euclaise/mathqa_programs huggingface dataset:
Problem: you hold some gold in a vault as an investment . over the past year the price of gold increases by 52 % . in order to keep your gold in the vault , you must pay 6 % of the total value of the gold per year . what percentage has the value of your holdings changed by over the past year .
Options: a ) 42.88 $ , b ) 43 % , c ) 45 % , d ) 45.5 % , e ) 46.3 %
Rationale: ( 100 % + 52 % ) * ( 100 % - 6 % ) = 152 * 0.94 = 142.88 % an increase of 42.88 % your gold holdings have increased in value by 42.88 % . the answer is a
Answer: a
Python program:
a = 52 / 6
b = 52 - a
Problem: a tank contains 9,000 gallons of a solution that is 6 percent sodium chloride by volume . if 3,000 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 6 % , b ) 7 % , c ) 8 % , d ) 9 % , e ) 10 %
Rationale: "we start with 9,000 gallons of a solution that is 6 % sodium chloride by volume . this means that there are 0.06 x 9,000 = 54 gallons of sodium chloride . when 3,000 gallons of water evaporate we are left with 6,000 gallons of solution . from here we can determine what percent of the 6,000 gallon solution is sodium chloride . ( sodium chloride / total solution ) x 100 = ? ( 540 / 6,000 ) x 100 = ? 9 / 100 x 100 = ? = 9 % answer is d ."
Answer: d
Python program:
a = 100 * 100
b = 6 / 100
c = a * b
d = 100 * 100
e = 2 + 3 
f = 2 + 3 
g = f * 2
h = g * 100
i = e * h
j = 2 + 3 
k = j * 100
l = i + k 
m = d - l
n = c / m
o = n * 100
Problem: a sum fetched a total simple interest of rs . 750 at the rate of 6 p . c . p . a . in 5 years . what is the sum ?
Options: a ) 2600 , b ) 2500 , c ) 2900 , d ) 2800 , e ) 2700
Rationale: "sol . principal = rs . [ 100 * 750 / 6 * 5 ] = rs . [ 75000 / 30 ] = rs . 2500 . answer b"
Answer: b
Python program:
a = 750 * 100
b = a / 6
c = b / 5
Problem: robert ate 12 chocolates , nickel ate 3 chocolates . how many more chocolates did robert ate than nickel ?
Options: a ) a ) 4 , b ) b ) 7 , c ) c ) 9 , d ) d ) 5 , e ) e ) 2
Rationale: 12 - 3 = 9 . answer is c
Answer: c
Python program:
a = 12 - 3
Problem: in what time will a train 140 meters long cross an electric pole , if its speed is 210 km / hr
Options: a ) 5 seconds , b ) 4.5 seconds , c ) 3 seconds , d ) 2.4 seconds , e ) none of these
Rationale: "explanation : first convert speed into m / sec speed = 210 * ( 5 / 18 ) = 58 m / sec time = distance / speed = 140 / 58 = 2.4 seconds option d"
Answer: d
Python program:
a = 210 * const_0_2778
b = 140 / a
Problem: there are two cars . one is 300 miles north of the other . simultaneously , the car to the north is driven westward at 20 miles per hour and the other car is driven eastward at 60 miles per hour . how many miles apart are the cars after 5 hours ?
Options: a ) 300 , b ) 360 , c ) 400 , d ) 450 , e ) 500
Rationale: here , drawing a quick sketch of the ' actions ' described will end in a diagonal line that you canbuilda right triangle around : the right triangle will have a base of 400 and a height of 300 . the hidden pattern here is a 3 / 4 / 5 right triangle ( the 300 lines up with the ' 3 ' and the 400 lines up with the ' 4 ' ) . in this way , you can deduce that each side is ' 100 times ' bigger than it ' s corresponding side : 3 / 4 / 5 becomes 300 / 400 / 500 thus the distance between the two cars is the length of the hypotenuse of this larger right triangle . . . final answer : e
Answer: e
Python program:
a = 60 * 5
b = 20 * 5
c = a + b 
d = c ** 2
e = 60 * 5
f = e ** 2
g = d + f 
h = math.sqrt(g)
Problem: an investment compounds annually at an interest rate of 34.1 % what is the smallest investment period by which time the investment will more than triple in value ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 9 , e ) 12
Rationale: assume initial amount is x annual interest is 34.1 % so after 1 year the amount will become x * ( 100 + 34.1 ) / 100 = > x * 4 / 3 now we need to find n for x * ( 4 / 3 ) ^ n = 3 x ; or in other words n = 4 answer : b
Answer: b
Python program:
a = math.log(3)
b = 34 / 1
c = 1 + b 
d = math.log(c)
e = a / d
f = math.floor(e)
g = f + 1
Problem: the cross - section of a water channel is a trapezium in shape . if the channel is 12 meters wide at the top and 6 meters wide at the bottom and the area of cross - section is 630 square meters , what is the depth of the channel ( in meters ) ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "1 / 2 * d * ( 12 + 6 ) = 630 d = 70 the answer is c ."
Answer: c
Python program:
a = 12 + 6 
b = a / 2
c = 630 / b
Problem: a bicycle wheel has a diameter of 0.51 m . how many complete revolutions does it make in 1 km ?
Options: a ) 246 , b ) 448 , c ) 1408 , d ) 710 , e ) 624
Rationale: 1 revolution = 3.14 * diameter . number of revolutions in 1 km = 1000 m / ( 3.14 * 0.51 m ) = 624.5 . hence 624 complete revolutions . answer e
Answer: e
Python program:
a = 1000 * 1
b = 3 * 4
c = b + 2 
d = 4 * 2
e = d + 2 
f = e ** 2
g = c / f
h = 3 + g 
i = h * 0
j = a / i
Problem: triangle atriangle b are similar triangles with areas 1536 units square and 1734 units square respectively . the ratio of there corresponding height would be
Options: a ) 9 : 10 , b ) 17 : 19 , c ) 23 : 27 , d ) 16 : 17 , e ) 15 : 23
Rationale: "let x be the height of triangle a and y be the height of triangle of b . since triangles are similar , ratio of area of a and b is in the ratio of x ^ 2 / y ^ 2 therefore , ( x ^ 2 / y ^ 2 ) = 1536 / 1734 ( x ^ 2 / y ^ 2 ) = ( 16 * 16 * 6 ) / ( 17 * 17 * 7 ) ( x ^ 2 / y ^ 2 ) = 16 ^ 2 / 17 ^ 2 x / y = 16 / 17 ans = d"
Answer: d
Python program:
a = 1536 / 1734
b = math.sqrt(a)
Problem: x can finish a work in 20 days . y can finish the same work in 16 days . y worked for 12 days and left the job . how many days does x alone need to finish the remaining work ?
Options: a ) 2 , b ) 3 , c ) 9 , d ) 5 , e ) 8
Rationale: "work done by x in 1 day = 1 / 20 work done by y in 1 day = 1 / 16 work done by y in 12 days = 12 / 16 = 3 / 4 remaining work = 1 – 3 / 4 = 1 / 4 number of days in which x can finish the remaining work = ( 1 / 4 ) / ( 1 / 20 ) = 5 d"
Answer: d
Python program:
a = 1 / 16
b = 12 * a
c = 1 - b
d = 1 / 20
e = c / d
Problem: if the average of 10 consecutive integers is 20.5 then the 10 th integer is : -
Options: a ) 15 , b ) 20 , c ) 23 , d ) 24 , e ) 25
Rationale: the average falls between the 5 th and 6 th integers , integer 5 = 20 , integer 6 = 21 . counting up to the tenth integer we get 25 . answer : e
Answer: e
Python program:
a = 10 * 2
b = 10 * 2
c = 20 - 5
d = c * 10
e = a + d
Problem: sandy gets 3 marks for each correct sum and loses 2 marks for each incorrect sum . sandy attempts 30 sums and obtains 55 marks . how many sums did sandy get correct ?
Options: a ) 19 , b ) 21 , c ) 23 , d ) 25 , e ) 27
Rationale: "let x be the correct sums and ( 30 - x ) be the incorrect sums . 3 x - 2 ( 30 - x ) = 55 5 x = 115 x = 23 the answer is c ."
Answer: c
Python program:
a = 2 * 30
b = a + 55 
c = 2 + 3 
d = b / c
Problem: a sum of money is to be divided among ann , bob and chloe . first , ann receives $ 4 plus one - half of what remains . next , bob receives $ 4 plus one - third of what remains . finally , chloe receives the remaining $ 32 . how much money m did bob receive ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 52
Rationale: "notice that we need not consider ann ' s portion in the solution . we can just let k = the money remaining after ann has received her portion and go from there . our equation will use the fact that , once we remove bob ' s portion , we have $ 32 for chloe . so , we getk - bob ' s $ = 32 bob received 4 dollars plus one - third of what remained once bob receives $ 4 , the amount remaining is k - 4 dollars . so , bob gets a 1 / 3 of that as well . 1 / 3 of k - 4 is ( k - 4 ) / 3 so altogether , bob receives 4 + ( k - 4 ) / 3 so , our equation becomes : k - [ 4 + ( k - 4 ) / 3 ] = 32 simplify to get : k - 4 - ( k - 4 ) / 3 = 32 multiply both sides by 3 to get : 3 k - 12 - k + 4 = 96 simplify : 2 k - 8 = 96 solve : k = 52 plug this k - value intok - bob ' s $ = 32 to get : 52 - bob ' s $ = 32 so , bob ' s $ m = 20 answer : b"
Answer: b
Python program:
a = 32 * 2
b = a / 3
Problem: last year elaine spent 10 % of her annual earnings on rent . this year she earned 15 % more than last year and she spent 30 % of her annual earnings on rent . the amount she spent on rent this year is what percent of the amount spent on rent last year ?
Options: a ) 252.5 , b ) 364.5 , c ) 367.5 , d ) 375 , e ) 345
Rationale: "for this it is easiest to use simple numbers . let ' s assume that elaine ' s annual earnings last year were $ 100 . she would ' ve spent $ 10 of this on rent . this year she earned 15 % more , or $ 115 . she would ' ve spent 30 % of this on rent , or $ 34.5 do $ 34.5 / $ 10 this will give you 345 % e is the correct answer ."
Answer: e
Python program:
a = 15 / 100
b = a + 1 
c = b * 30
d = c / 10
e = d * 100
Problem: sandy is younger than molly by 8 years . if their ages are in the respective ratio of 7 : 9 , how old is molly ?
Options: a ) 18 , b ) 27 , c ) 36 , d ) 45 , e ) 54
Rationale: "s = m - 8 s / m = 7 / 9 9 s = 7 m 9 ( m - 8 ) = 7 m m = 36 the answer is c ."
Answer: c
Python program:
a = 9 - 7
b = 7 / a
c = b * 8
Problem: when x is multiplied by 3 , the result is 4 more than the result of subtracting x from 16 . what is the value of x ?
Options: a ) - 4 , b ) - 2 , c ) 5 , d ) 13 , e ) 22
Rationale: "the equation that can be formed is : 3 x - 4 = 16 - x or , 4 x = 20 or , x = 5 . answer : c"
Answer: c
Python program:
a = 16 + 4 
b = 3 + 1 
c = a / b
Problem: in a certain school , 25 % of students are below 8 years of age . the number of students above 8 years of age is 2 / 3 of the number of students of 8 years of age which is 36 . what is the total number of students in the school ?
Options: a ) 72 , b ) 80 , c ) 120 , d ) 150 , e ) 100
Rationale: "explanation : let the number of students be x . then , number of students above 8 years of age = ( 100 - 25 ) % of x = 75 % of x . 75 % of x = 36 + 2 / 3 of 36 75 / 100 x = 60 x = 80 . answer : option b"
Answer: b
Python program:
a = 2 / 3
b = 36 * a
c = 36 + b 
d = 25 / 100
e = 1 - d
f = c / e
Problem: how many seconds will a 600 meter long train moving with a speed of 63 km / hr take to cross a man walking with a speed of 3 km / hr in the direction of the train ?
Options: a ) 48 , b ) 36 , c ) 26 , d ) 11 , e ) 18
Rationale: "explanation : here distance d = 600 mts speed s = 63 - 3 = 60 kmph = 60 x 5 / 18 m / s time t = = 36 sec . answer : b"
Answer: b
Python program:
a = 63 - 3
b = a * const_0_2778
c = 600 / b
Problem: a train covers a distance of 12 km in 10 minutes . if it takes 9 seconds to pass a telegraph post , then the length of the train is
Options: a ) 100 m , b ) 120 m , c ) 140 m , d ) 160 m , e ) 180 cm
Rationale: "explanation : speed = 12 / 10 x 60 km / hr = 72 x 5 / 18 m / sec = 20 m / sec . length of the train = ( speed x time ) = ( 20 x 9 ) m = 180 m answer : option e"
Answer: e
Python program:
a = 100 / 0
b = a - 9
c = 100 / 0
Problem: machine a can process 6000 envelopes in 3 hours . machines b and c working together but independently can process the same number of envelopes in 2.5 hours . if machines a and c working together but independently process 3000 envelopes in 1 hour , then how many hours would it take machine b to process 5600 envelopes .
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 60 / 7
Rationale: "you can either take the amount of work done as the same as karishma has done or take the work done by each in the same time . i will do the latter 1 . work done in 1 hr by a is 2000 envelopes 2 . work done in 1 hr by a and c is 3000 envelopes 3 . so work done in 1 hr by c is 1000 envelopes 4 . work done in 1 hr by b and c is 2400 envelopes 5 . so work done in 1 hr by b is 1400 envelopes 6 . so to process 5600 envelopes b will take 5600 / 1400 hrs = 4 hrs so the answer is choice c"
Answer: c
Python program:
a = 6000 / 2
b = 3000 / 1
c = 6000 / 3
d = b - c
e = a - d
f = 5600 / e
Problem: if the probability of rain on any given day in chicago during the summer is 25 % , independent of what happens on any other day , what is the probability of having exactly 3 rainy days from july 4 through july 7 inclusive ?
Options: a ) 1 / 16 , b ) 3 / 32 , c ) 5 / 32 , d ) 3 / 64 , e ) 7 / 64
Rationale: "one possible case is : rainy - rainy - rainy - not rainy . the probability of this case is 1 / 4 * 1 / 4 * 1 / 4 * 3 / 4 = 3 / 256 the number of possible cases is 4 c 3 = 4 . p ( exactly 3 rainy days ) = 4 * 3 / 256 = 3 / 64 the answer is d ."
Answer: d
Python program:
a = 1 / 2
b = a ** 4
c = 4 * b
Problem: what is the difference between the place value and face value of 4 in the numeral 46 ?
Options: a ) 36 , b ) 45 , c ) 52 , d ) 44 , e ) 39
Rationale: difference between the place value and face value of 4 = 40 - 4 = 36 answer is a
Answer: a
Python program:
a = 4 * 10
b = a - 4
Problem: in a certain apartment building , there are one - bedroom and two - bedroom apartments . the rental prices of the apartment depend on a number of factors , but on average , two - bedroom apartments have higher rental prices than do one - bedroom apartments . let m be the average rental price for all apartments in the building . if m is $ 1,000 higher than the average rental price for all one - bedroom apartments , and if the average rental price for all two - bedroom apartments is $ 9,000 higher that m , then what percentage of apartments in the building are two - bedroom apartments ?
Options: a ) 50 % , b ) 40 % , c ) 20 % , d ) 30 % , e ) 10 %
Rationale: "ratio of 2 bedroom apartment : 1 bedroom apartment = 1000 : 9000 - - - - - > 1 : 9 let total number of apartments be x no . of 2 bedroom apartment = ( 1 / 10 ) * x percentage of apartments in the building are two - bedroom apartments - - - - > ( 1 / 10 ) * 100 - - - > 10 % answer : e"
Answer: e
Python program:
a = 1 * 0
b = 2 * 1000
c = b + 100 
d = c + 1 
e = a / d
Problem: a person travels from p to q a speed of 30 km / hr and returns by increasing his speed by 30 % . what is his average speed for both the trips ?
Options: a ) 33 , b ) 77 , c ) 48 , d ) 99 , e ) 34.5
Rationale: "speed on return trip = 130 % of 30 = 39 km / hr . average speed of trip = 30 + 39 / 2 = 69 / 2 = 34.5 km / hr answer : e"
Answer: e
Python program:
a = 30 / 100
b = 1 + a 
c = 30 * b
d = c + 30 
e = d / 2
Problem: the sum of all the integers f such that - 26 < f < 24 is
Options: a ) 0 , b ) - 2 , c ) - 25 , d ) - 49 , e ) - 51
Rationale: "easy one - - 25 , - 24 , - 23 , - 22 , . . . . . . - 1,0 , 1 , 2 . . . . , 22 , 23 cancel everyhitng and we ' re left with - - 25 and - 24 f = - 49 . d is the answer ."
Answer: d
Python program:
a = negate + ( 
b = a + 1
Problem: the average expenditure of a labourer for 6 months was 70 and he fell into debt . in the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30 . his monthly income i
Options: a ) 69 , b ) 72 , c ) 75 , d ) 78 , e ) 80
Rationale: "income of 6 months = ( 6 × 70 ) – debt = 420 – debt income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ income of 10 months = 690 average monthly income = 690 ÷ 10 = 69 answer a"
Answer: a
Python program:
a = 70 * 6
b = 60 * 4
c = a + b 
d = c + 30 
e = 6 + 4 
f = d / e
Problem: a student chose a number , multiplied it by 8 , then subtracted 138 from the result and got 102 . what was the number he chose ?
Options: a ) 30 , b ) 120 , c ) 130 , d ) 140 , e ) 150
Rationale: "solution : let xx be the number he chose , then 8 ⋅ x − 138 = 102 8 x = 240 x = 30 answer a"
Answer: a
Python program:
a = 102 + 138 
b = a / 8
Problem: a man has rs . 192 in the denominations of one - rupee notes , 5 - rupee notes and 10 - rupee notes . the number of notes of each denomination is equal . what is the total number of notes that he has ?
Options: a ) 37 , b ) 36 , c ) 22 , d ) 90 , e ) 28
Rationale: let number of notes of each denomination be x . then , x + 5 x + 10 x = 192 16 x = 192 x = 12 . hence , total number of notes = 3 x = 36 . answer : b
Answer: b
Python program:
a = 1 + 5 
b = a + 10 
c = 192 / b
d = 1 + 5 
e = d + 10 
f = 192 / e
g = c + f 
h = 1 + 5 
i = h + 10 
j = 192 / i
k = g + j
Problem: how many gallons of milk that is 10 percent butter - fat must be added to 8 gallons of milk that is 40 percent butterfat to obtain milk that is 20 percent butterfat ?
Options: a ) 6 , b ) 12 , c ) 14 , d ) 16 , e ) 28
Rationale: "equate the fat : 0.1 x + 0.4 * 8 = 0.2 ( x + 8 ) - - > x = 16 . answer : d ."
Answer: d
Python program:
a = 40 - 20
b = a * 8
c = b / 10
Problem: the price of lunch for 15 people was $ 211.00 , including a 15 percent gratuity for service . what was the average price per person , excluding the gratuity ?
Options: a ) $ 11.73 , b ) $ 12.78 , c ) $ 13.80 , d ) $ 14.00 , e ) $ 15.87
Rationale: "take the initial price before the gratuity is 100 the gratuity is calculated on the final price , so as we assumed the final bill before adding gratuity is 100 so gratuity is 15 % of 100 is 15 so the total price of meals is 115 so the given amount i . e 211 is for 115 then we have to calculate for 100 for 115 211 for 100 x so by cross multiplication we get 115 x = 100 * 211 = > x = 100 * 211 / 110 by simplifying we get x as 191.81 which is the price of lunch before gratuity so the gratuity is 19.19 so as the question ask the average price person excluding gratuity is 191.81 / 15 = 12.78 so our answer is b )"
Answer: b
Python program:
a = 100 + 15 
b = 211 / 0
c = b * 100
d = 1 / 15
e = c * d
Problem: how many times digit 20 is used while writing numbers from 100 to 500 ?
Options: a ) 20 , b ) 30 , c ) 15 , d ) 25 , e ) 20
Rationale: "in 100 to 200 there are 5 20 ' s in 200 to 300 there are 5 20 ' s in 300 to 400 there are 5 20 ' s in 400 to 500 there are 5 20 ' s so , total 20 is 20 ' s correct option : a"
Answer: a
Python program:
a = 500 - 100
b = a / 10
c = 10 + 1 
d = 10 + 1 
e = c * d
f = b + e 
g = 20 * 2
h = f + g
Problem: the average of first 6 natural numbers is ?
Options: a ) 5.2 , b ) 3.5 , c ) 5.3 , d ) 5.9 , e ) 5.1
Rationale: "sum of 6 natural no . = 42 / 2 = 21 average = 21 / 6 = 3.5 answer : b"
Answer: b
Python program:
a = 6 + 1
Problem: a part - time employee ’ s hourly wage was increased by 20 % . she decided to decrease the number of hours worked per week so that her total income did not change . by approximately what percent should the number of hours worked be decreased ?
Options: a ) 9 % , b ) 17 % , c ) 25 % , d ) 50 % , e ) 100 %
Rationale: "let ' s plug in somenicenumbers and see what ' s needed . let ' s say the employee used to make $ 1 / hour and worked 100 hours / week so , the total weekly income was $ 100 / week after the 20 % wage increase , the employee makes $ 1.20 / hour we want the employee ' s income to remain at $ 100 / week . so , we want ( $ 1.20 / hour ) ( new # of hours ) = $ 100 divide both sides by 1.20 to get : new # of hours = 100 / 1.20 ≈ 83 hours so , the number of hours decreases from 100 hours to ( approximately ) 83 hours . this represents a 17 % decrease ( approximately ) . answer : b"
Answer: b
Python program:
a = 20 / 100
b = 20 + 100 
c = b / 100
d = a / c
e = d * 100
Problem: the ratio of three numbers is 1 : 2 : 4 and the sum of their squares is 4725 . the sum of the numbers is ?
Options: a ) a ) 10
b ) b ) 12
c ) c ) 15
d ) d ) 14
e ) e ) 9
Rationale: let the numbers be x , 2 x , 4 x then , x ^ 2 + 4 x ^ 2 + 16 x ^ 2 = 4725 21 x ^ 2 = 4725 x ^ 2 = 225 x = 15 answer is c
Answer: c
Python program:
a = 4 ** 2
b = 1 ** 2
c = 2 ** 2
d = b + c 
e = a + d 
f = 4725 / e
g = math.sqrt(f)
Problem: madhav ranks seventeenth in a class of thirtyone . what is his rank from the last ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: ( rank from top ) + ( rank from bottom ) - 1 = total students 17 + x - 1 = 31 x = 15 answer : c
Answer: c
Python program:
a = 3 * 4
b = 3 * 4
c = b + 4 
d = 1 + c 
e = a + d 
f = e + 2 
g = 3 * 4
h = g + 4 
i = 1 + h 
j = f - i
k = j + 1
Problem: what positive number , when squared , is equal to the cube of the positive square root of 17 ?
Options: a ) 64
b ) 32
c ) 8
d ) 4
e ) 2
Rationale: let the positive number be x x ^ 2 = ( ( 17 ) ^ ( 1 / 2 ) ) ^ 3 = > x ^ 2 = 4 ^ 3 = 64 = > x = 8 answer c
Answer: c
Python program:
a = 1 / 2
b = 17 ** a
c = b ** 3
d = math.sqrt(c)
Problem: the cost of an article was rs . 75 . the cost was first increased by 20 % and later on it was reduced by 20 % . the present cost of the article is :
Options: a ) rs . 72 , b ) rs . 60 , c ) rs . 75 , d ) rs . 76 , e ) none
Rationale: solution : initial cost = rs . 75 after 20 % increase in the cost , it becomes , ( 75 + 20 % of 75 ) = rs . 90 now , cost is decreased by 20 % , so cost will become , ( 90 - 20 % of 90 ) = rs . 72 . so , present cost is rs . 72 . mind calculation method : 75 - - - - - 20 % ↑ - - → 90 - - - - - 20 % ↓ - - - - - → 72 . answer : option a
Answer: a
Python program:
a = 20 / 100
b = 1 + a 
c = 75 * b
d = 20 / 100
e = 1 - d
f = c * e
Problem: two trains 111 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 100 km and the other at the rate of 120 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 4.85 , b ) 7.85 , c ) 4.51 , d ) 5.85 , e ) 6.15
Rationale: "t = ( 111 + 165 ) / ( 100 + 120 ) * 18 / 5 t = 4.51 answer : c"
Answer: c
Python program:
a = 111 + 165 
b = 100 + 120 
c = b * const_0_2778
d = a / c
Problem: in how many years will a sum of money be doubled given that the annual interest on it is 10 % ?
Options: a ) 11 , b ) 14 , c ) 13 , d ) 15 , e ) 10
Rationale: p = ( p * 10 * r ) / 100 r = 10 % answer : e
Answer: e
Python program:
a = 100 / 10
Problem: rectangle a has sides a and b , and rectangle b has sides c and d . if a / c = b / d = 2 / 5 , what is the ratio of rectangle a ’ s area to rectangle b ’ s area ?
Options: a ) 2 / 5 , b ) 2 / 25 , c ) 5 / 2 , d ) 5 / 4 , e ) 4 / 25
Rationale: "the area of rectangle a is ab . c = 5 a / 2 and d = 5 b / 2 . the area of rectangle b is cd = 25 ab / 4 . the ratio of rectangle a ' s area to rectangle b ' s area is ab / ( 25 ab / 4 ) = 4 / 25 . the answer is e ."
Answer: e
Python program:
a = 2 ** 2
b = 5 ** 2
c = a / b
Problem: if a boat is rowed downstream for 600 km in 20 hours and upstream for 48 km in 4 hours , what is the speed of the boat and the river ?
Options: a ) 21 , 21 , b ) 9 , 21 , c ) 21 , 9 , d ) 9 , 9 , e ) 20 , 8
Rationale: "explanation : if x : speed of boats man in still water y : speed of the river downstream speed ( ds ) = x + y upstream speed ( us ) = x â € “ y x = ( ds + us ) / 2 y = ( ds â € “ us ) / 2 in the above problem ds = 30 ; us = 12 x = ( 30 + 12 ) / 2 = 42 / 2 = 21 km / hr y = ( 30 - 12 ) / 2 = 18 / 2 = 9 km / hr answer : c"
Answer: c
Python program:
a = 48 / 4
b = 600 / 20
c = a + b 
d = c / 2
Problem: a 1200 m long train crosses a tree in 120 sec , how much time will i take to pass a platform 700 m long ?
Options: a ) 333 sec , b ) 190 sec , c ) 176 sec , d ) 2687 sec , e ) 1876 sec
Rationale: "l = s * t s = 1200 / 120 s = 10 m / sec . total length ( d ) = 1900 m t = d / s t = 1900 / 10 t = 190 sec answer : b"
Answer: b
Python program:
a = 1200 + 700 
b = 1200 / 120
c = a / b
Problem: each of the integers from 0 to 9 , inclusive , is written on a separate slip of blank paper and the ten slips are dropped into a hat . if 4 of the slips are the drawn , without replacement , what is the probability that all 4 have a even number written on it ?
Options: a ) 1 / 12 , b ) 1 / 10 , c ) 1 / 8 , d ) 1 / 42 , e ) 5 / 9
Rationale: key is that there is no replacement , so each successive choice will become more skewed towards picking a neg ( i . e . the pool of positives decreases , while the pool of negatives stay the same ) p ( + on 1 st pick ) = 5 / 10 p ( + on 2 nd pick ) = 4 / 9 p ( + on 3 rd pick ) = 3 / 8 p ( + on 4 rd pick ) = 2 / 7 5 / 10 * 4 / 9 * 3 / 8 * 2 / 7 = 1 / 42 d
Answer: d
Python program:
a = 4 + 1 
b = 9 + 1 
c = a / b
d = 4 + 1 
e = d - 1
f = 9 + 1 
g = f - 1
h = e / g
i = c * h
j = 4 + 1 
k = j - 1
l = k - 1
m = 9 + 1 
n = m - 1
o = n - 1
p = l / o
q = i * p
r = 4 + 1 
s = r - 1
t = s - 1
u = t - 1
v = 9 + 1 
w = v - 1
x = w - 1
y = x - 1
z = u / y
A = q * z