euclaise/mathqa_programs huggingface dataset:
Problem: one side of the bottom layer of a triangular pyramid has 12 balls . how many are there in the whole pyramid ? note that the pyramid is equilateral and solid .
Options: a ) 286
b ) 364
c ) 504
d ) 164
e ) 165
Rationale: as there are 12 balls along one side , it means that there are 12 layers of balls . the top most layer has 1 ball . the second layer has 3 ( 1 + 2 ) balls . the third layer has 6 ( 1 + 2 + 3 ) balls . the fourth layer has 10 ( 1 + 2 + 3 + 4 ) balls . the fifth layer has 15 ( 1 + 2 + 3 + 4 + 5 ) balls . similarly , there are 21 , 28 , 36 , 45 , 55 , 66 and 78 balls in the remaining layers . hence , the total number of balls are = 1 + 3 + 6 + 10 + 15 + 21 + 28 + 36 + 45 + 55 + 66 + 78 = 364 balls answer : b
Answer: b
Python program:
a = 360 + const_0_33
Problem: in a company of 15 employees , 6 employees earn $ 37,000 , 5 employees earn $ 42,000 , and the 4 highest - paid employees earn the same amount . if the average annual salary for the 15 employees is $ 45,000 , what is the annual salary for each of the highest - paid employees ?
Options: a ) $ 56,250 , b ) $ 57,750 , c ) $ 59,250 , d ) $ 60,750 , e ) $ 62,250
Rationale: "6 * 37,000 + 5 * 42,000 + 4 x = 15 * 45,000 4 x = 675,000 - 222,000 - 210,000 4 x = 243,000 x = 60,750 the answer is d ."
Answer: d
Python program:
a = 4 * 4
b = 5 + 1 
c = a * b
d = c + 2 
e = 1 / 2
f = d + e 
g = f * 15
h = 15 * 4
i = 5 + 1 
j = h * i
k = g - j
l = 4 * 4
m = 5 + 1 
n = l * m
o = n * 5
p = k - o
q = p / 4
r = q * 1000
s = r / 1000
t = s - 6
Problem: what is the units digit of ( 493 ) ( 915 ) ( 381 ) ( 756 ) ( 22 )
Options: a ) 0 , b ) 1 , c ) 4 , d ) 5 , e ) 6
Rationale: "just multiply the digits in the units place for each term and you will get the answer . it should be 0 . you got a 5 as a unit digit and an even number term . so the multiplication of this will definitely yield a 0 . answer has to be 0 . i also tried it using the calculator and the answer is 1 . imo b ."
Answer: b
Python program:
a = math.factorial(493)
b = math.factorial(915)
c = a * b
d = math.factorial(493)
e = math.factorial(756)
f = d * e
g = c + f 
h = g / 493
Problem: a furniture dealer purchased a desk for $ 150 and then set the selling price equal to the purchase price plus a markup that was 25 % of the selling price . if the dealer sold the desk at the selling price , what was the amount of the dealer ' s gross profit from the purchase and the sale of the desk ?
Options: a ) 40 % , b ) 38 % , c ) 36 % , d ) 33.33 % , e ) 35 %
Rationale: "anyway , in this question , there is no discount but the mark up is given as 25 % of the selling price . so it is not 25 % of $ 150 but instead , 40 % of selling price which is obtained by adding mark up to $ 150 . so if selling price is s , 150 + 25 % of s = s s = 200 profit = 50 which is calculated on cost price in % terms . so 50 / 150 * 100 = 33.33 % is profit . d"
Answer: d
Python program:
a = 25 / 100
b = 1 - a
c = 150 / b
d = c - 150
e = d * 100
f = e / 150
Problem: two trains of length 100 m and 200 m are 100 m apart . they start moving towards each other on parallel tracks , at speeds 90 kmph and 108 kmph . in how much time will the trains cross each other ?
Options: a ) 80 / 8 , b ) 80 / 7 , c ) 80 / 5 , d ) 80 / 3 , e ) 80 / 11
Rationale: "relative speed = ( 90 + 108 ) * 5 / 18 = 11 * 5 = 55 mps . the time required = d / s = ( 100 + 100 + 200 ) / 55 = 400 / 55 = 80 / 11 sec . answer : e"
Answer: e
Python program:
a = 90 + 108 
b = a * const_0_2778
c = 100 / b
Problem: how many 4 digit odd numbers do not use any digit more than once
Options: a ) 1720 , b ) 2160 , c ) 224 , d ) 2460 , e ) none of these
Rationale: the way i solved it is a b c d ( thousand , hundreds , tens , units ) d can be 1 3 5 7 9 ( any of the 5 digits ) a can be anything except ( d or 0 ) so 8 possibilities c can be anything execpt a and b so 8 possibilities b can be anything execpt ( a d c ) so 7 possibilities total ways are 8 * 7 * 8 * 5 = 2240 ans e
Answer: e
Python program:
a = 4 + 1 
b = 10 - 1
c = b - 1
d = a * c
e = 10 - 1
f = e - 1
g = d * f
h = 10 - 1
i = h - 1
j = i - 1
k = g * j
Problem: a paint store mixes 3 / 4 pint of red paint and 2 / 3 pint of white paint to make a new paint color called perfect pink . how many pints of red paint would be needed to make 36 pints of perfect pink paint ?
Options: a ) 9 , b ) 16 , c ) 19 , d ) 25 1 / 3 , e ) 28 1 / 2
Rationale: "3 / 4 pint is required to make 3 / 4 + 2 / 3 = 17 / 12 pint of perfect pink so 17 / 12 pint requires 3 / 4 pint of red . . 1 pint will require 3 / 4 * 12 / 17 = 9 / 17 . . 36 pints will require 9 / 17 * 36 = 19 pints . . c"
Answer: c
Python program:
a = 3 * 2
b = 4 * 3
c = a / b
d = 36 * c
Problem: a certain car ' s price decreased by 2.5 % ( from the original price ) each year from 1996 to 2002 , during that time the owner of the car invested in a new carburetor and a new audio system for the car , which increased car ' s price by $ 3000 . if the price of the car in 1996 was $ 22000 , what is the car ' s price in 2002 ?
Options: a ) $ 21,700 , b ) $ 19,500 , c ) $ 20,200 , d ) $ 20,400 , e ) $ 21,100
Rationale: price in 96 = 22000 price decrease each year = 2.5 / 100 * 22000 = 550 price in 97 = 22000 - 550 price in 98 = 22000 - 2 * 550 price in 99 = 22000 - 3 * 550 price in 00 = 22000 - 4 * 550 price in 01 = 22000 - 5 * 550 price in 02 = 22000 - 6 * 550 = 18700 investment in the car = 1500 net price of the car in 02 = 18700 + 3000 = $ 21700 correct option : a
Answer: a
Python program:
a = 2002 - 1996
b = 2 * 5
c = 100 - b
d = c / 100
e = 22000 * d
f = e + 3000 
g = f / 1000
Problem: the lenght of a room is 5.5 m and width is 4 m . find the cost of paving the floor by slabs at the rate of rs . 850 per sq . metre .
Options: a ) s . 15,550 , b ) s . 15,600 , c ) s . 16,500 , d ) s . 17,600 , e ) s . 18,700
Rationale: "area of the floor = ( 5.5 ã — 4 ) m 2 = 22 m 2 . cost of paving = rs . ( 850 ã — 22 ) = rs . 18700 answer : option e"
Answer: e
Python program:
a = 5 * 5
b = 850 * a
Problem: at a conference table , 6 employees gather around a table . one of the employees is the manager and he sits at the head of the table . two of the employees sit on either side of the table . how many different seating arrangements can be made with these 6 employees ?
Options: a ) 60 , b ) 80 , c ) 100 , d ) 120 , e ) 140
Rationale: head ' s sit is fixed . now 5 people is left with 5 seats . 5 people can sit on 5 seats in 5 ! ways or 120 ways . ans is d
Answer: d
Python program:
a = 6 - 1
b = math.factorial(a)
Problem: if q and t are positive integers , qt + q + t can not be
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: let qt + t + q = x add 1 on both sides : qt + t + q + 1 = x + 1 tq + 1 ) + q + 1 = x + 1 ( q + 1 ) ( t + 1 ) = x + 1 minimum value of ( q + 1 ) = 2 minimum value of ( t + 1 ) = 2 hence x + 1 can not be prime substitute x from the given options : 6 + 1 = 7 - - > prime - - > qt + t + s can not be 6 answer : b
Answer: b
Python program:
a = 1 * 2
b = 1 + 2 
c = a + b 
d = c + 1
Problem: an urn contains 5 red , 6 blue and 8 green balls . 4 balls are randomly selected from the urn , find the probability that the drawn ball are 1 blue and 1 red and 2 green balls ?
Options: a ) 70 / 323 , b ) 50 / 323 , c ) 52 / 969 , d ) 60 / 323 , e ) 25 / 321
Rationale: "sample space = no . of ways 4 balls were drawn from urn = 19 c 4 = 3876 no . ways 1 blue and 1 red and 2 green balls were drawn from bag = 6 c 1 * 5 c 1 * 8 c 2 = 840 probability = 840 / 3876 = 70 / 323 ans - a"
Answer: a
Python program:
a = math.comb(6, 1)
b = math.comb(5, 1)
c = a * b
d = 5 + 6 
e = d + 8 
f = math.comb(e, 4)
g = c / f
Problem: a toy factory stores its toys in either a big box or a small box . the big box can store 35 toys while the small box can store 14 toys . if the factory is to store 86 newly manufactured toys , what is the least number of toys that will be left unboxed ?
Options: a ) 2 , b ) 1 , c ) 3 , d ) 5 , e ) 4
Rationale: total toys to be stored 86 the big box can store 35 small box can store 14 storing 85 toys in big box 85 / 35 = 2 r 16 store remainder in small box 16 / 14 = 1 r 2 least number of toys that will be left unboxed = 2 answer : a
Answer: a
Python program:
a = 86 / 35
b = math.floor(a)
c = b * 35
d = 86 - c
e = min(reminder)
Problem: a tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume . if 3,500 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 6.43 % , b ) 6.89 % , c ) 7.69 % , d ) 8.21 % , e ) 8.75 %
Rationale: "the amount of sodium chloride is 0.05 * 10,000 = 500 gallons 500 / 6500 = 1 / 13 which is about 7.69 % the answer is c ."
Answer: c
Python program:
a = 100 * 100
b = 5 / 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 train leaves delhi at 9 a . m . at a speed of 30 kmph . another train leaves at 2 p . m . at a speed of 35 kmph on the same day and in the same direction . how far from delhi , will the two trains meet ?
Options: a ) 1050 km , b ) 1150 km , c ) 1250 km , d ) 1550 km , e ) 850 km
Rationale: "d = 30 * 5 = 150 rs = 35 – 30 = 5 t = 150 / 5 = 30 d = 35 * 30 = 1050 km answer : a"
Answer: a
Python program:
a = 3 + 2 
b = 30 * a
c = 35 - 30
d = b / c
e = d * 35
Problem: total dinning bill for 9 people was $ 211.00 . if they add 15 % tip and divided the bill evenly , approximate . what was each persons find share
Options: a ) $ 30.14 , b ) 45.14 , c ) 34.66 , d ) 26.96 , e ) 33.16
Rationale: "211 * 15 = 3165 / 100 = 31.65 211 + 31.65 = 242.65 242.65 / 9 = 26.96 answer : d"
Answer: d
Python program:
a = 15 * 211
b = a / 100
c = 211 + 0 
d = c / 9
Problem: a sum of money at simple interest amounts to rs . 805 in 3 years and to rs . 854 in 4 years . the sum is :
Options: a ) s . 650 , b ) s . 690 , c ) s . 688 , d ) s . 700 , e ) s . 718
Rationale: "s . i . for 1 year = rs . ( 854 - 815 ) = rs . 39 . s . i . for 3 years = rs . ( 39 x 3 ) = rs . 117 . principal = rs . ( 805 - 117 ) = rs . 688 . answer : option c"
Answer: c
Python program:
a = 854 - 805
b = a * 3
c = b / 4
d = 805 - c
Problem: a shopkeeper fixes the marked price of an item 25 % above its cost price . the percentage of discount allowed to gain 8 % is
Options: a ) 11.59 % , b ) 12.59 % , c ) 13.59 % , d ) 14.59 % , e ) none of these
Rationale: "explanation : let the cost price = rs 100 then , marked price = rs 125 required gain = 8 % , so selling price = rs 108 discount = 125 - 108 = 17 discount % = ( 17 / 135 ) * 100 = 12.59 % option b"
Answer: b
Python program:
a = 8 + 100 
b = 25 + 100 
c = a / b
d = c * 100
e = 100 - d
Problem: a small company is planning to rent either computer a or computer b to print customer mailing lists . both computer a and computer b must be rented on an hourly basis . the rental fee is based only on the amount of time the computer is turned on . it will cost 40 percent more per hour to rent computer a than to rent computer b . computer b would , however , require 20 hours more than computer a to do the job . if either computer a , or computer b were rented the total cost to rent the computer would be $ 550.00 . what would be the approximate hourly charge to rent computer b ?
Options: a ) $ 7.85 , b ) $ 11.30 , c ) $ 13.20 , d ) $ 17.80 , e ) $ 22.10
Rationale: pa = price of a pb = price of b ta = time for a to complete the job tb = time for b to complete the job given pa = 1.4 pb ta + 20 = tb pa * ta = pb * tb = 550 1.4 pb * ( tb - 20 ) = pb * tb 1.4 pb tb - pb tb = 1.4 pb * 20 0.4 pbtb = 28 pb tb = 28 / 0.4 = 70 pb = 550 / 70 ~ 7.85 a
Answer: a
Python program:
a = 40 / 100
b = 4 + 3 
c = 40 / 100
d = 20 / 4
e = d / 100
f = c + e 
g = b + f 
h = a + g
Problem: a candidate got 30 % of the votes polled and he lost to his rival by 1760 votes . how many votes were cast ?
Options: a ) 4000 , b ) 4100 , c ) 4200 , d ) 4300 , e ) 4400
Rationale: "let x be the total number of votes . 0.3 x + 1760 = 0.7 x 0.4 x = 1760 x = 1760 / 0.4 = 4400 the answer is e ."
Answer: e
Python program:
a = 30 / 100
b = 1 - a
c = 30 / 100
d = b - c
e = 1760 / d
Problem: if 4 / p = 8 & 4 / q = 18 then p - q = ?
Options: a ) 5 / 18 , b ) 6 / 24 , c ) 7 / 24 , d ) 8 / 24 , e ) 9 / 24
Rationale: "p = 4 / 8 , q = 4 / 18 = > q = 2 / 9 therefore p - q = ( 1 / 2 ) - ( 2 / 9 ) = 5 / 18 answer : a"
Answer: a
Python program:
a = 4 / 8
b = 4 / 18
c = a - b
Problem: tom and john traveled in the same direction along the equal route at their constant speed rates of 15 km per hour and 10 km per hour , respectively . after 15 minutes tom passed john , tom reaches a certain gas station , how many q minutes it takes john to reach the station ?
Options: a ) 5 min , b ) 6 min , c ) 7 and 1 / 2 min , d ) 8 min , e ) 10 min
Rationale: since the question states “ after 15 minutes ” , we can say tom traveled 15 / 4 km for 15 minutes as he can travel 15 km per hour . hence , using the same logic , we can say john traveled 10 / 4 km as he travels 10 km per hour . so , john has to travel ( 15 / 4 ) - ( 10 / 4 ) km = 5 / 4 km more . since john ’ s speed is 10 km / hour , which means 1 km / 6 minutes . as he has to travel 5 / 4 km more , it is going to take him 6 ( 5 / 4 ) minutes . hence , q = 6 ( 5 / 4 ) = 15 / 2 minutes . the correct answer is c .
Answer: c
Python program:
a = 15 - 10
b = 15 / const_60
c = a * b
d = c * const_60
e = d / 10
f = e / 2
g = f - const_0_25
h = g * 10
Problem: a student completes a 3 part exam as follows . the student completes section a in 10 minutes and takes an equal time to complete the two remaining sections . what is the ratio of time spent on section c to section a if the total duration is 1 hour ?
Options: a ) 5 : 2 , b ) 4 : 1 , c ) 4 : 3 , d ) 3 : 2 , e ) 2 : 1
Rationale: the time spent on section b and section c is 25 minutes each . the ratio of c to a is 25 : 10 = 5 : 2 the answer is a .
Answer: a
Python program:
a = 1 * const_60
b = a - 10
c = b / 2
d = c / 10
Problem: a person ' s present age is two - fifth of the age of his father . after 8 years , he will be one - half of the age of his father . how old is the father at present ?
Options: a ) a ) 40 , b ) b ) 48 , c ) c ) 32 , d ) d ) 45 , e ) e ) 28
Rationale: "let the father ' s present age be x years then the person ' s present age = 2 x / 5 ( 2 x / 5 ) + 8 = 1 / 2 ( x + 8 ) 2 ( 2 x + 40 ) = 5 ( x + 8 ) x = 40 answer is a"
Answer: a
Python program:
a = 2 + 3 
b = 8 - a
c = 1 / 2
d = 2 + 3 
e = 2 / d
f = c - e
g = b / f
Problem: a certain drink of type a is prepared by mixing 4 parts milk with 3 parts fruit juice . another drink of type b is prepared by mixing 4 parts of fruit juice and 3 parts of milk . how many liters of fruit juice must be added to 21 liters of drink a to convert it to drink b ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "in 21 liters of drink a , there are 12 liters of milk and 9 liters of juice . with 12 liters of milk , we need a total of 16 liters of juice to make drink b . we need to add 7 liters of juice . the answer is e ."
Answer: e
Python program:
a = 4 + 3 
b = 4 / a
c = b * 21
d = c * 4
e = d / 3
f = 4 + 3 
g = 3 / f
h = g * 21
i = e - h
Problem: the l . c . m . of two numbers is 54 . the numbers are in the ratio 2 : 3 . then sum of the number is :
Options: a ) 28 , b ) 32 , c ) 40 , d ) 45 , e ) 54
Rationale: "let the numbers be 2 x and 3 x . then , their l . c . m . = 6 x . so , 6 x = 54 or x = 9 . the numbers are 18 and 27 . hence , required sum = ( 18 + 27 ) = 45 . answer : option d"
Answer: d
Python program:
a = 2 * 3
b = 54 / a
c = b * 3
d = 2 * 3
e = 54 / d
f = e * 2
g = c + f
Problem: simple interest on a certain sum of money for 3 years at 8 % per annum is half the compound interest on rs . 4000 for 2 years at 10 % per annum . the sum placed on simple interest is
Options: a ) rs 1650 , b ) rs 1750 , c ) rs 1850 , d ) rs 1950 , e ) none of these
Rationale: "explanation : c . i . = ( 4000 × ( 1 + 10 / 100 ) 2 − 4000 ) = 4000 ∗ 11 / 10 ∗ 11 / 10 − 4000 = 840 so s . i . = 840 / 2 = 420 so sum = s . i . ∗ 100 / r ∗ t = 420 ∗ 100 / 3 ∗ 8 = rs 1750 option b"
Answer: b
Python program:
a = 4000 * 10
b = a / 100
c = 4000 * 10
d = c / 100
e = 4000 + d 
f = e * 10
g = f / 100
h = b + g 
i = h / 2
j = i / 3
k = j * 100
l = k / 8
Problem: a car is purchased on hire - purchase . the cash price is $ 21 000 and the terms are a deposit of 10 % of the price , then the balance to be paid off over 60 equal monthly instalments . interest is charged at 12 % p . a . what is the monthly instalment ?
Options: a ) $ 503 , b ) $ 504 , c ) $ 505 , d ) $ 506 , e ) $ 507
Rationale: explanation : cash price = $ 21 000 deposit = 10 % × $ 21 000 = $ 2100 loan amount = $ 21000 − $ 2100 = $ 18900 i = p * r * t / 100 i = 11340 total amount = 18900 + 11340 = $ 30240 regular payment = total amount / number of payments answer : b
Answer: b
Python program:
a = 21 * 1000
b = 10 / 100
c = 1 - b
d = a * c
e = d / 60
f = 12 / 100
g = f / 12
h = 21 * 1000
i = 10 / 100
j = 1 - i
k = h * j
l = g * k
m = e + l
Problem: in a garden , there are 10 rows and 12 columns of mango trees . the distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden . the length of the garden is
Options: a ) 20 m , b ) 22 m , c ) 24 m , d ) 26 m , e ) 28 m
Rationale: "explanation : each row contains 12 plants . there are 11 gapes between the two corner trees ( 11 x 2 ) metres and 1 metre on each side is left . therefore length = ( 22 + 2 ) m = 24 m . answer : c"
Answer: c
Python program:
a = 12 - 1
b = a * 2
c = 10 / 2
d = b + c 
e = 10 / 2
f = d + e
Problem: the radius of a wheel is 25.4 cm . what is the distance covered by the wheel in making 500 resolutions ?
Options: a ) 724 m , b ) 798.3 m , c ) 287 m , d ) 278 m , e ) 927 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 500 resolutions . = 500 * 2 * 22 / 7 * 25.4 = 79829 cm = 798.3 m answer : b"
Answer: b
Python program:
a = 3 + 4 
b = a * 3
c = b + 1 
d = 3 + 4 
e = c / d
f = e * 25
g = f * 2
h = g * 500
i = h / 100
Problem: divide $ 2000 among b , c in the ratio 4 : 16 . how many $ that c get ?
Options: a ) $ 1200 , b ) $ 1400 , c ) $ 1600 , d ) $ 1800 , e ) $ 2000
Rationale: sum of ratio terms = 4 + 16 = 20 c = 2000 * 16 / 20 = $ 1600 answer is c
Answer: c
Python program:
a = 4 + 16 
b = 16 / a
c = 2000 * b
Problem: an agent , gets a commission of 2.5 % on the sales of cloth . if on a certain day , he gets rs . 15 as commission , the cloth sold through him on that day is worth
Options: a ) 333 , b ) 600 , c ) 887 , d ) 299 , e ) 132
Rationale: "explanation : let the total sale be rs . x . then , 2.5 % . of x = 15 < = > ( 25 / 10 * 1 / 100 * x ) = 15 < = > x = 600 . answer : b )"
Answer: b
Python program:
a = 2 / 5
b = 15 / a
Problem: what is the smallest integer that is multiple of 5 , 7,8
Options: a ) a ) 70 , b ) b ) 35 , c ) c ) 200 , d ) d ) 280 , e ) e ) 140
Rationale: "it is the lcm of 5 , 7 and 8 which is 280 . the answer is d ."
Answer: d
Python program:
a = 3 + 4
Problem: the smallest 6 digit number exactly divisible by 111 is ?
Options: a ) 100009 , b ) 100010 , c ) 100011 , d ) 100015 , e ) 100017
Rationale: the smallest 6 - digit number 100000 . 111 ) 100000 ( 900 999 - - - - - 100 - - - required number = 100000 + ( 111 - 100 ) = 100011 option c
Answer: c
Python program:
a = 1000 * 100
b = 1000 * 100
c = 111 - reminder
d = a + c
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 12 - ounce cans of the concentrate are required to prepare 272 6 - ounce servings of orange juice ?
Options: a ) 25 , b ) 34 , c ) 50 , d ) 67 , e ) 100
Rationale: "orange juice concentrate : water : : 1 : 3 total quantity of orange juice = 272 * 6 = 1632 oz so orange juice concentrate : water : : 408 oz : 1224 oz no . of 12 oz can = 408 oz / 12 oz = 34 answer b , 34 cans"
Answer: b
Python program:
a = 6 * 272
b = 272 / 10
c = a / b
Problem: the length of a rectangular field is 7 / 5 its width . if the perimeter of the field is 432 meters , what is the width of the field ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "let l be the length and w be the width . l = ( 7 / 5 ) w perimeter : 2 l + 2 w = 432 , 2 ( 7 / 5 ) w + 2 w = 432 solve the above equation to find : w = 90 m and l = 126 m . correct answer e ) 90"
Answer: e
Python program:
a = 7 / 5
b = 7 / 5
c = a + b 
d = c + 2 
e = 432 / d
Problem: a train 160 m long is running at 30 kmph . in how much time will it pass a platform 120 m long ?
Options: a ) 15.89 seconds , b ) 24.36 seconds , c ) 15.96 seconds , d ) 14.93 seconds , e ) 22.23 seconds
Rationale: distance travelled = 160 + 120 m = 280 m speed = 30 * 5 / 8 = 75 / 4 m time = 280 * 4 / 75 = 14.93 seconds answer : d .
Answer: d
Python program:
a = 160 + 120 
b = 30 * const_0_2778
c = a / b
Problem: the salaries of a and b together amount to $ 2000 . a spends 95 % of his salary and b , 85 % of his . if now , their savings are the same , what is a ' s salary ?
Options: a ) $ 1000 , b ) $ 1250 , c ) $ 2500 , d ) $ 1500 , e ) $ 1200
Rationale: "let a ' s salary is x b ' s salary = 2000 - x ( 100 - 95 ) % of x = ( 100 - 85 ) % of ( 2000 - x ) x = $ 1500 answer is d"
Answer: d
Python program:
a = 100 - 85
b = 100 - 95
c = a / b
d = c + 1 
e = 2000 / d
f = 2000 - e
Problem: what is the least value of p , so that 123 p 578 is divisible by 11
Options: a ) 7 , b ) 8 , c ) 6 , d ) 5 , e ) 4
Rationale: "explanation : 123 p 578 1 + 3 + 5 + 8 = 17 2 + p + 7 = 17 = > 9 + p = 17 = > p = 17 - 9 = > p = 8 answer : option b"
Answer: b
Python program:
a = math.lcm(123, 578)
b = a / 578
c = b / 4
d = c / 4
Problem: a train covers a distance of 12 km in 10 min . if it takes 11 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 177 m , b ) 189 m , c ) 220 m , d ) 178 m , e ) 188 m
Rationale: "speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 11 = 220 m . answer : c"
Answer: c
Python program:
a = 12 / 10
b = a - 11
c = 12 / b
Problem: a man invested rs . 14,400 in rs . 100 shares of a company at 20 % premium . if his company declares 5 % dividend at the end of the year , then how much does he get ?
Options: a ) 234 , b ) 600 , c ) 388 , d ) 278 , e ) 129
Rationale: "explanation : number of shares = = 120 . face value = rs . ( 100 x 120 ) = rs . 12000 . annual income = = rs . 600 answer : b ) rs . 600"
Answer: b
Python program:
a = 10 * 1000
b = 4 * 1000
c = a + b 
d = 4 * 100
e = c + d 
f = 20 / 100
g = 100 * f
h = 100 + g 
i = e / h
j = 100 * i
k = 5 / 100
l = j * k
Problem: a man sold 18 toys for rs . 27300 , gaining thereby the cost price of 3 toy find the cost price of a toy
Options: a ) s . 600 , b ) s . 800 , c ) s . 500 , d ) s . 900 , e ) s . 1300
Rationale: "let the cost of one toy = x . then , cost of 18 toys = 18 x . gain = 3 x . sp of 18 toys = rs . 27300 . gain = sp â € “ cp 3 x = 27300 â € “ 18 x 21 x = 27300 x = rs . 1300 . answer : option e"
Answer: e
Python program:
a = 18 + 3 
b = 27300 / a
Problem: if 5 < x < 11 and y = x + 7 , what is the greatest possible integer value of x + y ?
Options: a ) 26 , b ) 27 , c ) 28 , d ) 29 , e ) 30
Rationale: x + y = x + x + 7 = 2 x + 7 we need to maximize this value and it needs to be an integer . 2 x is an integer when the decimal of x is . 0 or . 5 the largest such value is 10.5 then x + y = 10.5 + 17.5 = 28 . the answer is c .
Answer: c
Python program:
a = 7 + 10 
b = a + 10
Problem: having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.75 at the candy store . what is john ’ s weekly allowance ?
Options: a ) $ 2.40 , b ) $ 2.80 , c ) $ 3.20 , d ) $ 3.60 , e ) $ 4.80
Rationale: total allowance = x amount spent at the arcade = 3 / 5 x amount remaining = 2 / 5 x amount spent at the toy store = 2 / 5 * 1 / 3 x = 2 / 15 x amount remaining = 2 / 5 x - 2 / 15 x = 4 / 15 x now , 4 / 15 x = $ 0.8 therefore , x = $ 2.80 . answer b
Answer: b
Python program:
a = 3 / 5
b = 1 / 3
c = 3 / 5
d = 1 - c
e = b * d
f = a + e 
g = 1 - f
h = 0 / 75