euclaise/mathqa_programs huggingface dataset:
Problem: ratio of two numbers x and y is 2 : 5 . if x is increased by 50 % and y is increased by 8 then the new ratio becomes 3 : 10 . what is the ratio 3 y : ( x + 6 )
Options: a ) 15 : 8 , b ) 8 : 15 , c ) 2 : 5 , d ) 5 : 2 , e ) 13 : 6
Rationale: "let : x = 2 n y = 5 n 3 n / ( 5 n + 5 ) = 3 / 10 30 n = 3 * ( 5 n + 5 ) n = 1 so , x = 2 ; y = 5 3 y / ( x + 6 ) = 15 / 8 answer = a"
Answer: a
Python program:
a = 100 + 50 
b = a / 100
c = b * 10
d = 5 / 2
e = c - d
f = 8 / e
g = 5 / 2
h = f * g
i = 3 * h
j = 100 + 50 
k = j / 100
l = k * 10
m = 5 / 2
n = l - m
o = 8 / n
p = o + 6 
q = i / p
Problem: the first doughnut is priced at $ 1 and then if you purchase additional doughnuts as dozens then the price is $ 6 / dozen . what is the total number of doughnut purchased if you paid $ 19 ?
Options: a ) 24 , b ) 25 , c ) 35 , d ) 36 , e ) 37
Rationale: "a is the number of dozen of doughnuts at a price of $ 6 / dozen 1 + 6 a = 19 a = 3 the total number of doughnuts purchased - - > 1 + 3 * 12 = 37 answer : e"
Answer: e
Python program:
a = 19 / 6
b = a * 12
Problem: factory x ' s bulbs work for over 4000 hours in 59 % of cases , whereas factory y ' s bulbs work for over 4000 hours in 65 % of cases . it is known that factory x supplies 60 % of the total bulbs available . what is the chance that a purchased bulb will work for longer than 4000 hours ?
Options: a ) 66.4 % , b ) 61.4 % , c ) 77.4 % , d ) 65 % , e ) 53.9 %
Rationale: "for x , 60 % of 59 % will work . for y , 40 % of 65 % will work . * 40 % is the rest of the bulb supply in the market . so , the probability that a purchased bulb will work is : 0.60 ( 0.59 ) = . 354 0.40 ( 0.65 ) = 0.26 the combined probability then is 35.4 + 26.00 = 61.4 % ans b"
Answer: b
Python program:
a = 59 + 65 
b = a / 2
Problem: walking 6 / 7 of his usual rate , a boy reaches his school 4 min early . find his usual time to reach the school ?
Options: a ) 28 m , b ) 20 m , c ) 22 m , d ) 23 m , e ) 24 m
Rationale: speed ratio = 1 : 6 / 7 = 7 : 6 time ratio = 6 : 4 1 - - - - - - - - 6 4 - - - - - - - - - ? = > 24 m answer : e
Answer: e
Python program:
a = 4 * 6
Problem: if 6 a = 7 b = 20 , then 84 ab =
Options: a ) 50 , b ) 100 , c ) 625 , d ) 800 , e ) 1250
Rationale: "6 a * 7 b = 20 * 20 = 400 42 ab = 400 i . e . 84 ab = 800 answer : option d"
Answer: d
Python program:
a = 20 / 6
b = 20 / 7
c = a * b
d = 84 * c
Problem: a 180 meter long train crosses a man standing on the platform in 6 sec . what is the speed of the train ?
Options: a ) 109 , b ) 108 , c ) 109 , d ) 106 , e ) 101
Rationale: "s = 180 / 6 * 18 / 5 = 108 kmph answerb"
Answer: b
Python program:
a = 180 / 6
b = a * const_3_6
Problem: a is twice efficient as b and together they do the same work in as much time as c and d together . if c and d can complete the work in 20 and 30 daysrespectively , working alone , then in how many days a can complete the work individually :
Options: a ) 12 days , b ) 18 days , c ) 24 days , d ) 30 days , e ) none of these
Rationale: explanation : a + b = c + d | | | | ratio of efficiency 10 x + 5 x 9 x + 6 x | ________| | _________| 15 x 15 x therefore , ratio of efficiency of a : c = 10 : 9 therefore , ratio of days taken by a : c = 9 : 10 therefore , number of days taken by a = 18 days answer : b
Answer: b
Python program:
a = 30 - 20
b = a - 1
c = 30 - 20
d = b / c
e = d * 20
Problem: a $ 500 investment and a $ 1,500 investment have a combined yearly return of 19 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 ) 23 % , d ) 21 % , e ) 22 %
Rationale: "the equation we can form the question : return on total investment = sum of individual investments ( 500 + 1500 ) ( 19 ) = ( 500 â ˆ — 7 ) + ( 1500 x ) , where x is the return on investment of 1500 . solving the equation , we get x = 23 % ( option c ) answer : c"
Answer: c
Python program:
a = 3 * 500
b = 500 + a 
c = 19 / 100
d = b * c
e = 7 / 100
f = 500 * e
g = d - f
h = 3 * 500
i = g / h
j = i * 100
Problem: it is well known that a triangle ’ s area is √ ( p ( p - a ) ( p - b ) ( p - c ) ) , when p = ( a + b + c ) / 2 , such that a , b , c are the lengths of sides of the triangle . if the triangle has 300 , 300 , and 300 as the side ’ s lengths , what is the triangle ’ s area ?
Options: a ) 34,200 , b ) 36,200 , c ) 38,200 , d ) 42,200 , e ) 38,971
Rationale: it is well known that a triangle ’ s area is √ ( p ( p - a ) ( p - b ) ( p - c ) ) , when p = ( a + b + c ) / 2 , - > p = ( 300 + 300 + 300 ) / 2 = 450 , area = √ ( 450 ( 450 - 300 ) ( 450 - 300 ) ( 450 - 300 ) ) = 38,971 . therefore , the answer is e .
Answer: e
Python program:
a = 300 + 300 
b = a + 300 
c = b / 2
d = c - 300
e = 300 + 300 
f = e + 300 
g = f / 2
h = g - 300
i = d * h
j = 300 + 300 
k = j + 300 
l = k / 2
m = l - 300
n = i * m
o = 300 + 300 
p = o + 300 
q = p / 2
r = n * q
s = math.sqrt(r)
t = s / 1000
Problem: in the fifth grade at parkway elementary school there are 450 students . 320 students are boys and 250 students are playing soccer . 86 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ?
Options: a ) 69 . , b ) 73 . , c ) 81 . , d ) 95 . , e ) 108 .
Rationale: "total students = 450 boys = 320 , girls = 130 total playing soccer = 250 86 % of 250 = 215 are boys who play soccer . girls who play soccer = 35 . total girls who do not play soccer = 130 - 35 = 95 . correct option : d"
Answer: d
Python program:
a = 450 - 320
b = 250 * 86
c = b / 100
d = 250 - c
e = a - d
Problem: excluding stoppages , the speed of a train is 48 kmph and including stoppages it is 32 kmph . of how many minutes does the train stop per hour ?
Options: a ) a ) 40 , b ) b ) 30 , c ) c ) 20 , d ) d ) 10 , e ) e ) 5
Rationale: "explanation : t = 16 / 48 * 60 = 20 answer : option c"
Answer: c
Python program:
a = 32 / 48
b = const_60 * a
c = const_60 - b
Problem: at a kennel with 80 dogs , 45 of the dogs wear tags and 40 wear flea collars . if 6 of the dogs wear both , then how many of the dogs wear neither a collar nor tags ?
Options: a ) 1 , b ) 6 , c ) 34 , d ) 79 , e ) 85
Rationale: dogs wear neither a collar nor tags = 80 - ( 45 + 40 - 6 ) dogs wear neither a collar nor tags = 80 - 79 dogs wear neither a collar nor tags = 80 - 79 hence , answer will be 1 answer : a
Answer: a
Python program:
a = 45 + 40 
b = a - 6
c = 80 - b
Problem: the ratio 9 : 5 expressed as a percent equals
Options: a ) 12.5 % , b ) 40 % , c ) 180 % , d ) 125 % , e ) none
Rationale: "solution 9 : 5 = 9 / 5 = ( 9 / 5 x 100 ) % . = 180 % . answer c"
Answer: c
Python program:
a = 9 / 5
b = a * 100
Problem: the sum of all two digit numbers divisible by 7 is
Options: a ) 910 , b ) 510 , c ) 728 , d ) 628 , e ) 810
Rationale: "required numbers are 14 , 21,28 . . . . . 98 this is an a . p . in which a = 14 , d = 7 and l = 98 . let the number of terms in it be n . then t = 98 so a + ( n - 1 ) d = 98 . 14 + ( n - 1 ) * 7 = 98 , 14 + 7 n - 7 = 98 7 + 7 n = 98 7 n = 98 - 7 n = 91 / 7 then n = 13 . required sum = n / 2 ( a + l ) = 13 / 2 ( 14 + 98 ) = 728 answer is c ."
Answer: c
Python program:
a = 10 + 1 
b = 7 * a
c = 1 * 7
d = b - c
e = 7 * 2
f = 1 * 7
g = e - f
h = d / g
i = h / 2
j = 7 * 2
k = 10 + 1 
l = 7 * k
m = j + l 
n = i * m
Problem: a number when divided by a certain divisor left remainder 241 , when twice the number was divided by the same divisor , the remainder was 115 . find the divisor ?
Options: a ) 370 , b ) 365 , c ) 380 , d ) 367 , e ) 460
Rationale: "easy solution : n = dq 1 + 241 2 n = 2 dq 1 + 482 - ( 1 ) 2 n = dq 2 + 115 - ( 2 ) as ( 1 ) = ( 2 ) = 2 n d * ( q 2 - 2 q 1 ) = 367 d * some integer = 367 checking all options only ( d ) syncs with it . answer d"
Answer: d
Python program:
a = 241 * 2
b = a - 115
Problem: find the value of x . ( 47 % of 1442 - 36 % of 1412 ) + 65 = x ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: e ) 5
Answer: e
Python program:
a = 47 / 100
b = a * 1442
c = 36 / 100
d = c * 1412
e = b - d
f = e + 65 
g = reminder + ( 
h = math.floor(g, 1)
Problem: the edges of three metal cubes are 1 cm , 2 cm , and 4 cm respectively . a new cube is made by melting these three cubes together . what is the edge of the new cube ( in centimeters ) ?
Options: a ) 3.8 , b ) 4.2 , c ) 4.6 , d ) 5.0 , e ) 5.4
Rationale: "the total volume is 1 ^ 3 + 2 ^ 3 + 4 ^ 3 = 73 the edge of the new cube is the cube root of 73 which is about 4.2 cm . the answer is b ."
Answer: b
Python program:
a = 4 ** 2
b = 2 ** 3
c = 1 + b 
d = a + c 
e = d ** const_0_33
Problem: every letter in the alphabet has a number value that is equal to its place in the alphabet . thus , the letter a has a value of 1 , the letter b has a value of 2 , the letter c has a value of 3 , etc . . . the number value of a word is obtained by adding up the value of the letters in the word and then multiplying that sum by the length of the word . what is the number value of the word ` ` dog ' ' ?
Options: a ) 72 , b ) 75 , c ) 78 , d ) 81 , e ) 84
Rationale: "` ` dog ' ' = ( 4 + 15 + 7 ) * 3 = 78 . the answer is c ."
Answer: c
Python program:
a = 2 * 10
b = a - 2
c = b + 1 
d = 2 * 10
e = c + d 
f = e * 3
Problem: the average of 1 st 3 of 4 numbers is 6 and of the last 3 are 5 . if the sum of the first and the last number is 21 . what is the last numbers ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: "a + b + c = 18 b + c + d = 15 a + d = 21 a – d = 3 a + d = 21 2 d = 18 d = 9 answer : e"
Answer: e
Python program:
a = 3 * 6
b = 21 - 6
c = b + 3 
d = a - c
e = d - 6
Problem: 15 ants can move 600 sugar cubes of 10 grams each to their home in 5 hours . then how many sugar cubes of 5 grams each , will 20 ants move in 3 hours ?
Options: a ) 360
b ) 480
c ) 720
d ) 960
e ) 1000
Rationale: d 15 ants move 600 / 5 = 120 sugar cubes of 10 grams in 1 hour . 5 grams sugar cubes will take less time to move . thus if weight of the sugar cube is 5 grams , 15 ants will move 120 x 10 / 5 = 240 sugar cubes in 1 hour . more ants , more sugar cubes they can move . 20 ants will move 240 x 20 / 15 = 320 sugar cubes in 1 hour thus in 3 hours , 20 ants will move 320 x 3 = 960 sugar cubes of 5 grams .
Answer: d
Python program:
a = 600 * 10
b = a / 5
c = b / 15
d = c * 20
e = d * 3
f = e / 5
Problem: find the sum the difference between the compound and s . i . on a certain sum of money for 6 years at 10 % per annum is rs . 80 of money ?
Options: a ) 1000 , b ) 1200 , c ) 4800 , d ) 3600 , e ) 8400
Rationale: "p = 80 ( 100 / 10 ) 6 = > p = 1500 answer : c"
Answer: c
Python program:
a = 10 * 6
b = 80 / a
c = b * 100
d = 10 * 6
e = c * d
Problem: a grocery store bought some mangoes at a rate of 5 for a dollar . they were separated into two stacks , one of which was sold at a rate of 4 for a dollar and the other at a rate of 6 for a dollar . what was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes ?
Options: a ) 1 : 4 , b ) 1 : 5 , c ) 2 : 3 , d ) 3 : 2 , e ) 2 : 5
Rationale: "the cost price of a mango = 1 / 5 dollars . the selling price of a mango from the first stack = 1 / 4 dollars - - > the profit from one mango = 1 / 4 - 1 / 5 = 1 / 20 dollars . the selling price of a mango from the second stack = 1 / 6 dollars - - > the loss from one mango = 1 / 5 - 1 / 6 = 1 / 30 dollars . the profit from one mango from the first stack is 4 times the loss from one mango from the second stack . the ratio is 1 / 20 * 30 / 1 = 3 : 2 d"
Answer: d
Python program:
a = 1 / 4
b = 1 / 5
c = a - b
d = 1 / 5
e = 2 * 4
f = 1 / e
g = d - f
h = c / g
Problem: what is the positive difference between the sum of the squares of the first 6 positive integers and the sum of the prime numbers between the first square and fourth square ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 50
Rationale: forget conventional ways of solving math questions . in ps , ivy approach is the easiest and quickest way to find the answer . the sum of the squares of the first 4 positive integers = 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + 4 ^ 2 + 5 ^ 2 + 6 ^ 2 = 91 the sum of the prime numbers between the first square ( = 1 ) and fourth square ( = 16 ) = 2 + 3 + 5 + 7 + 11 + 13 = 41 . so the difference between 41 and 91 is 50 . so the answer is ( e ) .
Answer: e
Python program:
a = 2 ** 2
b = 1 + a 
c = 3 ** 2
d = b + c 
e = 4 ** 2
f = d + e 
g = 4 + 1 
h = g ** 2
i = f + h 
j = 6 ** 2
k = i + j 
l = 4 + 3 
m = l + 6 
n = 2 + 3 
o = 4 + 1 
p = n + o 
q = 4 + 3 
r = p + q 
s = 2 + 3 
t = s + 6 
u = r + t 
v = m + u 
w = k - v
Problem: john makes $ 60 a week from his job . he earns a raise and now makes $ 80 a week . what is the % increase ?
Options: a ) 16 % , b ) 33.33 % , c ) 17 % , d ) 17.61 % , e ) 17.56 %
Rationale: "increase = ( 20 / 60 ) * 100 = ( 2 / 6 ) * 100 = 33.33 % . b"
Answer: b
Python program:
a = 80 - 60
b = a / 60
c = b * 100
Problem: find the area of a parallelogram with base 28 cm and height 32 cm .
Options: a ) 200 , b ) 384 , c ) 345 , d ) 244 , e ) 896
Rationale: "area of a parallelogram = base * height = 28 * 32 = 896 cm 2 answer : option e"
Answer: e
Python program:
a = 28 * 32
Problem: a can complete a work in 18 days and b can do the same work in 10 days . if a after doing 3 days , leaves the work , find in how many days b will do the remaining work ?
Options: a ) 2 days , b ) 8 days , c ) 6 days , d ) 7 days , e ) 10 days
Rationale: "the required answer = ( 18 - 3 ) * 5 / 18 = 150 / 18 = 8 days answer is b"
Answer: b
Python program:
a = 18 * 2
b = 18 / 3
c = a + b
Problem: what is the range of all the roots of | x ^ 2 - 5 | = x ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: "we get 2 quadratic equations here . . 1 ) x ^ 2 - x - 5 = 0 . . . . . . . roots 2 , - 1 2 ) x ^ 2 + x - 5 = 0 . . . . . . . . roots - 2 , 1 inserting each root in given equation , it can be seen that - 1 and - 2 do not satisfy the equations . so value of x for given equation . . . . x = 5 or x = 1 i guess range is 5 - 1 = 4 a"
Answer: a
Python program:
a = math.sqrt(5)
Problem: a man can swim in still water at 15 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?
Options: a ) 3.9 , b ) 5 , c ) 5.3 , d ) 1.5 , e ) 5.2
Rationale: "m = 15 s = x ds = 15 + x us = 15 - x 15 + x = ( 15 - x ) 2 15 + x = 30 - 2 x 3 x = 15 x = 5 answer : b"
Answer: b
Python program:
a = 15 / 3
Problem: there are 134 toys coloured red and white in a box . two red toys are removed from the lot and now there are twice as many red ones as white ones . how many of red colour toys are there now ?
Options: a ) 76 , b ) 86 , c ) 90 , d ) 88 , e ) 78
Rationale: r + w = 134 two red toys are removed from the lot and now there are twice red ones as white ones r - 2 = 2 w sub 1 st one we get 134 - w - 2 = 2 w 132 = 3 w w = 44 r = 88 actually red will be 90 now 88 answer : d
Answer: d
Python program:
a = 134 * 2
b = a + 2 
c = b / 3
d = c - 2
Problem: 2224 × 9997 = ?
Options: a ) 22244428 , b ) 22255538 , c ) 22233328 , d ) 22266628 , e ) 22233327
Rationale: "c 22233328 2224 × 9997 = 2224 × ( 10000 - 3 ) = 2224 × 10000 - 2224 × 3 = 22240000 - 6672 = 22233328"
Answer: c
Python program:
a = 2224 / 9997
b = a * 100
Problem: a train running at a speed of 36 kmph crosses an electric pole in 12 seconds . in how much time will it cross a 340 m long platform ?
Options: a ) 19 , b ) 27 , c ) 29 , d ) 46 , e ) 28
Rationale: "let the length of the train be x m . when a train crosses an electric pole , the distance covered is its own length . so , x = 12 * 36 * 5 / 18 m = 120 m . time taken to cross the platform = ( 120 + 340 ) / 36 * 5 / 18 = 46 min . answer : d"
Answer: d
Python program:
a = const_0_2778 * 36
b = a * 12
c = 340 + b 
d = const_0_2778 * 36
e = c / d
Problem: a shopkeeper sells 20 % of his stock at 20 % profit ans sells the remaining at a loss of 10 % . he incurred an overall loss of rs . 500 . find the total worth of the stock ?
Options: a ) 13500 , b ) 12000 , c ) 12500 , d ) 15000 , e ) 15500
Rationale: "let the total worth of the stock be rs . x . the sp of 20 % of the stock = 1 / 5 * x * 6 / 5 = 6 x / 25 the sp of 80 % of the stock = 4 / 5 * x * 0.9 = 24 x / 25 total sp = 6 x / 25 + 18 x / 25 = 49 x / 50 overall loss = x - 24 x / 50 = x / 25 x / 25 = 500 = > x = 12500 answer : c"
Answer: c
Python program:
a = 10 / 100
b = 100 - 20
c = b / 100
d = a * c
e = 20 / 100
f = 20 / 100
g = e * f
h = d - g
i = 500 / h
Problem: triangle xyz is an isosceles right triangle . if side xy is longer than side yz , and the area of the triangle is 25 , what is the measure of side xy ?
Options: a ) 10 , b ) 4 √ 2 , c ) 8 , d ) 8 √ 2 , e ) can not be determined from the information provided
Rationale: "ans a . . 10 . . xy being larger means it is the hyp . . area = ( 1 / 2 ) * ( yz ) ^ 2 = 25 or yz = 5 * \ sqrt { 2 } . . therefore hyp = xy = 10"
Answer: a
Python program:
a = math.sqrt(25)
b = math.sqrt(2)
c = a * b
d = c ** 2
e = math.sqrt(25)
f = math.sqrt(2)
g = e * f
h = g ** 2
i = d + h 
j = math.sqrt(i)
Problem: a pharmaceutical company received $ 2 million in royalties on the first $ 12 ; million in sales of generic equivalent of one of its products and then $ 4 million in royalties on the next $ 48 million in sales . by approximately what percent did the ratio of royalties to sales decrease from the first $ 12 million in sales to the next $ 48 million in sales ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 50 % , e ) 55 %
Rationale: change in ratio of royalties to sales = 2 / 12 - 4 / 48 = 1 / 12 % decrease = ( 1 / 12 ) / ( 2 / 12 ) * 100 = 50 % ( approx ) answer : d )
Answer: d
Python program:
a = 2 / 12
b = 4 / 48
c = a - b
d = 2 / 12
e = c / d
f = e * 100
Problem: an ore contains 25 % of an alloy that has 90 % iron . other than this , in remaining 75 % of the ore , there is no iron . how many kgs of the ore are needed to obtain 60 kg . of pure iron . ?
Options: a ) 266.69 , b ) 266.67 , c ) 266.66 , d ) 263.66 , e ) 266.61
Rationale: "explanation : let us take 100 x kgs of ore . now it contains 25 x kgs of alloy and it contains 90 % ( 25 x ) kgs of iron . 90 % ( 25 x ) = 60 kg ⇒ x = 60 × 10090 × 12560 × 10090 × 125 = 8383 so iron ore required = 100 × 8383 = 266.66 answer : d"
Answer: d
Python program:
a = 100 * 60
b = 25 * 90
c = b / 100
d = a / c
Problem: what is 15 % of 2 / 3 of 0.4 ?
Options: a ) 0.09 , b ) 0.9 , c ) 9 , d ) 90 , e ) none of the above
Rationale: "the best way to solve these questions is to convert every term into fraction ( 15 / 100 ) * ( 2 / 3 ) * ( 4 / 10 ) = 120 / 3000 = 0.04 option a"
Answer: a
Python program:
a = 3 + 2 
b = a * 2
c = 3 * 4
d = c * 100
e = b * d
f = 3 + 4 
g = 3 + 2 
h = f * g
i = 3 + 2 
j = i * 2
k = h * j
l = e + k 
m = 3 + 3 
n = l + m 
o = 15 * n
p = o / 100
Problem: the average temperature for monday , tuesday , wednesday and thursday was 48 degrees and for tuesday , wednesday , thursday and friday was 46 degrees . if the temperature on monday was 43 degrees . find the temperature on friday ?
Options: a ) 65 degrees , b ) 73 degrees , c ) 37 degrees , d ) 35 degrees , e ) 74 degrees
Rationale: m + tu + w + th = 4 * 48 = 192 tu + w + th + f = 4 * 46 = 184 m = 43 tu + w + th = 192 - 43 = 149 f = 184 – 149 = 35 answer : d
Answer: d
Python program:
a = 48 * 4
b = 46 * 4
c = a - b
d = 43 - c
Problem: what is the probability that the sum of two dice will yield a 4 , and then when both are thrown again , their sum will again yield a 4 ? assume that each die has 3 sides with faces numbered 1 to 3 .
Options: a ) 1 / 144 , b ) 1 / 36 , c ) 1 / 9 , d ) 1 / 6 , e ) 1 / 3
Rationale: "solution - rolling dices is an independent event . the combinations to get 4 are ( 1,3 ) , ( 3,1 ) , ( 2,2 ) , and total combinations of both dices is 9 . the probability of getting 4 in first attempt is 3 / 9 = 1 / 3 . probability of getting 4 again in second attempt = ( 1 / 3 ) * ( 1 / 3 ) = 1 / 9 . ans c"
Answer: c
Python program:
a = 3 ** 2
b = 3 / a
c = 3 ** 2
d = 3 / c
e = b * d
Problem: in a graduating class of 232 students , 144 took geometry and 119 took biology . what is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology ?
Options: a ) 144 , b ) 119 , c ) 113 , d ) 88 , e ) 31
Rationale: "greatest possible number taken both should be 144 ( as it is maximum for one ) smallest possible number taken both should be given by total - neither = a + b - both both = a + b + neither - total ( neither must be 0 to minimize the both ) so 144 + 119 + 0 - 232 = 31 greatest - smallest is 144 - 31 = 113 so answer must be c . 113"
Answer: c
Python program:
a = 144 + 119 
b = a - 232
c = 119 - b
Problem: albert father was 48 years of age when she was born while her mother was 46 years old when her brother 2 years younger to her was born . what is the difference between the ages of her parents ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: mother ' s age when albert ' s brother was born = 46 years father ' s age when albert ' s brother was born = 48 + 2 = 50 years required difference = 50 - 46 = 4 years answer is b
Answer: b
Python program:
a = 2 + 3 
b = a + 4 
c = 2 + 3 
d = b - c
Problem: what was the principal , if at 12 % per annum the interest after 3 years amounted to rs . 5888 less than the sum lent ?
Options: a ) 9000 , b ) 3000 , c ) 5000 , d ) 1300 , e ) 9200
Rationale: p - 2336 = ( p * 12 * 3 ) / 100 p = 9200 answer : e
Answer: e
Python program:
a = 12 * 3
b = a / 100
c = 1 - b
d = 5888 / c
Problem: what is the 14 th digit to the right of the decimal point in the decimal equivalent of 82 / 11 ?
Options: a ) 4 , b ) 3 , c ) 1 , d ) 5 , e ) 7
Rationale: "82 / 11 = 7.4545 . . . . 45 is non - repeating terminating decimal . the 14 th digit to the right of decimal point will be 5 . answer d"
Answer: d
Python program:
a = 82 / 11
Problem: on thursday mabel handled 90 transactions . anthony handled 10 % more transactions than mabel , cal handled 2 / 3 rds of the transactions that anthony handled , and jade handled 14 more transactions than cal . how much transactions did jade handled ?
Options: a ) 80 , b ) 81 , c ) 82 , d ) 83 , e ) 84
Rationale: "solution : mabel handled 90 transactions anthony handled 10 % more transactions than mabel anthony = 90 + 90 × 10 % = 90 + 90 × 0.10 = 90 + 9 = 99 cal handled 2 / 3 rds of the transactions than anthony handled cal = 2 / 3 × 99 = 66 jade handled 14 more transactions than cal . jade = 66 + 14 = 80 jade handled = 80 transactions . answer : a"
Answer: a
Python program:
a = 90 / 100
b = 10 + 100 
c = a * b
d = c * 2
e = d / 3
f = e + 14
Problem: two vessels p and q contain 62.5 % and 87.5 % of alcohol respectively . if 12 litres from vessel p is mixed with 4 litres from vessel q , the ratio of alcohol and water in the resulting mixture is ?
Options: a ) 19 : 2 , b ) 18 : 3 , c ) 11 : 1 , d ) 11 : 5 , e ) 11 : 4
Rationale: "quantity of alcohol in vessel p = 62.5 / 100 * 2 = 15 / 2 litres quantity of alcohol in vessel q = 87.5 / 100 * 4 = 7 / 2 litres quantity of alcohol in the mixture formed = 15 / 2 + 7 / 2 = 11 litres as 16 litres of mixture is formed , ratio of alcohol and water in the mixture formed = 11 : 5 answer : d"
Answer: d
Python program:
a = 62 * 5
b = a / 100
c = 87 * 5
d = c / 100
e = b + d 
f = 62 * 5
g = f / 100
h = 12 - g
i = 87 * 5
j = i / 100
k = 4 - j
l = h + k 
m = e / l
Problem: two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.9 km and 2.1 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
Options: a ) 99 , b ) 277 , c ) 48 , d ) 96 , e ) 22
Rationale: "relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.9 + 2.1 = 4 km = 4000 m . required time = 4000 * 3 / 125 = 96 sec . answer : d"
Answer: d
Python program:
a = 1 * 9
b = 60 * 1000
c = b / 3600
d = a / c
e = 2 * 1
f = 90 * 1000
g = f / 3600
h = e / g
i = d - h