euclaise/mathqa_programs huggingface dataset:
Problem: a started a business with an investment of rs . 70000 and after 6 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 50000 , then the share of b is ?
Options: a ) 23077 , b ) 24000 , c ) 24005 , d ) 24009 , e ) 24002
Rationale: "ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 6 ) = 7 : 6 total profit = rs . 50000 share of b = 6 / 13 ( 50000 ) = rs . 23076.92 ~ 23077 answer : a"
Answer: a
Python program:
a = const_60 * 100
b = 50000 - a
Problem: if a * b * c = 130 , b * c * d = 65 , c * d * e = 500 and d * e * f = 250 the ( a * f ) / ( c * d ) = ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 3 / 4 , d ) 2 / 3 , e ) 1
Rationale: "explanation : a â ˆ — b â ˆ — c / b â ˆ — c â ˆ — d = 130 / 65 = > a / d = 2 d â ˆ — e â ˆ — f / c â ˆ — d â ˆ — e = 250 / 500 = > f / c = 1 / 2 a / d * f / c = 2 * 1 / 2 = 1 answer : e"
Answer: e
Python program:
a = 130 * 250
b = 500 * 65
c = a / b
Problem: how many internal diagonals does a heptagon ( seven sided polygon ) have ?
Options: a ) 7 , b ) 9 , c ) 14 , d ) 20 , e ) 35
Rationale: "number of diagonals in any polygon can be found using this formula : n ( n - 3 ) / 2 here n = 7 no . of diagonals = 7 ( 7 - 3 ) / 2 = 14 ans c"
Answer: c
Python program:
a = 2 * 4
b = a - 3
c = 2 * 4
d = c / 2
e = b * d
Problem: in the coordinate plane , points ( x , 5 ) and ( 7 , y ) are on line k . if line k passes through the origin and has slope 5 / 7 , then x + y =
Options: a ) 13 , b ) 14 , c ) 9 , d ) 10 , e ) 12
Rationale: "line k passes through the origin and has slope 5 / 7 means that its equation is y = 5 / 7 * x . thus : ( x , 5 ) = ( 7,5 ) and ( 7 , y ) = ( 7,5 ) - - > x + y = 7 + 5 = 12 . answer : e"
Answer: e
Python program:
a = 7 * 7
b = 5 / 7
c = a * b
Problem: a specialized type of sand consists of 40 % mineral x by volume and 60 % mineral y by volume . if mineral x weighs 2.5 grams per cubic centimeter and mineral y weighs 2 grams per cubic centimeter , how many grams does a cubic meter of specialized sand combination weigh ? ( 1 meter = 100 centimeters )
Options: a ) 5 , 500,000 , b ) 2 , 200,000 , c ) 55,000 , d ) 28,000 , e ) 280
Rationale: "let the volume be 1 m ^ 3 = 1 m * 1 m * 1 m = 100 cm * 100 cm * 100 cm = 1 , 000,000 cm ^ 3 by volume 40 % is x = 400,000 cm ^ 3 60 % is y = 600,000 cm ^ 3 by weight , in 1 cm ^ 3 , x is 2.5 gms in 400,000 cm ^ 3 , x = 2.5 * 400,000 = 1 , 000,000 grams in 1 cm ^ 3 , y is 2 gms in 600,000 cm ^ 3 , y = 2 * 600,000 = 1 , 200,000 gms total gms in 1 m ^ 3 = 1 , 000,000 + 1 , 200,000 = 2 , 200,000 answer : b"
Answer: b
Python program:
a = volume_cube / (
b = a * 10
c = b * 2
d = c + 2 
e = volume_cube / (
f = e * 10
g = 2 * 2
h = f * g
i = d - h
Problem: if the wheel is 56 cm then the number of revolutions to cover a distance of 1056 cm is ?
Options: a ) 10 , b ) 12 , c ) 3 , d ) 11 , e ) 9
Rationale: "2 * 22 / 7 * 56 * x = 1056 = > x = 3 answer : c"
Answer: c
Python program:
a = 3 * 100
b = 1 * 10
c = a + b 
d = c + 4 
e = d / 100
f = 2 * e
g = f * 56
h = 1056 / g
Problem: a rectangular farm has to be fenced one long side , one short side and the diagonal . if the cost of fencing is rs . 12 per meter . the area of farm is 1200 m 2 and the short side is 30 m long . how much would the job cost ?
Options: a ) 1440 , b ) 1200 , c ) 2832 , d ) 1299 , e ) 1236
Rationale: "explanation : l * 30 = 1200 è l = 40 40 + 30 + 50 = 120 120 * 12 = 1440 answer : option a"
Answer: a
Python program:
a = 1200 / 30
b = 30 + a 
c = 30 ** 2
d = 1200 / 30
e = d ** 2
f = c + e 
g = math.sqrt(f)
h = b + g 
i = h * 12
Problem: a boat moves upstream at the rate of 1 km in 40 minutes and down stream 1 km in 12 minutes . then the speed of the current is :
Options: a ) 1 kmph , b ) 2 kmph , c ) 1.75 kmph , d ) 2.5 kmph , e ) 3.5 kmph
Rationale: "rate upstream = ( 1 / 40 * 60 ) = 1.5 kmph rate dowm stream = 1 / 12 * 60 = 5 kmph rate of the current = ½ ( 5 - 1.5 ) = 1.75 kmph answer : c"
Answer: c
Python program:
a = 1 / 12
b = a * const_60
c = 1 / 40
d = c * const_60
e = b - d
f = e / 2
Problem: if 10 bulls can plough 20 identical fields in 3 days working 10 hours a day , then in how many days can 30 bulls plough 32 same identical fields working 8 hours a day ?
Options: a ) 8 , b ) 7 , c ) 5 , d ) 2.0 , e ) 1
Rationale: explanation : m 1 * d 1 * w 2 = m 2 * d 2 * w 1 10 * 3 * 10 * 32 = 30 * d * 8 * 20 d = 2 days answer : d
Answer: d
Python program:
a = 10 * 10
b = a * 3
c = b * 32
d = 30 * 8
e = d * 20
f = c / e
Problem: how many numbers from 2 to 7 are exactly divisible by 2 ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 7 , e ) 8
Rationale: "2 / 2 = 1 and 7 / 2 = 3 3 - 1 = 2 2 + 1 = 3 numbers . b )"
Answer: b
Python program:
a = 7 / 2
b = math.floor(a)
c = b * 2
d = 2 / 2
e = math.floor(d)
f = e + 1 
g = f * 2
h = c - g
i = h / 2
j = i + 1
Problem: the product of two numbers is 120 . the sum of their squares is 289 . the sum of the two numbers is :
Options: a ) 20 , b ) 23 , c ) 169 , d ) 172 , e ) 198
Rationale: "explanation : let the number be x and y . we know that , ( x + y ) 2 = ( x 2 + y 2 ) + 2 xy = 289 + 2 × 120 = 289 + 240 = 529 ⇒ x + y = √ 529 = 23 correct option : b"
Answer: b
Python program:
a = 2 * 120
b = 289 - a
c = math.sqrt(b)
d = c ** 2
e = 4 * 120
f = d + e 
g = math.sqrt(f)
Problem: the least number , which when divided by 8 , 15 , 20 and 54 leaves in each case a remainder of 8 is :
Options: a ) 448 , b ) 488 , c ) 542 , d ) 548 , e ) 1088
Rationale: "required number = ( l . c . m . of 8 , 15 , 20 , 54 ) + 8 = 1080 + 8 = 1088 . answer : e"
Answer: e
Python program:
a = 54 * 10
Problem: there are 10 slate rocks , 15 pumice rocks , and 6 granite rocks randomly distributed in a certain field . if 2 rocks are chosen at random and without replacement , what is the probability that both rocks will be slate rocks ?
Options: a ) 2 / 19 , b ) 3 / 31 , c ) 4 / 37 , d ) 5 / 41 , e ) 6 / 53
Rationale: "10 / 31 * 9 / 30 = 3 / 31 the answer is b ."
Answer: b
Python program:
a = 10 + 15 
b = a + 6 
c = 10 / b
d = 10 - 1
e = 10 + 15 
f = e + 6 
g = f - 1
h = d / g
i = c * h
Problem: the average of 6 no . ' s is 2.80 . the average of 2 of them is 2.4 , while the average of the other 2 is 2.3 . what is the average of the remaining 2 no ' s ?
Options: a ) 2.3 , b ) 2.6 , c ) 3.6 , d ) 3.7 , e ) 4.6
Rationale: sum of the remaining two numbers = ( 2.80 * 6 ) - [ ( 2.4 * 2 ) + ( 2.3 * 2 ) ] = 16.80 - ( 4.8 + 4.6 ) = 16.80 - 9.40 = 7.40 required average = ( 7.4 / 2 ) = 3.7 answer : d
Answer: d
Python program:
a = 6 * 2
b = 2 * 2
c = 2 * 2
d = b + c 
e = a - d
f = e / 2
Problem: if x and y are integers and | x - y | = 12 , what is the minimum possible value of xy ?
Options: a ) - 12 , b ) - 18 , c ) - 24 , d ) - 36 , e ) - 48
Rationale: "we are given | x - y | = 12 , minimum possible value of xy would be maximum numeric value with a - ive sign . . so one of x or y will be negative and other negative . . | x - y | = 12 in this case means that the numeric sum of x and y is 12 . . various combinations could be - 1 and 11 , - 2 and 10 , - 6 and 6 , - 11 and 1 and so on . . when the sum of two numbers is given , the max product is when both x and y are same numeric value . . . so xy will have max numeric value when numeric value of x and y = 12 / 2 = 6 . . so numeric value of xy = 36 but one of x and y is - ive . . so answer is - 36 answer : d"
Answer: d
Python program:
a = 2 + 3 
b = negate * (
Problem: what is the smallest positive perfect square that is divisible by 4 , 10 , and 18 ?
Options: a ) 900
b ) 1,600
c ) 2,500
d ) 3,600
e ) 4,900
Rationale: the number needs to be divisible by 2 ^ 2 , 2 * 5 , and 2 * 3 ^ 2 . the smallest such perfect square is 2 ^ 2 * 3 ^ 2 * 5 ^ 2 = 900 the answer is a .
Answer: a
Python program:
a = 3 ** 2
b = 4 * a
c = b * 10
d = c * 2
e = 10 * 18
f = d + e
Problem: if grapes are 91 % water and raisins are 19 % water , then how many kilograms did a quantity of raisins , which currently weighs 9 kilograms , weigh when all the raisins were grapes ? ( assume that the only difference between their raisin - weight and their grape - weight is water that evaporated during their transformation . )
Options: a ) 63 , b ) 72 , c ) 81 , d ) 90 , e ) 99
Rationale: "let x be the original weight . the weight of the grape pulp was 0.09 x . since the grape pulp is 81 % of the raisins , 0.09 x = 0.81 ( 9 kg ) . then x = 9 * 9 = 81 kg . the answer is c ."
Answer: c
Python program:
a = 100 - 19
b = a / 100
c = b * 9
d = 100 - 91
e = d / 100
f = c / e
Problem: a bag contains an equal number of one rupee , 50 paise and 25 paise coins respectively . if the total value is 210 , how many coins of each type are there ?
Options: a ) 20 coins , b ) 50 coins , c ) 100 coins , d ) 120 coins , e ) none of these
Rationale: "let number of each type of coin = x . then , 1 × x + . 50 × x + . 25 x = 210 ⇒ 1.75 x = 210 ⇒ x = 120 coins answer d"
Answer: d
Python program:
a = 1/(4)
b = 1/(2)
c = a + b 
d = c + 1 
e = 210 / d
Problem: a metallic sphere of radius 12 cm is melted and drawn into a wire , whose radius of cross section is 4 cm . what is the length of the wire ?
Options: a ) 116 cm , b ) 144 cm , c ) 168 cm , d ) 173 cm , e ) 189 cm
Rationale: "volume of the wire ( in cylindrical shape ) is equal to the volume of the sphere . π ( 4 ) ^ 2 * h = ( 4 / 3 ) π ( 12 ) ^ 3 = > h = 144 cm answer : b"
Answer: b
Python program:
a = 12 ** 3
b = 4 ** 2
c = a / b
d = 4 * c
e = d / 3
Problem: a train crosses a platform of 150 m in 15 sec , same train crosses another platform of length 250 m in 20 sec . then find the length of the train ?
Options: a ) 150 m , b ) 188 m , c ) 267 m , d ) 268 m , e ) 287 m
Rationale: "length of the train be ‘ x ’ x + 150 / 15 = x + 250 / 20 4 x + 600 = 3 x + 750 x = 150 m answer : a"
Answer: a
Python program:
a = 15 / 3
b = 15 / a
c = 250 * b
d = 15 / 3
e = 20 / d
f = 150 * e
g = c - f
Problem: find √ ? / 19 = 4 ?
Options: a ) 76 , b ) 5776 , c ) 304 , d ) 1296 , e ) none
Rationale: "answer let √ n / 19 = 4 then √ n = 19 x 4 = 76 ∴ n = 76 x 76 = 5776 . correct option : b"
Answer: b
Python program:
a = 4 * 19
b = a ** 2
Problem: a certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint . if 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans , what is the least amount of paint , in gallons , that must be purchased in order to measure out the portions needed for the mixture ?
Options: a ) 2 , b ) 2 1 / 2 , c ) 3 , d ) 3 1 / 2 , e ) 4
Rationale: "ratio ; white : black : gray = 3 : 5 : ( 3 + 5 ) = 3 : 5 : 8 if 2 gallons of the mixture is needed < = = > need 2 gallons of gray paint . then , 3 : 5 : 8 = x : y : 2 3 / 8 = x / 2 ; x = 3 / 4 5 / 8 = y / 2 ; y = 5 / 4 you need 3 / 4 gallon of white . you have to buy 1 gallons . you need 5 / 4 gallons of black . you have to buy 1 gallon and another 1 / 2 gallon of black . the least amount of paint = 1 + 1 + 1 / 2 = 2.5 . answer : b"
Answer: b
Python program:
a = const_0_25 * 2
b = 2 * 5
c = a + b
Problem: if the radius of a circle that centers at the origin is 5 , how many j points on the circle have integer coordinates ?
Options: a ) 4
b ) 8
c ) 12
d ) 15
e ) 20
Rationale: i understand this might not be required but i used the equation of a circle . since the origin is at 0 , x ^ 2 + y ^ 2 = 5 ^ 2 . x , y could be + / - ( 0,5 or 5,0 ) - 4 possibilities . x , y could be + / - ( 3,4 or 4,3 ) - 8 possibilities . ans : j = c
Answer: c
Python program:
a = 5 * 5
b = 5 + 4 
c = a - b
d = 2 ** 2
e = c - d
Problem: an automobile parts supplier charges $ 25 per package of gaskets . when a customer orders more than 10 packages of gaskets , the supplier charges 4 / 5 the price for each package in excess of 10 . during a certain week , the supplier sold 50 packages of gaskets . if 20 percent of the gaskets went to company x , 15 percent to company y , and the rest to company z , what was the total amount , in dollars , that the parts supplier received in payment for the gaskets ?
Options: a ) 1105 , b ) 1245 , c ) 1275 , d ) 1215 , e ) 1150
Rationale: "$ 25 per packet of gasket in case a customer orders less than 10 in case a customer orders > 10 price per gasket = 25 * 4 / 5 = 20 a certain week the supplier sold 60 gasket 1 . he sold 20 % of the gaskets to x = 10 gaskets = 25 * 10 = 250 2 . he sold 30 % of the gaskets to y = 15 gaskets = 25 * 10 + 20 * 5 = 350 3 . he sold remaining 50 % to z = 25 gaskets = 25 * 10 = 250 + 20 * 15 = 550 thus , total money earned 250 + 350 + 550 = 1150 answer is e"
Answer: e
Python program:
a = 4 / 5
b = 25 * a
c = 20 / 100
d = 50 * c
e = 50 - d
f = 20 / 100
g = 50 * f
h = e - g
i = h - 10
j = b * i
k = 25 * 10
l = j + k 
m = 20 / 100
n = 50 * m
o = 25 * n
p = 20 / 100
q = 50 * p
r = 25 * q
s = o + r 
t = l + s
Problem: ravi can do a piece of work in 15 days while prakash can do it in 30 days . in how many days will they finish it together ?
Options: a ) 11 days , b ) 9 days , c ) 8 days , d ) 12 days , e ) 10 days
Rationale: "1 / 15 + 1 / 30 = 3 / 30 10 / 1 = 10 days answer : e"
Answer: e
Python program:
a = 1/(15)
b = 1/(30)
c = a + b 
d = 1 / c
Problem: ( 1000 ) 7 ÷ ( 10 ) 16 = ?
Options: a ) 10 , b ) 100 , c ) 1000 , d ) 100000 , e ) none of these
Rationale: "explanation : = ( 103 ) 7 / ( 10 ) 16 = ( 10 ) 21 / ( 10 ) 16 = 10 ( 5 ) = 100000 option d"
Answer: d
Python program:
a = 1000 * 10
Problem: what is remainder of the division ( 1425 * 1427 * 1429 ) / 12 ?
Options: a ) 5 , b ) 0 , c ) 1 , d ) 2 , e ) 3
Rationale: "remainder will be number / 100 here as the divisor is two digit number = 12 . hence checking for the last two digits = 5 * 7 * 9 = 15 thus remainder = 3 . answer : e"
Answer: e
Python program:
a = 1425 * 1427
b = a * 1429
c = 1425 * 1427
d = c * 1429
e = d - 3
f = b - e
Problem: two men a and b start from place x walking at 4 ½ kmph and 5 ¾ kmph respectively . how many km apart they are at the end of 5 ½ hours if they are walking in the same direction ?
Options: a ) 7 km , b ) 6 km , c ) 6 7 / 8 km , d ) 9 km , e ) 5 km
Rationale: "rs = 5 ¾ - 4 ½ = 1 ¼ t = 3 ½ h . d = 5 / 4 * 11 / 2 = 55 / 8 = 6 7 / 8 km answer : c"
Answer: c
Python program:
a = 1 / 2
b = 5 + a 
c = 3 / 4
d = 5 + c 
e = 1 / 2
f = 4 + e 
g = d - f
h = b * g
i = h + 2
Problem: a man walking at a rate of 10 km / hr crosses a bridge in 10 minutes . the length of the bridge is ?
Options: a ) 1521 , b ) 1492 , c ) 1667 , d ) 1254 , e ) 1112
Rationale: "speed = 10 * 5 / 18 = 50 / 18 m / sec distance covered in 10 minutes = 50 / 18 * 10 * 60 = 1667 m answer is c"
Answer: c
Python program:
a = 10 * 1000
b = a / const_60
c = b * 10
Problem: the distance from steve ' s house to work is 40 km . on the way back steve drives twice as fast as he did on the way to work . altogether , steve is spending 6 hours a day on the roads . what is steve ' s speed on the way back from work ?
Options: a ) 5 . , b ) 10 . , c ) 14 . , d ) 15 . , e ) 20 .
Rationale: "time is in the ratio 2 : 1 : : to : fro office therefore , 2 x + 1 x = 6 hrs time take to come back - 2 hrs , distance travelled - 40 km = > speed = 20 kmph e"
Answer: e
Python program:
a = 40 / 2
b = 40 + a 
c = b / 6
d = c * 2
Problem: the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 67 kg . what is the weight of the new person ?
Options: a ) 75 , b ) 65 , c ) 87 , d ) 95 , e ) 80
Rationale: "total increase in weight = 8 × 2.5 = 20 if x is the weight of the new person , total increase in weight = x − 67 = > 20 = x - 67 = > x = 20 + 67 = 87 answer is c ."
Answer: c
Python program:
a = 8 * 2
b = a + 67
Problem: if a # b = ab – b + b ^ 2 , then 3 # 8 =
Options: a ) 80 , b ) 8 , c ) 15 , d ) 21 , e ) 35
Rationale: "solution - simply substitute 3 and 8 in equation in the place of a and b respectively . 3 # 8 = 3 * 8 - 8 + 8 ^ 2 = 24 - 8 + 64 = 80 . ans a"
Answer: a
Python program:
a = 3 * 8
b = a - 8
c = 8 ** 2
d = b + c
Problem: a marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each . there can be no less than 8 musicians per row and no more than 30 musicians per row . how many different rectangular formations z are possible ?
Options: a ) 3 , b ) z = 4 , c ) z = 5 , d ) z = 6 , e ) z = 8
Rationale: "the combinations could be { ( 1,240 ) , ( 2,120 ) , ( 3,80 ) , ( 4,60 ) , ( 5,48 ) , ( 6,40 ) , ( 8,30 ) , ( 10,24 ) , ( 12,20 ) , ) 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) , ( 40,6 ) , ( 48,5 ) , ( 60,4 ) , ( 80,3 ) , ( 120,2 ) , ( 240,1 ) } of these we are told 8 < = t < = 30 so we can remove these pairs , and we are left only with . { ( 8,30 , ( 10,24 ) , ( 12,20 ) , ( 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) } hence 8 . e"
Answer: e
Python program:
a = 240 / 30
Problem: find the sum of first 10 odd numbers
Options: a ) 10 , b ) 40 , c ) 200 , d ) 100 , e ) 540
Rationale: "explanation : n 2 = 102 = 100 answer : option d"
Answer: d
Python program:
a = 10 / 2
b = a / 2
c = b / 2
d = c / 2
e = d / 2
f = 10 / e
g = f / 2
h = 10 / 2
i = h / 2
j = i / 2
k = j / 2
l = k / 2
m = 10 / l
n = m / 2
o = math.sqrt(n)
p = 1 + o 
q = g + p
Problem: two trains 200 m and 150 m long are running on parallel rails at the rate of 40 kmph and 44 kmph respectively . in how much time will they cross each other , if they are running in the same direction ?
Options: a ) 140 sec , b ) 132 sec , c ) 192 sec , d ) 252 sec , e ) none
Rationale: "solution relative speed = ( 44 - 40 ) kmph = 4 kmph = ( 4 x 5 / 18 ) m / sec = ( 20 / 18 ) m / sec time taken = ( 350 x 18 / 20 ) sec = 140 sec . answer a"
Answer: a
Python program:
a = 200 + 150 
b = a / 1000
c = 44 - 40
d = b / c
e = 3600 * d
Problem: tom reads at an average rate of 30 pages per hour , while jan reads at an average rate of 37 pages per hour . if tom starts reading a novel at 4 : 00 , and jan begins reading an identical copy of the same book at 4 : 56 , at what time will they be reading the same page ?
Options: a ) 7 : 26 , b ) 7 : 56 , c ) 8 : 26 , d ) 8 : 56 , e ) 9 : 26
Rationale: "since tom reads an average of 1 page every 2 minutes , tom will read 28 pages in the first 56 minutes . jan can catch tom at a rate of 7 pages per hour , so it will take 4 hours to catch tom . the answer is d ."
Answer: d
Python program:
a = 4 - 4
b = 56 - 0
c = b / const_60
d = a + c 
e = d * 30
f = 37 - 30
g = e / f
h = 4 + g 
i = h / 56
Problem: ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 42 years . what is deepak present age .
Options: a ) 14 , b ) 15 , c ) 20 , d ) 22 , e ) 27
Rationale: "explanation : present age is 4 x and 3 x , = > 4 x + 6 = 42 = > x = 9 so deepak age is = 3 ( 9 ) = 27 option e"
Answer: e
Python program:
a = 42 - 6
b = a * 3
c = b / 4
Problem: an outlet pipe can empty 2 / 3 of a cistern in 20 minutes . in 8 minutes , what part of the cistern will be emptied ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 9 , d ) 4 / 15 , e ) 9 / 20
Rationale: "8 / 20 * 2 / 3 = 4 / 15 the answer is d ."
Answer: d
Python program:
a = 2 / 3
b = 8 * a
c = b / 20
Problem: the number of diagonals of a polygon of n sides is given by the formula f = n ( n - 3 ) / 2 . if a polygon has twice as many diagonals as sides , how many sides does it have ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "f = n ( n - 3 ) f = 2 * n 2 n = n ( n - 3 ) = > 2 = n - 3 = > n = 5 answer b"
Answer: b
Python program:
a = 3 + 2
Problem: a 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 16 sec . what is the length of the platform ?
Options: a ) 287 m , b ) 431.25 m , c ) 267 m , d ) 287.25 m , e ) 656 m
Rationale: "speed = 300 / 16 = 75 / 4 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 75 / 4 = > x = 731.25 m answer : b ( 431.25 )"
Answer: b
Python program:
a = speed * (
b = a - 39
Problem: two poles of height 6 meters and 11 meters stand on a plane ground . if the distance between their feet is 12 meters then find the difference in the distance between their tops :
Options: a ) 12 m , b ) 5 m , c ) 13 m , d ) 11 m , e ) 12 m
Rationale: distance between their tops = sqrt ( 12 ^ 2 + ( 11 - 6 ) ^ 2 ) = sqrt 169 = 13 m answer : c
Answer: c
Python program:
a = 12 ** 2
b = 11 - 6
c = b ** 2
d = a + c 
e = math.sqrt(d)
Problem: if teena is driving at 55 miles per hour and is currently 7.5 miles behind loe , who is driving at 40 miles per hour in the same direction then in how many minutes will teena be 15 miles ahead of loe ?
Options: a ) 15 , b ) 60 , c ) 75 , d ) 90 , e ) 105
Rationale: "this type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30 - 40 seconds for a difficult one . teena covers 55 miles in 60 mins . loe covers 40 miles in 60 mins so teena gains 15 miles every 60 mins teena need to cover 7.5 + 15 miles . teena can cover 7.5 miles in 30 mins teena will cover 15 miles in 60 mins so answer 30 + 60 = 90 mins . d"
Answer: d
Python program:
a = 55 - 40
b = a + 7 
c = 55 - 40
d = b / c
e = d * const_60
Problem: a bag contains 4 red , 5 blue and 3 green balls . if 3 ballsare picked at random , what is the probability that both are red ?
Options: a ) 1 / 33 , b ) 1 / 22 , c ) 1 / 12 , d ) 1 / 44 , e ) 1 / 55
Rationale: "p ( both are red ) , = 4 c 3 / 12 c 3 = 1 / 55 e"
Answer: e
Python program:
a = math.comb(4, 3)
b = 4 + 5 
c = b + 3 
d = math.comb(c, 3)
e = a / d
Problem: the length of a rectangular plot is thrice its width . if the area of the rectangular plot is 507 sq meters , then what is the width ( in meters ) of the rectangular plot ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "area = l * w = 3 w ^ 2 = 507 w ^ 2 = 169 w = 13 the answer is c ."
Answer: c
Python program:
a = 507 / 3
b = a / 3
c = b / 4
Problem: the amount of time that three people worked on a special project was in the ratio of 3 to 5 to 6 . if the project took 140 hours , how many more hours did the hardest working person work than the person who worked the least ?
Options: a ) 32 hours , b ) 40 hours , c ) 35 hours , d ) 30 hours , e ) 36 hours
Rationale: "let the persons be a , b , c . hours worked : a = 3 * 140 / 14 = 30 hours b = 5 * 140 / 14 = 50 hours c = 6 * 140 / 14 = 60 hours c is the hardest worker and a worked for the least number of hours . so the difference is 60 - 30 = 30 hours . answer : d"
Answer: d
Python program:
a = 3 + 5 
b = a + 6 
c = 140 / b
d = c * 6
e = 3 + 5 
f = e + 6 
g = 140 / f
h = g * 3
i = d - h
Problem: a student gets 60 % in one subject , 80 % in the other . to get an overall of 75 % how much should get in third subject .
Options: a ) 75 % , b ) 25 % , c ) 85 % , d ) 55 % , e ) 65 %
Rationale: let the 3 rd subject % = x 60 + 80 + x = 3 * 75 140 + x = 225 x = 225 - 140 = 85 answer : c
Answer: c
Python program:
a = 75 * 3
b = 60 + 80 
c = a - b
Problem: according to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . how many 20 - ounce cans of the concentrate are required to prepare 200 6 - ounce servings of orange juice ?
Options: a ) 15 , b ) 34 , c ) 50 , d ) 67 , e ) 100
Rationale: "orange juice concentrate : water : : 1 : 3 total quantity of orange juice = 200 * 6 = 1200 oz so orange juice concentrate : water : : 300 oz : 900 oz no . of 20 oz can = 300 oz / 20 oz = 15 answer a , 15 cans"
Answer: a
Python program:
a = 6 * 200
b = 200 / 10
c = a / b
Problem: john and jane went out for a dinner and they ordered the same dish . both used a 10 % discount coupon . john paid a 15 % tip over the original price of the dish , while jane paid the tip over the discounted price for the coupon . if john paid $ 0.36 more than jane , what was the original price of the dish ?
Options: a ) 24 , b ) 34.8 , c ) 37.8 , d ) 42 , e ) 84
Rationale: "the difference between the amounts john paid and jane paid is the deference between 15 % of p and 15 % of 0.9 p : 0.15 p - 0.15 * 0.9 p = 0.36 - - > 15 p - 13.5 p = 36 - - > p = 24 . answer : a ."
Answer: a
Python program:
a = 15 / 100
b = 10 / 100
c = 1 - b
d = 15 / 100
e = c * d
f = a - e
g = 0 / 36