 will come and complete the list that ’ s ( naughty or nice ) under 250 . answer choice d is correct here .
Answer: d
Python program:
a = 4 + 4 
b = a - 1
c = math.factorial(b)
d = math.factorial(4)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: jill invests $ 10000 in an account that pays an annual rate of 3.96 % , compounding semi - annually . approximately how much e does she have in her account after two years ?
Options: a ) $ 10079.44 , b ) e = $ 10815.83 , c ) $ 12652.61 , d ) $ 14232.14 , e ) $ 20598.11
Rationale: "ps . i guess one can use simple interest to solve cause the answer choices are quite spread between you can easily arrive at something near 8 % hence b the answer"
Answer: b
Python program:
a = 3 / 96
b = a / 2
c = 1 + b 
d = c ** 4
e = 10000 * d
Problem: two numbers are respectively 19 % and 40 % more than a third number . the percentage that is first of the second is ?
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 35 %
Rationale: i ii iii 119 140 100 140 - - - - - - - - - - 119 100 - - - - - - - - - - - ? = > 15 % answer : a
Answer: a
Python program:
a = 19 + 100 
b = 40 + 100 
c = a / b
d = c * 100
e = 100 - d
Problem: the c . p of 5 books is equal to the s . p of 20 books . find his gain % or loss % ?
Options: a ) 35 % , b ) 20 % , c ) 5 % , d ) 25 % , e ) 75 %
Rationale: "explanation : 5 cp = 20 sp 20 - - - 15 cp loss 100 - - - ? = > 75 % loss answer : e"
Answer: e
Python program:
a = 5 / 20
b = 1 - a
c = b * 100
Problem: for all positive integers m and v , the expression m θ v represents the remainder when m is divided by v . what is the value of ( ( 90 θ 33 ) θ 17 ) - ( 99 θ ( 33 θ 17 ) ) ?
Options: a ) 10 , b ) 8 , c ) 6 , d ) 4 , e ) 2
Rationale: "( ( 90 θ 33 ) θ 17 ) the remainder of 90 divided by 33 is 24 ; the remainder of 24 divided by 17 is 7 ; ( 99 θ ( 33 θ 17 ) ) the remainder of 33 divided by 17 is 16 ; 7 - 3 = 4 . answer : d ."
Answer: d
Python program:
a = reminder - (
Problem: convert the 10 / 36 m / s into kilometers per hour ?
Options: a ) 2.9 kmph , b ) 9.9 kmph , c ) 1.3 kmph , d ) 1 kmph , e ) 5.7 kmph
Rationale: "10 / 36 m / s = 10 / 36 * 18 / 5 = 1 / 1 = 1 kmph . answer : d"
Answer: d
Python program:
a = 10 / 36
b = const_3_6 * a
Problem: what is the remainder when 9 ^ 1 + 9 ^ 2 + 9 ^ 3 + . . . + 9 ^ 9 is divided by 3 ?
Options: a ) 0 , b ) 3 , c ) 2 , d ) 5 , e ) none of the above
Rationale: "notice that in the brackets we have the sum of 8 odd multiples of 3 , which yields remainder of 0 upon division by 3 . answer : a"
Answer: a
Python program:
a = 9 ** 1
b = 9 ** 1
c = a - b
d = c / 9
Problem: if the price of gasoline increases by 25 % and a driver intends to spend only 10 % more on gasoline , by how much percent should the driver reduce the quantity of gasoline that he buys ?
Options: a ) 5 % , b ) 8 % , c ) 10 % , d ) 12 % , e ) 15 %
Rationale: "let x be the amount of gasoline the driver buys originally . let y be the new amount of gasoline the driver should buy . let p be the original price per liter . ( 1.25 * p ) y = 1.1 ( p * x ) y = ( 1.1 / 1.25 ) * x = 0.88 x which is a reduction of 12 % . the answer is d ."
Answer: d
Python program:
a = 25 + 100 
b = 10 + 100 
c = a - b
d = 25 + 100 
e = c / d
f = e * 100
Problem: a square was given . inside the square there are white tiles and black tiles . black tiles was among the diagonal of the square and dimensions of both white as well as black tiles is 1 cm x 1 cm . if there are 81 black tiles in the square . then find the no of white tiles in it .
Options: a ) 2399
b ) 1600
c ) 2679
d ) 1697
e ) 1711
Rationale: in a square , number of squares on the diagonal is equal to the tiles on a single row . if there are even number of square on a side , then total squares on the diagonal is 2 n - 1 , otherwise 2 n . as the total tiles on the diagonal are given as 81 , then number of tiles on a side = 2 n - 1 = 81 so n = 41 . so number of white tiles = 412 − 81 = 1681 − 81412 − 81 = 1681 − 81 = 1600 answer : b
Answer: b
Python program:
a = 81 + 1 
b = a / 2
c = b ** 2
d = c - 81
Problem: if each edge of cube increased by 15 % , the percentage increase in
Options: a ) 30.25 , b ) 32.25 , c ) 38.25 , d ) 37.25 , e ) 41.25
Rationale: "100 × ( 115 ) / 100 × ( 115 ) / 100 = 132.25 = > 32.25 % answer is b ."
Answer: b
Python program:
a = 100 + 15 
b = a ** 3
c = 100 ** 3
d = b - c
e = 100 ** 3
f = d / e
g = 100 * f
Problem: the average age of 16 students of a class is 16 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years , the age of the 12 th student is
Options: a ) 11 , b ) 66 , c ) 18 , d ) 16 , e ) 42
Rationale: "explanation : age of the 16 th student = [ 16 * 16 - ( 14 * 5 + 16 * 9 ) ] = ( 256 - 214 ) = 42 years . answer : e"
Answer: e
Python program:
a = 16 * 16
b = 5 * 14
c = 9 * 16
d = b + c 
e = a - d
Problem: the difference between the place value and the face value of 8 in the numeral 856973 is
Options: a ) 973 , b ) 6973 , c ) 5994 , d ) 6084 , e ) none of these
Rationale: "( place value of 8 ) - ( face value of 8 ) = ( 800000 - 8 ) = 799992 answer : option e"
Answer: e
Python program:
a = 10 * 8
b = a - 8
Problem: the average speed of a car is 1 4 / 5 times the avg speed of a bike . a tractor covers 575 km in 23 hrs . how much distance will the car cover in 6 hrs if the speed of the bike is twice speed of the tractor ?
Options: a ) 400 km , b ) 500 km , c ) 360 km , d ) 540 km , e ) 600 km
Rationale: "sol . average speed of a tractor = 25 km / h the speed of a bus in an hour = 25 × 2 = 50 km the speed of a car in an hour = 9 / 5 * 50 = 90 km so , the distance covered by car in 6 h is 90 × 6 = 540 km ans . ( d )"
Answer: d
Python program:
a = 4 / 5
b = 1 + a 
c = 575 / 23
d = 2 * c
e = b * d
f = e * 6
Problem: 33 men can complete a piece of work in 18 days . in how many days will 27 men complete the same work ?
Options: a ) 22 , b ) 77 , c ) 36 , d ) 25 , e ) 13
Rationale: "explanation : less men , means more days { indirect proportion } let the number of days be x then , 27 : 33 : : 18 : x [ please pay attention , we have written 27 : 33 rather than 33 : 27 , in indirect proportion , if you get it then chain rule is clear to you : ) ] { \ color { blue } x = \ frac { 33 \ times 18 } { 27 } } x = 22 so 22 days will be required to get work done by 27 men . answer : a"
Answer: a
Python program:
a = 18 * 33
b = a / 27
Problem: john makes $ 65 a week from his job . he earns a raise andnow makes $ 70 a week . what is the % increase ?
Options: a ) 7.69 % , b ) 16.66 % , c ) 17.8 % , d ) 19 % , e ) 21 %
Rationale: "increase = ( 5 / 65 ) * 100 = ( 1 / 13 ) * 100 = 7.69 % . a"
Answer: a
Python program:
a = 70 - 65
b = a / 65
c = b * 100
Problem: in kaya ' s teacher ' s desk there are 6 pink highlighters , 2 yellow highlighters , and 4 blue highlighters . how many highlighters are there in all ?
Options: a ) 11 , b ) 12 , c ) 77 , d ) 33 , e ) 88
Rationale: "add the numbers of highlighters . 6 + 2 + 4 = 12 . answer is b ."
Answer: b
Python program:
a = 6 + 2 
b = a + 4
Problem: if a speaks the truth 20 % of the times , b speaks the truth 80 % of the times . what is the probability that at least one will tell the truth
Options: a ) 0.82 , b ) 0.84 , c ) 1.5 , d ) 1.2 , e ) 1.4
Rationale: "probability of a speaks truth p ( a ) = 2 / 10 ; false = 8 / 10 probability of b speaks truth p ( b ) = 8 / 10 ; false = 2 / 10 . for given qtn ans = 1 - ( neither of them tell truth ) . because a & b are independent events = 1 - [ ( 8 / 10 ) * ( 2 / 10 ) ] = 1 - 16 / 100 = 1 - 0.16 = 0.84 answer : b"
Answer: b
Python program:
a = 4 * 5
b = a * 5
c = 20 / b
d = 4 * 5
e = d * 5
f = 80 / e
g = c * f
Problem: a man can do a piece of work in 15 days , but with the help of his son , he can do it in 6 days . in what time can the son do it alone ?
Options: a ) 13 , b ) 9 , c ) 15 , d ) 8 , e ) 10
Rationale: "son ' s 1 day ' s work = ( 1 / 6 ) - ( 1 / 15 ) = 3 / 30 = 1 / 10 the son alone can do the work in 10 days answer is e"
Answer: e
Python program:
a = 15 * 6
b = 15 - 6
c = a / b
Problem: how many of the positive factors of 45 , 16 and how many common factors are there in numbers ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "factors of 45 - 1 , 3 , 9 , 15 and 45 factors of 16 - 1 , 2 , 4 , 8 and 16 comparing both , we have three common factors of 45,16 - 1 answer ( a )"
Answer: a
Python program:
a = 16 / 45
Problem: if y is the smallest positive integer such that 8820 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: "8820 = 2 ^ 2 * 3 ^ 2 * 5 * 7 ^ 2 to be perfect square , we need to multiply by at least 5 . the answer is b ."
Answer: b
Python program:
a = 2 + 3 
b = a * 2
Problem: if 20 typists can type 60 letters in 20 minutes , then how many letters will 30 typists working at the same rate complete in 1 hour ?
Options: a ) 240 , b ) 200 , c ) 270 , d ) 300 , e ) 310
Rationale: "no . of letters typing by 20 typists in 20 minutes = 60 no . of letters typing by 20 typists in 60 minutes = 60 * 3 = 180 no . of letters typing by 30 typists in 60 minutes = 180 / 20 * 30 = 270 answer : c"
Answer: c
Python program:
a = 60 * 3
b = a / 20
c = b * 30
Problem: a batsman makes a score of 85 runs in the 17 th inning and thus increases his averages by 3 . find his average after 17 th inning ?
Options: a ) 19 , b ) 29 , c ) 37 , d ) 49 , e ) 59
Rationale: "let the average after 17 th inning = x then average after 16 th inning = ( x - 3 ) therefore 16 ( x - 3 ) + 85 = 17 x therefore x = 37 answer : c"
Answer: c
Python program:
a = 17 * 3
b = 85 - a
c = b + 3
Problem: of the families in city x in 1998 , 20 percent owned a personal computer . the number of families in city x owning a computer in 2002 was 40 percent greater than it was in 1998 , and the total number of families in city x was 8 percent greater in 2002 than it was in 1998 . what percent of the families in city x owned a personal computer in 2002 ?
Options: a ) 49.66 % , b ) 52.66 % , c ) 28.22 % , d ) 33.33 % , e ) 25.92 %
Rationale: "say a 100 families existed in 1998 then the number of families owning a computer in 1998 - 20 number of families owning computer in 2002 = 20 * 140 / 100 = 28 number of families in 2002 = 108 the percentage = 28 / 108 * 100 = 25.92 % . answer : e"
Answer: e
Python program:
a = 40 + 100 
b = a * 20
c = b / 100
d = 100 + 8 
e = c / d
f = 100 * e
Problem: three numbers are in the ratio of 2 : 3 : 4 and their l . c . m . is 240 . their h . c . f . is :
Options: a ) 30 , b ) 20 , c ) 40 , d ) 60 , e ) 70
Rationale: "explanation : let the number be 2 x , 3 x and 4 x lcm of 2 x , 3 x and 4 x = 12 x 12 x = 240 = > x = 240 / 12 = 20 hcf of 2 x , 3 x and 4 x = x = 20 answer : option b"
Answer: b
Python program:
a = 2 * 4
Problem: if the radius of a circle is increased by 10 % then the area is increased by :
Options: a ) 44 % , b ) 120 % , c ) 144 % , d ) 40 % , e ) 21 %
Rationale: "initially a = pi * r 2 now r 2 = 110 / 100 r then area = pi * ( 110 r / 100 ) 2 area = 121 r / 100 that is area increases from 100 to 121 = increase in area = 21 % answer : e"
Answer: e
Python program:
a = 100 / 100
b = 100 / 100
c = 10 / 100
d = b - c
e = d ** 2
f = a - e
g = f * 100
Problem: 217 x 217 + 183 x 183 = ?
Options: a ) 79698 , b ) 80578 , c ) 80698 , d ) 81268 , e ) none of them
Rationale: "= ( 217 ) ^ 2 + ( 183 ) ^ 2 = ( 200 + 17 ) ^ 2 + ( 200 - 17 ) ^ 2 = 2 [ ( 200 ) ^ 2 + ( 17 ) ^ 2 ] = 2 [ 40000 + 289 ] = 2 x 40289 = 80578 answer is b"
Answer: b
Python program:
a = 217 ** 183
b = 217 * a
Problem: kim has 6 pairs of shoes ; each pair is a different color . if kim randomly selects 2 shoes without replacement from the 12 shoes , what is the probability that she will select 2 shoes of the same color ?
Options: a ) 2 / 5 , b ) 1 / 5 , c ) 1 / 9 , d ) 1 / 11 , e ) 1 / 25
Rationale: total pairs = 12 c 2 = 66 ; same color pairs = 6 c 1 * 1 c 1 = 6 ; prob = 1 / 11 ans d
Answer: d
Python program:
a = math.comb(12, 2)
b = 6 / a
Problem: in a kilometer race , a beats b by 40 meters or 10 seconds . what time does a take to complete the race ?
Options: a ) 290 sec , b ) 190 sec , c ) 199 sec , d ) 192 sec , e ) 240 sec
Rationale: "time taken by b run 1000 meters = ( 1000 * 10 ) / 40 = 250 sec . time taken by a = 250 - 10 = 240 sec . answer : e"
Answer: e
Python program:
a = 1 * 1000
b = 40 / 10
c = a / b
d = c - 10
Problem: a crow leaves its nest , and flies back and forth from its nest to a nearby ditch to gather worms . the distance between the nest and the ditch is 100 meters . in one and a half hours , the crow manages to bring worms to its nest 15 times . what is the speed of the crow in kilometers per hour ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 7
Rationale: the distance between the nest and the ditch is 100 meters . 15 times mean = a crow leaves its nest , and flies back ( going and coming back ) i . e . 2 times we get total 30 rounds . so the distance is 30 * 100 = 3000 . d = st 3000 / 1.5 = t , i think we can take 3000 meters as 3 km , then only we get t = 2 . ( 1000 meters = 1 km ) d )
Answer: d
Python program:
a = 15 * 2
b = 100 * a
c = b / 1000
d = 15 / 10
e = c / d
Problem: s is a set of 100 consecutive multiples of 8 . if the smallest number in s is 108 , then the greatest number in s is
Options: a ) 998 , b ) 297 , c ) 999 , d ) 902 , e ) 900
Rationale: "last term = first term + ( total no . of terms - 1 ) consecutive difference s is a set of 100 consecutive multiples of 8 . if the smallest number in s is 108 , then the greatest number in s is first term = 102 ; total terms = 100 ; difference = 3 108 + ( 99 ) 8 = 900 ans e"
Answer: e
Python program:
a = 100 - 1
b = a * 8
c = 108 + b
Problem: the batting average of a particular batsman is 62 runs in 46 innings . if the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs , find his highest score .
Options: a ) 179 , b ) 208 , c ) 210 , d ) 225 , e ) 229
Rationale: "explanation : total runs scored by the batsman = 62 * 46 = 2852 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2852 – 2552 = 300 runs . let the highest score be x , hence the lowest score = x – 150 x + ( x - 150 ) = 300 2 x = 450 x = 225 runs answer d"
Answer: d
Python program:
a = 62 * 46
b = 46 - 2
c = 58 * b
d = a - c
e = 150 + d 
f = e / 2
Problem: what is the greatest value of positive integer x such that 2 ^ x is a factor of 100 ^ 50 ?
Options: a ) 70 , b ) 80 , c ) 90 , d ) 100 , e ) 120
Rationale: put in simple words , we need to find the highest power of 2 in 100 ^ 50 100 = 2 ^ 2 * 5 ^ 2 therefore 100 ^ 50 = ( 2 ^ 2 * 5 ^ 2 ) ^ 50 = 2 ^ 100 * 5 ^ 100 answer : d
Answer: d
Python program:
a = 100 / 50
b = 2 ** a
c = b - 1
d = 100 - c
Problem: a towel , when bleached , lost 10 % of its length and 20 % of its breadth . what is the percentage decrease in area ?
Options: a ) 28 % , b ) 30 % , c ) 44 % , d ) 54 % , e ) 64 %
Rationale: "percentage change in area = ( − 10 − 20 + ( 10 × 20 ) / 100 ) % = − 28 % i . e . , area is decreased by 28 % answer : a"
Answer: a
Python program:
a = 100 * 100
b = 100 - 10
c = 100 - 20
d = b * c
e = a - d
f = e / 100
Problem: if 5 ^ 5 × 5 ^ 7 = ( 5 ^ 4 ) ^ x , then what is the value of x ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: 5 ^ 5 × 5 ^ 7 = ( 5 ^ 4 ) ^ x 5 ^ ( 5 + 7 ) = 5 ^ ( 12 ) with multiplying numbers with exponents it ' s the same as adding the exponents 5 ^ 12 = ( 5 ^ 4 ) ^ x since base is same , we can equate powers : when raising an exponent to an exponent , it ' s the same as multiplying them , therefore : 12 = 4 x x = 3 ans . b ) 3
Answer: b
Python program:
a = 5 ** 5
b = 5 ** 7
c = a * b
d = math.log(c)
e = 5 ** 4
f = math.log(e)
g = d / f
Problem: in a group of cows and hens , the number of legs are 16 more than twice the number of heads . the number of cows is
Options: a ) 5 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "explanation : let the number of cows be x and the number of hens be y . then , 4 x + 2 y = 2 ( x + y ) + 16 4 x + 2 y = 2 x + 2 y + 16 2 x = 16 x = 8 . answer : b"
Answer: b
Python program:
a = 16 - 4
Problem: on rainy mornings , mo drinks exactly n cups of hot chocolate ( assume that n is an integer ) . on mornings that are not rainy , mo drinks exactly 2 cups of tea . last week mo drank a total of 16 cups of tea and hot chocolate together . if during that week mo drank 4 more tea cups than hot chocolate cups , then how many rainy days were there last week ?
Options: a ) 6 , b ) 3 , c ) 4 , d ) 5 , e ) 2
Rationale: "t = the number of cups of tea c = the number of cups of hot chocolate t + c = 16 t - c = 4 - > t = 10 . c = 6 . mo drinks 5 cups of tea a day then number of days that are not rainy = 10 / 2 = 5 so number of rainy days = 7 - 5 = 2 e is the answer ."
Answer: e
Python program:
a = 4 + 2 
b = 16 + 4 
c = b / 2
d = c / 2
e = a - d
Problem: if the price of a tv is first decreased by 20 % and then increased by 30 % , then the net change in the price will be :
Options: a ) 4 % increase , b ) 10 % increase , c ) 10 % decrease , d ) 6 % increase , e ) none of these
Rationale: explanation : solution : let the original price be rs . 100 . new final price = 130 % of ( 80 % of 100 ) = rs . 130 / 100 * 80 / 100 * 100 = rs . 104 . . ' . increase = 4 % answer : a
Answer: a
Python program:
a = 100 - 20
b = 100 + 30 
c = a * b
d = c / 100
e = d - 100
Problem: equal amount of water were poured into two empty jars of different capacities , which made one jar 1 / 5 full and other jar 1 / 4 full . if the water in the jar with lesser capacity is then poured into the jar with greater capacity , what fraction of the larger jar will be filled with water ?
Options: a ) 1 / 7 , b ) 2 / 5 , c ) 1 / 2 , d ) 7 / 12 , e ) 2 / 3
Rationale: "same amount of water made bigger jar 1 / 5 full , then the same amount of water ( stored for a while in smaller jar ) were added to bigger jar , so bigger jar is 1 / 5 + 1 / 5 = 2 / 5 full . answer : b ."
Answer: b
Python program:
a = 2 / 5
Problem: if the average ( arithmetic mean ) of x + 3 , x + 4 , and x + 5 is 0 , then x =
Options: a ) – 4 , b ) – 3 , c ) – 2 , d ) – 1 , e ) 0
Rationale: "( x + 3 + x + 4 + x + 5 ) / 3 = 0 = > 3 x + 12 = 0 = > x = - 4 answer a"
Answer: a
Python program:
a = 4 * 2
b = 3 * 2
c = a - b
Problem: dan can do a job alone in 15 hours . annie , working alone , can do the same job in just 10 hours . if dan works alone for 6 hours and then stops , how many hours will it take annie , working alone , to complete the job ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "dan can complete 1 / 15 of the job per hour . in 6 hours , dan completes 6 ( 1 / 15 ) = 2 / 5 of the job . annie can complete 1 / 10 of the job per hour . to complete the job , annie will take 3 / 5 / 1 / 10 = 6 hours . the answer is c ."
Answer: c
Python program:
a = 6 / 15
b = 1 - a
c = b * 10
Problem: when processing flower - nectar into honey bees ' extract , a considerable amount of water gets reduced . how much flower - nectar must be processed to yield 1 kg of honey , if nectar contains 50 % water , and the honey obtained from this nectar contains 20 % water ?
Options: a ) 1.2 kg , b ) 1.5 kg , c ) 1.7 kg , d ) 1.6 kg , e ) none of these
Rationale: "explanation : flower - nectar contains 50 % of non - water part . in honey this non - water part constitutes 80 % ( 100 - 20 ) . therefore 0.5 x amount of flower - nectar = 0.80 x amount of honey = 0.80 x 1 kg therefore amount of flower - nectar needed = ( 0.80 / 0.51 ) kg = 1.6 kgs answer : d"
Answer: d
Python program:
a = 100 - 20
b = a / 100
c = 50 / 100
d = b / c
Problem: in a throw of dice what is the probability of ge æ « ing number greater than 2
Options: a ) 2 / 3 , b ) 1 / 3 , c ) 1 / 5 , d ) 1 / 6 , e ) none of these
Rationale: "explanation : number greater than 2 is 3 , 4 , 5 & 6 , so only 4 number total cases of dice = [ 1,2 , 3,4 , 5,6 ] so probability = 4 / 6 = 2 / 3 answer : a"
Answer: a
Python program:
a = 6 - 2
b = a / 6
Problem: find the area of a cuboid of length 8 cm , breadth 10 cm . and height 12 cm .
Options: a ) 900 cm cube , b ) 910 cm cube , c ) 920 cm cube , d ) 930 cm cube , e ) 960 cm cube
Rationale: "area of a cuboid = lxbxh = 8 cm x 10 cm x 12 cm = 960 cm cube answer : e"
Answer: e
Python program:
a = 8 * 10
b = a * 12
Problem: if a car went the first third of the distance at 60 kmh , the second third at 24 kmh , and the last third at 48 kmh , what was the average speed of the car for the entire trip ?
Options: a ) 38 kmh , b ) 40 kmh , c ) 42 kmh , d ) 44 kmh , e ) 50 kmh
Rationale: "assume d / 3 = 240 ( this number is convenient because it is divisible by 60 , 24 and 48 ) so : 240 = 60 * t 1 = 4 hrs 240 = 24 * t 2 = 10 hrs 240 = 48 * t 3 = 5 hrs t = t 1 + t 2 + t 3 = 19 hrs d = rt ( 240 * 3 ) = r * 19 r = 38 answer : a"
Answer: a
Python program:
a = 1 / 60
b = 1 / 24
c = a + b 
d = 1 / 48
e = c + d 
f = 3 / e
Problem: a reduction of 10 % in the price of oil enables a house wife to obtain 6 kgs more for rs . 900 , what is the reduced price for kg ?
Options: a ) 13 , b ) 15 , c ) 25 , d ) 17 , e ) 19
Rationale: "900 * ( 10 / 100 ) = 90 - - - - 6 ? - - - - 1 = > rs . 15 answer : b"
Answer: b
Python program:
a = 900 * 10
b = a / 100
c = b / 6
Problem: the triplicate ratio of 3 : 5 is ?
Options: a ) 27 : 125 , b ) 1 : 62 , c ) 1 : 34 , d ) 3 : 64 , e ) 5 : 64
Rationale: "3 ^ 3 : 5 ^ 3 = 27 : 125 answer : a"
Answer: a
Python program:
a = 2 ** 0
b = 5 ** 5
c = a / b
Problem: a , b and c are partners . a receives 2 / 3 of profits , b and c dividing the remainder equally . a ' s income is increased by rs . 200 when the rate to profit rises from 5 to 7 percent . find the capital of a ?
Options: a ) 3377 , b ) 2899 , c ) 2500 , d ) 2778 , e ) 10000
Rationale: "a : b : c = 2 / 3 : 1 / 6 : 1 / 6 = 4 : 1 : 1 x * 2 / 100 * 2 / 3 = 200 a capital = 15000 * 2 / 3 = 10000 answer : e"
Answer: e
Python program:
a = 200 * 100
b = a / 2
Problem: find out the square of a number which when doubled exceeds its quarter by 7 ?
Options: a ) 16 , b ) 11 , c ) 31 , d ) 29 , e ) 19
Rationale: "a 16 explanation : let the number be p , then the square will be p ^ 2 according to question : 2 p = ( p / 4 ) + 7 = > 8 p = p + 28 = > p = 4 p ^ 2 = 4 ^ 2 = 16 ."
Answer: a
Python program:
a = 4 + 1 
b = 1 / a
c = 2 - b
d = 7 / c
e = d ** 2
Problem: a sports equipment store sold ping pong rackets for a total of $ 490 . if the average ( arithmetic mean ) price of a pair of rackets is $ 9.8 , how many pairs were sold ?
Options: a ) 50 , b ) 100 , c ) 490 , d ) 500 , e ) 980
Rationale: "average price for a pair of rackets = $ 9.8 total cost = $ 9.8 * x = $ 490 x = 50 pairs were sold . answer : a"
Answer: a
Python program:
a = 490 / 9
Problem: a little girl went to the farm to buy fruits . she bought a bag of apples and grabbed a bag of oranges which was 5 times as heavy as the apples . she brought home a total of 12 pounds of fruits . how many pounds was the oranges ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 10 , e ) 12
Rationale: pounds of apples = x pounds of oranges = 5 x x + 5 x = 12 6 x = 12 x = 12 / 6 = 2 oranges = 5 x = 5 * 2 = 10 answer : d
Answer: d
Python program:
a = 5 * 12
b = 5 + 1 
c = a / b
Problem: a batsman scored 120 runs which included 3 boundaries and 8 sixes . what percent of his total score did he make by running between the wickets .
Options: a ) 40 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 75 %
Rationale: "explanation : number of runs made by running = 110 - ( 3 x 4 + 8 x 6 ) = 120 - ( 60 ) = 60 now , we need to calculate 60 is what percent of 120 . = > 60 / 120 * 100 = 50 % answer is b"
Answer: b
Python program:
a = 3 * 8
b = 8 * 3
c = a + b 
d = 120 - c
e = d / 120
f = e * 100