euclaise/mathqa_programs huggingface dataset:
Problem: a alone can finish a work in 10 days which b alone can finish in 15 days . if they work together and finish it , then out of a total wages of rs . 3500 , a will get :
Options: a ) rs . 1200 , b ) rs . 1500 , c ) rs . 2100 , d ) rs . 2000 , e ) none of these
Rationale: "explanation : ratio of working days of a : b = 10 : 15 therefore , their wages ratio = reverse ratio = 15 : 10 therefore , a will get 15 units of ratio total ratio = 25 1 unit of ratio = 3500 / 25 = 140 so , a ’ s amount = 120 × 15 = rs . 2100 . answer : option c"
Answer: c
Python program:
a = 15 * 2
b = a / 10
c = 15 * 2
d = c / 10
e = 15 * 2
f = e / 15
g = d + f 
h = b / g
i = h * 3500
Problem: the probability that a number selected at random from the first 50 natural numbers is a composite number is - .
Options: a ) 17 / 25 , b ) 17 / 27 , c ) 17 / 18 , d ) 17 / 22 , e ) 17 / 09
Rationale: "the number of exhaustive events = ⁵ ⁰ c ₁ = 50 . we have 15 primes from 1 to 50 . number of favourable cases are 34 . required probability = 34 / 50 = 17 / 25 . answer : a"
Answer: a
Python program:
a = 6 * 3
b = a - 1
c = b * 2
d = c / 50
Problem: there are certain number of hats and gloves in a box . they are of 41 red , 23 green , 11 orange . power gone but a woman can differentiate between hats and gloves . how many draws are required to obtain a pair of each color ?
Options: a ) 66 , b ) 67 , c ) 68 , d ) 69 , e ) 70
Rationale: the worst case senario will be first take 40 red then take 22 green then take 1 + 1 red + green then take 2 orange . so total 40 + 22 + 2 + 2 = 66 answer : a
Answer: a
Python program:
a = 41 + 23 
b = a + 2
Problem: 19.19 / 2000 is equal to :
Options: a ) 1.01252633 , b ) 0.01262533 , c ) 0.12526333 , d ) 0.012793333 , e ) 0.12725333
Rationale: "19.19 / 2000 = 2525 / 200000 = 0.012793333 answer : d"
Answer: d
Python program:
a = 19 / 19
Problem: the average weight of 20 persons sitting in a boat had some value . a new person added to them whose weight was 49 kg only . due to his arrival , the average weight of all the persons decreased by 5 kg . find the average weight of first 20 persons ?
Options: a ) 55 , b ) 56 , c ) 57 , d ) 58 , e ) 59
Rationale: "20 x + 49 = 21 ( x – 5 ) x = 56 answer : b"
Answer: b
Python program:
a = 20 + 1 
b = a * 5
c = b - 49
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 3 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 3 * x his total tip for the 7 months = 6 * ( average tip for the months other than august ) + 3 x = 9 x august tips as a fraction of total tips = 3 x / 9 x = 1 / 3 . so answer is a"
Answer: a
Python program:
a = 3 * 1
b = 3 * 1
c = 3 * 1
d = b + c 
e = a / d
Problem: how many shots of 1 cm radius can be prepared from a sphere of 3 cm radius ?
Options: a ) 33 , b ) 88 , c ) 27 , d ) 88 , e ) 99
Rationale: "4 / 3 π * 3 * 3 * 3 = 4 / 3 π * 1 * 1 * 1 * x x = 27 answer : c"
Answer: c
Python program:
a = 3 ** 2
b = a * 3
Problem: two trains each 190 m in length each , are running on two parallel lines in opposite directions . if one goes at the speed of 65 km / h while the other travels at 50 km / h . how long will it take for them to pass each other completely .
Options: a ) 10.7 sec , b ) 2.7 sec , c ) 11.9 sec , d ) 12.7 sec , e ) 25.7 sec
Rationale: "explanation : d = 190 m + 190 m = 380 m rs = 65 + 50 = 115 * 5 / 18 = 319 / 10 t = 380 * 10 / 319 = 11.9 sec answer : option c"
Answer: c
Python program:
a = 190 + 190 
b = a / 1000
c = 65 + 50 
d = b / c
e = 3600 * d
Problem: a 600 m long train crosses a tree in 60 sec , how much time will it take to pass a platform 450 m long ?
Options: a ) 288 , b ) 190 , c ) 188 , d ) 188 , e ) 105
Rationale: "l = s * t s = 600 / 60 s = 10 m / sec . total length ( d ) = 1050 m t = d / s t = 1050 / 10 t = 105 sec answer : e"
Answer: e
Python program:
a = 600 + 450 
b = 600 / 60
c = a / b
Problem: the price of rice falls by 10 % . how much rice can be bought now with the money that was sufficient to buy 20 kg of rice previously ?
Options: a ) 5 kg , b ) 15 kg , c ) 25 kg , d ) 30 kg , e ) none
Rationale: "solution : let rs . 100 be spend on rice initially for 20 kg . as the price falls by 10 % , new price for 20 kg rice , = ( 100 - 10 % of 100 ) = 90 new price of rice = 90 / 20 = rs . 4,5 per kg . rice can bought now at = 100 / 4,5 = 22,22 kg . answer : option e"
Answer: e
Python program:
a = 100 - 10
b = a / 20
c = 100 / b
Problem: the least number , which when divided by 12 , 15 , 20 and 63 leaves in each case a remainder of 8 is :
Options: a ) 448 , b ) 488 , c ) 542 , d ) 1268 , e ) 560
Rationale: "required number = ( l . c . m . of 12 , 15 , 20 , 63 ) + 8 = 1260 + 8 = 1268 . answer : d"
Answer: d
Python program:
a = 63 * 10
Problem: in a class of 50 students , 3 / 5 went away do painting , 1 / 5 went to play in the field . how many students are left in the classroom ?
Options: a ) 20 , b ) 30 , c ) 5 , d ) 8 , e ) 10
Rationale: 3 / 5 + 1 / 5 are the students who have left the classroom 3 / 5 + 1 / 5 = ( 3 + 1 ) / 5 , since denominator is same for both fractions = 4 / 5 remaining students in the classroom = 1 - 4 / 5 = 5 / 5 - 4 / 5 = ( 5 - 4 ) / 5 = 1 / 5 1 / 5 of 50 = 10 ans : e
Answer: e
Python program:
a = 3 / 5
b = 50 * a
c = 1 / 5
d = 50 * c
e = b + d 
f = 50 - e
Problem: a statue is being carved by a sculptor . the original piece of marble weighed 300 kg . in the first week 30 percent is cut away . in the second week 30 percent of the remainder is cut away . in the third week the statue is completed when 15 percent of the remainder is cut away . what is the weight of the final statue ?
Options: a ) 105 kg , b ) 103 kg , c ) 108 kg , d ) 125 kg , e ) 117 kg
Rationale: "d 125 kg 300 ã — 0.7 ã — 0.7 ã — 0.85 = 125 kg ."
Answer: d
Python program:
a = 15 / 100
b = 1 - a
c = 30 / 100
d = 1 - c
e = 30 / 100
f = 1 - e
g = 300 * f
h = d * g
i = b * h
Problem: a $ 500 investment and a $ 1,500 investment have a combined yearly return of 10 percent of the total of the two investments . if the $ 500 investment has a yearly return of 7 percent , what percent yearly return does the $ 1,500 investment have ?
Options: a ) 9 % , b ) 10 % , c ) 105 / 8 % , d ) 11 % , e ) 12 %
Rationale: the equation we can form the question : return on total investment = sum of individual investments ( 500 + 1500 ) ( 10 ) = ( 500 â ˆ — 7 ) + ( 1500 x ) , where x is the return on investment of 1500 . solving the equation , we get x = 11 % ( option d ) answer : d
Answer: d
Python program:
a = 3 * 500
b = 500 + a 
c = 10 / 100
d = b * c
e = 7 / 100
f = 500 * e
g = d - f
h = 3 * 500
i = g / h
j = i * 100
Problem: the number of positive integer solutions for the equation x + y + z + t = 18 is
Options: a ) 640 , b ) 780 , c ) 380 , d ) 540 , e ) 680
Rationale: "the number of positive integer solutions for the equatio fx 1 + x 2 + ⋯ + xn = k ( k - 1 ) c ( n - 1 ) - where k is the number and n is number of variable in the equation . 18 - 1 c 4 - 1 = 17 c 3 = 680 answer : e"
Answer: e
Python program:
a = 18 - 1
b = math.factorial(a)
c = 4 - 1
d = math.factorial(c)
e = 18 - 1
f = 4 - 1
g = e - f
h = math.factorial(g)
i = d * h
j = b / i
Problem: the average age of a group of n people is 15 years old . one more person aged 37 joins the group and the new average is 17 years old . what is the value of n ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "15 n + 37 = 17 ( n + 1 ) 2 n = 20 n = 10 the answer is a ."
Answer: a
Python program:
a = 37 - 17
b = 17 - 15
c = a / b
Problem: the ratio between the speeds of two trains is 7 : 8 . if the second train runs 400 km in 4 hours , what is the the speed of the first train ?
Options: a ) 87.0 , b ) 87.5 , c ) 87.2 , d ) 87.1 , e ) 87.4
Rationale: speed and time are inversely proportional ( when distance is constant ) ⇒ speed ∝ 1 time ( when distance is constant ) here distance is constant and hence speed and time are inversely proportionalspeed ∝ 1 time ⇒ speed 1 speed 2 = time 2 time 1 ⇒ 78 = 4 time 1 ⇒ time 1 = 4 × 87 hr ⇒ speed of the first train = distancetime 1 = 400 ( 4 × 87 ) = 100 × 78 = 12.5 × 7 = 87.5 km / hr answer : b
Answer: b
Python program:
a = 400 / 4
b = a / 8
c = b * 7
Problem: what is the unit digit of ( 8 ! * 4 ! / 8 ! * 3 ! ) ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "( 8 ! * 4 ! / 8 ! * 3 ! ) = ( 4 ! / 3 ! ) = 24 / 6 = 4 units digit of the above product will be equal to 4 answer e"
Answer: e
Python program:
a = math.factorial(8)
b = math.factorial(8)
c = a * b
d = math.factorial(8)
e = math.factorial(3)
f = d * e
g = c / f
Problem: area of square with side x is equal to the area of a triangle with base x . the altitude of the triangle is
Options: a ) x / 2
b ) x
c ) 2 x
d ) 4 x
e ) 3 x
Rationale: x ^ 2 = 1 / 2 ã ƒ â € ” x ã ƒ â € ” h or h = 2 x ^ 2 / x = 2 x answer : c
Answer: c
Python program:
a = 1 ** 2
b = a * 2
Problem: a baseball card decreased in value 60 % in its first year and 10 % in its second year . what was the total percent decrease of the card ' s value over the two years ?
Options: a ) 28 % , b ) 30 % , c ) 32 % , d ) 36 % , e ) 64 %
Rationale: let the initial value of baseball card = 100 after first year , value of baseball card = ( 1 - 60 / 100 ) * 100 = 40 after second year , value of baseball card = ( 1 - 10 / 100 ) * 40 = 36 total percent decrease of the card ' s value over the two years = ( 100 - 36 ) / 100 * 100 % = 64 % answer e
Answer: e
Python program:
a = 10 / 100
b = 1 - a
c = 60 / 100
d = 1 - c
e = b * d
f = e * 100
g = 100 - f
Problem: there are 10 books on a shelf , of which 4 are paperbacks and 6 are hardbacks . how many possible selections of 5 books from the shelf contain at least one paperback and at least one hardback ?
Options: a ) 75 , b ) 120 , c ) 210 , d ) 246 , e ) 252
Rationale: "paperbacks - 4 , hardbacks - 6 5 books in total and at least 1 from each . total combinations for 5 books = ( 1 pb , 4 hb ) + ( 4 pb , 1 hb ) + ( 3 pb , 2 hb ) + ( 2 pb , 3 hb ) 1 pb , 4 hb = 4 c 1 * 6 c 4 = 60 4 pb , 1 hb = 4 c 4 * 6 c 1 = 6 3 pb , 2 hb = 4 c 3 * 6 c 2 = 60 2 pb , 3 hb = 4 c 2 * 6 c 3 = 120 total combinations of 5 books = 60 + 6 + 60 + 120 = > 246 ans d ."
Answer: d
Python program:
a = math.comb(10, 5)
b = math.comb(6, 5)
c = a - b
Problem: a walk 20 m towards north east . b walk towards east 8 m and then 12 m south . now calculate distance between a and b ?
Options: a ) 30 m , b ) 20 m , c ) 35 m , d ) 40 m , e ) 38 m
Rationale: its coming 30.4 m since 1 st triangle we get 18.31 and extra 12 so 18.31 + 12 = 30.31 = 30 m answer : a
Answer: a
Python program:
a = 20 ** 2
b = 8 ** 2
c = a - b
d = math.sqrt(c)
e = 12 + d
Problem: if the difference between compound interest ( interest compounded yearly ) and simple interest on a sum for 3 years at 20 % p . a . is rs . 132 , then the sum is
Options: a ) rs . 3500 , b ) rs . 1500 , c ) rs . 2500 , d ) rs . 3000 , e ) none
Rationale: "c . i - s . i = 132 c . i = a - p a = p ( 1 + ( r / 100 ) ) ^ n a = x ( 1 + ( 20 / 100 ) ) ^ 3 a = x ( 6 / 5 ) ^ 3 a = 216 / 125 ( x ) c . i = ( 91 / 125 ) x s . i = ( pnr ) / 100 = ( x * 3 * 20 ) / 100 = ( 6 / 10 ) x diff = 132 diff = ( 91 / 25 ) x - ( 6 / 10 ) x = ( 182 x - 150 x ) / 250 = 32 x / 250 32 x / 250 = 132 x = ( 132 * 250 ) / 32 x = 1031.25 answer : e"
Answer: e
Python program:
a = 132 * 20
b = a * 20
Problem: the mass of 1 cubic meter of a substance is 700 kilograms under certain conditions . what is the volume , in cubic centimeters , of 1 gram of this substance under these conditions ? ( 1 kilogram = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters )
Options: a ) 0.8 , b ) 1.42 , c ) 8.0 , d ) 12.5 , e ) 80.0
Rationale: "density is mass divided by volume . so density of the given substance will be mass / volume = 700 kg / 1 m ^ 3 = 700 kg / m ^ 3 or 1 g / 1.42 cm ^ 3 = 0.7 g / cm ^ 3 . next , ask yourself if 700,000 g is equivalent to 1 , 000,000 cubic centimeters then 1 g is equivalent to how many cubic centimeters ? - - > 1 g - 1 , 000,000 / 700,000 = 10 / 8 = 1.42 cubic centimeters . answer is b"
Answer: b
Python program:
a = 100 ** 3
b = 700 * 1
c = a / b
d = c - 2
Problem: a plot abcd is as shown in figure , where af = 30 m , ce = 40 m , ed = 50 m , ae = 120 m . find the area of the plot abcd ?
Options: a ) 7207
b ) 7206
c ) 7203
d ) 7200
e ) 7201
Rationale: area of plot abcd = area of ade + area of afb + area of bcef = 1 / 2 * 50 * 120 + 1 / 2 * 40 * 30 + 40 * 90 = 3000 + 600 + 3600 = 7200 sq . m answer : d
Answer: d
Python program:
a = triangle_area + ( 
b = a + triangle_area
Problem: in what time will a train 100 meters long cross an electric pole , if its speed is 126 km / hr
Options: a ) 8.5 seconds , b ) 2.86 seconds , c ) 3.5 seconds , d ) 2.5 seconds , e ) 2.6 seconds
Rationale: "first convert speed into m / sec speed = 126 * ( 5 / 18 ) = 35 m / sec time = distance / speed = 100 / 35 = 2.86 seconds answer : b"
Answer: b
Python program:
a = 126 * const_0_2778
b = 100 / a
Problem: two bullet train s 140 m and 170 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time ( in seconds ) which they take to cross each other , is :
Options: a ) 15.8 sec . , b ) 12.8 sec . , c ) 11.16 sec . , d ) 10.8 sec . , e ) 08.8 sec .
Rationale: "relative speed = ( 60 + 40 ) km / hr = 100 x 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = ( 140 + 170 ) m = 310 m . required time = 310 x 9 / 250 = 11.16 sec . answer c"
Answer: c
Python program:
a = 140 + 170 
b = 60 + 40 
c = b * const_0_2778
d = a / c
Problem: a rectangular garden is 12 m by 5 m , what is its area ?
Options: a ) 12 square meters
b ) 5 square meters
c ) 44 square meters
d ) 60 square meters
e ) 22 square meters
Rationale: area of a rectangle : a = w × h d ) 60 square meters
Answer: d
Python program:
a = 12 * 5
Problem: indu gave bindu rs . 3125 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 ) s . 10 , b ) s . 2 , c ) s . 5 , d ) s . 3 , e ) s . 4
Rationale: "3125 = d ( 100 / 4 ) 2 d = 5 answer : c"
Answer: c
Python program:
a = 4 / 100
b = 1 + a 
c = b ** 2
d = 3125 * c
e = d - 3125
f = 4 / 100
g = 3125 * f
h = g * 2
i = e - h
Problem: if the ratio of a to b is 7 to 3 and the ratio of b to c is 1 to 5 , what is the ratio of a to c ?
Options: a ) 4 / 15 , b ) 1 / 3 , c ) 2 / 5 , d ) 4 / 5 , e ) 7 / 15
Rationale: "a : b = 7 : 3 - - 1 b : c = 1 : 5 = > b : c = 3 : 15 - - 2 from 1 and 2 , we get a : c = 7 : 15 answer e"
Answer: e
Python program:
a = 7 * 1
b = 3 * 5
c = a / b
Problem: the average of first 18 even numbers is ?
Options: a ) 19 , b ) 18 , c ) 16 , d ) 11 , e ) 17
Rationale: "sum of 18 even numbers = 18 * 19 = 342 average = 342 / 18 = 19 answer : a"
Answer: a
Python program:
a = 18 + 1
Problem: a person lent a certain sum of money at 4 % per annum at simple interest and in 8 years the interest amounted to rs . 238 less than the sum lent . what was the sum lent ?
Options: a ) 228 , b ) 350 , c ) 289 , d ) 500 , e ) 821
Rationale: "p - 238 = ( p * 4 * 8 ) / 100 p = 350 answer : b"
Answer: b
Python program:
a = 4 * 8
b = a / 100
c = 1 - b
d = 238 / c
Problem: for every integer n ≥ 3 , the function g ( n ) is defined as the product of all the odd integers from 1 to n , inclusive . what is the value of g ( 99 ) – g ( 97 ) ?
Options: a ) 98 , b ) 100 , c ) 0 , d ) 99 , e ) 97
Rationale: g ( 99 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 g ( 97 ) = 1 * 3 * 5 * 7 * 9 * . . . * 97 g ( 99 ) - g ( 97 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 - 1 * 3 * 5 * 7 * 9 * . . . * 97 = 1 * 3 * 5 * 7 * 9 * . . . * 97 * ( 99 - 1 ) = 1 * 3 * 5 * 7 * 9 * . . . * 97 * 98 hence : a .
Answer: a
Python program:
a = 99 - 1
Problem: in the first 5 overs of a cricket game , the run rate was only 2.1 . what should be the rate in the remaining 30 overs to reach the target of 200 runs ?
Options: a ) 6.25 , b ) 6.28 , c ) 6.31 , d ) 6.19 , e ) 6.21
Rationale: "required run rate = [ 200 - ( 2.1 * 5 ) ] / 30 = 189.50 / 30 = 6.31 answer : c"
Answer: c
Python program:
a = 5 * 2
b = 200 - a
c = b / 30
Problem: what is the sum of all even numbers from 1 to 901 ?
Options: a ) 122821 , b ) 202950 , c ) 281199 , d ) 122850 , e ) 128111
Rationale: "explanation : 900 / 2 = 450 450 * 451 = 202950 answer : b"
Answer: b
Python program:
a = 1 * 901
b = a / 4
Problem: the lcm and hcf of two numbers are 100 and 10 respectively . find the larger of the two numbers if their sum is 110 .
Options: a ) 100 , b ) 12 , c ) 35 , d ) 466 , e ) 56
Rationale: "there are 2 approaches in solving this . methode 1 . hcf * lcm = the actual number . 100 * 10 = 1000 so the answer which we are looking for has to be a factor of 1000 . so among the options shortlist the answers by eliminating those numbers which is not divisible by 1000 . and then take the highest number as the answer as the question asks abt the highest number . answer is a"
Answer: a
Python program:
a = 100 * 10
b = a / 110
Problem: a couple decides to have 4 children . if they succeed in having 4 children and each child is equally likely to be a boy or a girl , what is the probability that they will have exactly 3 girls and 1 boy ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 1 / 2
Rationale: "sample space = 2 ^ 4 = 16 . favourable events = { bbgg } , { bgbg } , { bggb } , { ggbb } , { gbgb } , { gbbg } . { bggg } , { gbbb ) probability = 8 / 16 = 1 / 2 . ans ( e ) ."
Answer: e
Python program:
a = math.factorial(3)
b = math.factorial(2)
c = a / b
d = 3 / 1
e = d ** 4
f = c * e
g = 3 - f
Problem: what will be the compound interest on a sum of rs . 40,000 after 3 years at the rate of 12 % p . a . ?
Options: a ) s : 10123.19 , b ) s : 10123.29 , c ) s : 10123.20 , d ) s : 10123.28 , e ) s : 16197.12
Rationale: "amount = [ 40000 * ( 1 + 12 / 100 ) 3 ] = 40000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 56197.12 c . i . = ( 56197.12 - 40000 ) = rs : 16197.12 answer : e"
Answer: e
Python program:
a = 4 * 100
b = a * 100
c = 12 / 100
d = 1 + c 
e = d ** 3
f = b * e
g = 4 * 100
h = g * 100
i = f - h
Problem: a theater charges $ 12 for seats in the orchestra and $ 8 for seats in the balcony . on a certain night , a total of 370 tickets were sold for a total cost of $ 3,320 . how many more tickets were sold that night for seats in the balcony than for seats in the orchestra ?
Options: a ) 90 , b ) 190 , c ) 120 , d ) 130 , e ) 220
Rationale: orchestra seats - a balcony seats - b a + b = 370 and 12 a + 8 b = 3320 solving equations simultaneously ( multiply equation 1 with 8 and subtract from second equation ) 4 a = 3320 - 8 * 370 = 3320 - 2960 = 360 i . e . a = 90 and b = 370 - 90 = 280 more seats in balcony than orchestra = b - a = 280 - 90 = 190 answer : option b
Answer: b
Python program:
a = 12 * 370
b = 3 * 1000
c = 3 * 100
d = b + c 
e = 2 * 10
f = d + e 
g = a - f
h = 12 - 8
i = g / h
j = 12 * 370
k = 3 * 1000
l = 3 * 100
m = k + l 
n = 2 * 10
o = m + n 
p = j - o
q = 12 - 8
r = p / q
s = 370 - r
t = i - s
Problem: if bill can buy 3 pairs of jeans and 2 shirts for $ 69 or 2 pairs of jeans and 3 shirts for $ 81 , how much does one shirt cost ?
Options: a ) $ 10 , b ) $ 12 , c ) $ 13.20 , d ) $ 21 , e ) $ 16.80
Rationale: "3 j + 2 s = 69 2 j + 3 s = 81 - - - - - - - - - - - - - - - - 5 j + 5 s = 150 - - - - ( divide by 5 ) - - - > j + s = 30 3 j + 2 s = j + 2 ( j + s ) = j + 60 = 69 - - - > j = 9 3 * 9 + 2 s = 69 27 + 2 s = 69 2 s = 42 s = 21 answer : d"
Answer: d
Python program:
a = 81 * 3
b = 69 * 2
c = a - b
d = 3 * 3
e = 2 * 2
f = d - e
g = c / f
Problem: a squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 3 feet . how many feet does the squirrel travels if the post is 27 feet tall and 3 feet in circumference ?
Options: a ) 10 feet , b ) 12 feet , c ) 27 feet , d ) 15 feet , e ) 18 feet
Rationale: "total circuit = 27 / 3 = 9 total feet squirrel travels = 9 * 3 = 27 feet answer : c"
Answer: c
Python program:
a = 27 / 3
b = a * 3
Problem: how many zeroes are there at the end of the number n , if n = 60 ! + 120 ! ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: the number of zeroes at the end of 60 ! will be less than the number of zeroes at the end of 120 ! hence it is sufficient to calculate the number of zeroes at the end of 60 ! the number of zeroes = [ 60 / 5 ] + [ 60 / 25 ] + [ 60 / 125 ] = 12 + 2 + 0 = 14 the answer is b .
Answer: b
Python program:
a = 4 + 1 
b = 60 / a
c = b + 2
Problem: if x is a sum of all even integers on the interval 13 . . . 61 and y is their number , what is the gcd ( x , y ) ?
Options: a ) 1 , b ) 13 , c ) 26 , d ) 24 , e ) 1014
Rationale: "x = 14 + 16 + . . . + 60 = ( largest + smallest ) / 2 * ( # of terms ) = ( 14 + 60 ) / 2 * 24 = 37 * 24 . gcd of 24 and 37 * 22 is 24 . answer : d ."
Answer: d
Python program:
a = 13 - 10
b = a + 2 
c = 13 - 10
d = c + 2 
e = b * d
Problem: a train leaves delhi at 11 a . m . at a speed of 30 kmph . another train leaves at 2 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 ) 360 , b ) 288 , c ) 600 , d ) 888 , e ) 121
Rationale: "d = 30 * 3 = 90 rs = 40 – 30 = 10 t = 90 / 10 = 9 d = 40 * 9 = 360 km answer : a"
Answer: a
Python program:
a = 3 + 2 
b = 30 * a
c = 40 - 30
d = b / c
e = d * 40
Problem: if a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land tails up exactly twice in 2 consecutive flips ?
Options: a ) 0.125 , b ) 0.25 , c ) 0.375 , d ) 0.5 , e ) 0.666
Rationale: "total number of ways in which h or t can appear in 3 tosses of coin is = 2 * 2 = 4 ways for 2 h tt , thus probability is = p ( tt ) = 1 / 4 = . 25 answer : b"
Answer: b
Python program:
a = 1 / 2
b = a ** 2
c = b * 2
Problem: how many multiples of 8 are less than 7600 , and also multiples of 19 ?
Options: a ) 104 , b ) 100 , c ) 50 , d ) 89 , e ) 90
Rationale: "lcm of 8 & 19 = 152 tried dividing 7600 by 152 got quotient 50 ' so c is answer"
Answer: c
Python program:
a = 19 - 7600
b = a / 8
c = b + 1
Problem: in a rectangular axis system , what is the area of a parallelogram with the coordinates : ( 5,7 ) , ( 12,7 ) , ( 2,3 ) , ( 9,3 ) ?
Options: a ) 21 , b ) 28 . , c ) 35 . , d ) 49 . , e ) 52 .
Rationale: "area of parallelogram = b * h . base = distance in x coordinates between ( 2,3 ) and ( 9,3 ) = 7 height = difference in y coordinates between ( 5,7 ) and ( 2,3 ) = 3 . area = 7 * 3 = 21 . answer : a"
Answer: a
Python program:
a = 3 + 2
Problem: on dividing 265 by a number , the quotient is 12 and the remainder is 1 . find the divisor .
Options: a ) a ) 12 , b ) b ) 14 , c ) c ) 16 , d ) d ) 18 , e ) e ) 22
Rationale: "d = ( d - r ) / q = ( 265 - 1 ) / 12 = 264 / 12 = 22 e )"
Answer: e
Python program:
a = 265 / 12
b = math.floor(a)