euclaise/mathqa_programs huggingface dataset:
Problem: if 15 students in a class average 70 % on an exam and 10 students average 90 % on the same exam , what is the average in percent for all 25 students ?
Options: a ) 78 % , b ) 79 % , c ) 80 % , d ) 81 % , e ) 82 %
Rationale: ( 15 * 70 + 10 * 90 ) / 25 = 78 % the answer is a .
Answer: a
Python program:
a = 15 * 70
b = 10 * 90
c = a + b 
d = c / 25
Problem: the average ( arithmetic mean ) of all scores on a certain algebra test was 90 . if the average of the 8 male students ’ grades was 87 , and the average of the female students ’ grades was 92 , how many female students took the test ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "total marks of male = m total marks of female = f number of males = 8 number of females = f given : ( m + f ) / ( 8 + f ) = 90 - - - - - - - - - - - - - 1 also given , m / 8 = 87 thus m = 696 - - - - - - - - - 2 also , f / f = 92 thus f = 92 f - - - - - - - - - 3 put 2 and 3 in 1 : we get ( 696 + 92 f ) / ( 8 + f ) = 90 solving this we get f = 12 answer : e"
Answer: e
Python program:
a = 90 * 8
b = 87 * 8
c = a - b
d = 92 - 90
e = c / d
Problem: ajith and rana walk around a circular course 115 km in circumference , starting together from the same point . if they walk at speed of 4 and 5 kmph respectively , in the same direction , when will they meet ?
Options: a ) after 20 hours , b ) after 115 hours , c ) after 115 minutes , d ) after 20 minutes , e ) after 30 minutes
Rationale: rana is the faster person . he gains 1 km in 1 hour . so rana will gain one complete round over ajith in 115 hours . i . e . they will meet after 115 hours . answer : b
Answer: b
Python program:
a = 5 - 4
b = 115 * a
Problem: two pipes a and b fill at a certain rate . b is filled at 1020 , 4080 ( 10 in 1 hour , 20 in 2 hours , 40 in 3 hrs and so on ) . if 1 / 16 of b is filled in 17 hrs , what time it will take to get completely filled ?
Options: a ) 20 hrs , b ) 21 hrs , c ) 22 hrs , d ) 23 hrs , e ) 24 hrs
Rationale: 1 / 16 in 17 hrs so 1 / 8 in 18 hrs 1 / 4 in 19 hrs 1 / 2 in 20 hrs and complete tank in 21 hrs answer : b
Answer: b
Python program:
a = math.log(16)
b = 17 + a
Problem: two numbers are respectively 20 % and 50 % more than a third number . the ratio of the two numbers is :
Options: a ) 3 : 5 , b ) 4 : 5 , c ) 5 : 5 , d ) 4 : 3 , e ) 2 : 1
Rationale: "third no is x first no - 120 % of x = 6 x / 5 second no = 150 x / 100 = 3 x / 2 ration of first nos = 6 x / 5 : 3 x / 2 = 12 x : 15 x = 4 : 5 answer b"
Answer: b
Python program:
a = 20 + 100 
b = 50 + 100 
c = a / b
d = c * 100
e = 100 - d
Problem: a car is purchased on hire - purchase . the cash price is $ 26 000 and the terms are a deposit of 10 % of the price , then the balance to be paid off over 60 equal monthly installments . interest is charged at 12 % p . a . what is the monthly installment ?
Options: a ) $ 603 , b ) $ 624 , c ) $ 625 , d ) $ 626 , e ) $ 627
Rationale: "explanation : cash price = $ 26 000 deposit = 10 % ã — $ 26 000 = $ 2600 loan amount = $ 26000 â ˆ ’ $ 2600 number of payments = 60 = $ 23400 i = p * r * t / 100 i = 14040 total amount = 23400 + 14040 = $ 37440 regular payment = total amount / number of payments = 624 answer : b"
Answer: b
Python program:
a = 26 * 1000
b = 10 / 100
c = 1 - b
d = a * c
e = d / 60
f = 12 / 100
g = f / 12
h = 26 * 1000
i = 10 / 100
j = 1 - i
k = h * j
l = g * k
m = e + l
Problem: a certain industrial loom weaves 0.129 meters of cloth every second . approximately how many seconds will it take for the loom to weave 15 meters of cloth ?
Options: a ) 114 , b ) 115 , c ) 116 , d ) 117 , e ) 118
Rationale: "let the required number of seconds be x more cloth , more time , ( direct proportion ) hence we can write as ( cloth ) 0.129 : 15 : : 1 : x = > 0.129 * x = 15 = > x = 15 / 0.129 = > x = 116 answer : c"
Answer: c
Python program:
a = 15 / 0
Problem: a gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same . if there are 6 rows or 4 rows or 8 rows , then no tree will be left . find the least number of trees required
Options: a ) 24 , b ) 60 , c ) 28 , d ) 76 , e ) 21
Rationale: "explanation : the least number of trees that are required = lcm ( 6 , 4,8 ) = 24 answer : a"
Answer: a
Python program:
a = 8 * 4
b = a * 6
c = b / 2
Problem: a number is selected at random from the first 30 natural numbers . what is the probability that the number is a multiple of either 2 or 19 ?
Options: a ) 17 / 30 , b ) 2 / 5 , c ) 7 / 15 , d ) 8 / 15 , e ) 11 / 30
Rationale: "number of multiples of 2 from 1 through 30 = 30 / 2 = 15 number of multiples of 19 from 1 through 30 = 30 / 19 = 1 number of multiples of 2 and 19 both from 1 through 30 = number of multiples of 19 * 2 ( = 38 ) = 0 total favourable cases = 15 + 1 - 0 = 16 probability = 16 / 30 = 8 / 15 answer : option d"
Answer: d
Python program:
a = 30 / 2
b = math.floor(a)
c = 30 / 19
d = b + c 
e = d / 30
Problem: the cash difference between the selling prices of an article at a profit of 6 % and 8 % is rs 3 . the ratio of two selling prices is
Options: a ) 51 : 52 , b ) 52 : 53 , c ) 53 : 54 , d ) 54 : 55 , e ) none of these
Rationale: "explanation : let the cost price of article is rs . x required ratio = ( 106 % of x ) / ( 108 % of x ) = 106 / 108 = 53 / 54 = 53 : 54 . answer : c"
Answer: c
Python program:
a = 100 + 6 
b = 100 + 8 
c = a / b
Problem: working simultaneously and independently at an identical constant rate , 30 machines of a certain type can produce a total of x units of product p in 3 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 5 x units of product p in 10 days ?
Options: a ) 41 , b ) 44 , c ) 45 , d ) 47 , e ) 50
Rationale: "the rate of 30 machines is rate = job / time = x / 3 units per day - - > the rate of 1 machine 1 / 30 * ( x / 3 ) = x / 90 units per day ; now , again as { time } * { combined rate } = { job done } then 10 * ( m * x / 90 ) = 5 x - - > m = 45 . answer : c ."
Answer: c
Python program:
a = 30 * 5
b = 3 / 10
c = a * b
Problem: 30 men shake hands with each other . maximum no of handshakes without cyclic handshakes .
Options: a ) 190 , b ) 200 , c ) 210 , d ) 220 , e ) 435
Rationale: "or , if there are n persons then no . of shakehands = nc 2 = 30 c 2 = 435 answer : e"
Answer: e
Python program:
a = 30 - 1
b = 30 / 2
c = a * b
Problem: a car traveled 448 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city . if the car traveled 6 fewer miles per gallon in the city than on the highway , how many miles per gallon did the car travel in the city ?
Options: a ) 14 , b ) 18 , c ) 21 , d ) 22 , e ) 27
Rationale: "let the speed in highway be h mpg and in city be c mpg . h = c + 6 h miles are covered in 1 gallon 462 miles will be covered in 462 / h . similarly c miles are covered in 1 gallon 336 miles will be covered in 336 / c . both should be same ( as car ' s fuel capacity does not change with speed ) = > 336 / c = 448 / h = > 336 / c = 448 / ( c + 6 ) = > 336 c + 336 * 6 = 448 c = > c = 336 * 6 / 112 = 18 answer b ."
Answer: b
Python program:
a = 448 - 336
b = a / 6
c = 336 / b
Problem: at what rate percent on simple interest will rs . 750 amount to rs . 950 in 5 years ?
Options: a ) 3.33 % , b ) 5.93 % , c ) 4.33 % , d ) 5.33 % , e ) 6.33 %
Rationale: "200 = ( 750 * 5 * r ) / 100 r = 5.33 % answer : d"
Answer: d
Python program:
a = 950 - 750
b = a / 750
c = b / 5
d = c * 100
Problem: from the sale of sleeping bags , a retailer made a gross profit of 15 % of the wholesale cost . if each sleeping bag was sold for $ 28 , what was the wholesale cost per bag ?
Options: a ) 3.0 , b ) 3.36 , c ) 24.34 , d ) 25.0 , e ) 31.36
Rationale: "cost price * 1.15 = selling price - - > cost price * 1.15 = $ 28 - - > cost price = $ 24.34 . answer : c ."
Answer: c
Python program:
a = 28 * 100
b = 100 + 15 
c = a / b
Problem: find 40 % of 240
Options: a ) 96 , b ) 94 , c ) 86 , d ) 74 , e ) 110
Rationale: "we know that r % of m is equal to r / 100 × m . so , we have 40 % of 240 40 / 100 × 240 = 96 answer : a"
Answer: a
Python program:
a = 40 / 240
Problem: sara bought both german chocolate and swiss chocolate for some cakes she was baking . the swiss chocolate cost $ 3.5 per pound , and german chocolate cost $ 2.5 per pound . if the total the she spent on chocolate was $ 70 and both types of chocolate were purchased in whole number of pounds , how many total pounds of chocolate she purchased ?
Options: a ) 7 , b ) 8 , c ) 10 , d ) 24 , e ) 15
Rationale: if there were all the expensive ones , 3.5 . . . . there would be 70 / 3.5 or 20 of them but since 2.5 $ ones are also there , answer has to be > 20 . . . . if all were 2.5 $ ones , there will be 70 / 2.5 or 28 . . so only 24 is left ans d . .
Answer: d
Python program:
a = 3 + 5 
b = a / 2
c = 70 / b
Problem: two men start from opposite banks of a river . they meet 340 meters away from one of the banks on forward journey . after that they meet at 170 meters from the other bank of the river on their backward journey . what will be the width of the river ( in meters ) ?
Options: a ) 750 , b ) 850 , c ) 900 , d ) 980 , e ) 950
Rationale: let p , q are two persons then their speeds be a , b - > m / hr x - - - - 340 - - - - - - - - - - - - - - - - - - - - - - | - - - ( d - 340 ) - - - - - - - - - y in forward journey time taken by p = 340 / a ; time taken by q = d - 340 / b ; in forward journey , time taken by p = time taken by q so 340 / a = d - 340 / b a / b = 340 / d - 340 - - - - - - - - - - - - ( 1 ) after that they continue their journeyand reach other banks now in backward journey , x - - - - - - - - - - - - - - - ( d - 170 ) - - - - - - - - - - - - - - - - - - - - - - - - - - | - - - - - 170 - - - - - - y distance travelled by p from meet 1 to meet 2 = ( d - 340 ) + 170 distance travelled by p from meet 1 to meet 2 = 340 + ( d - 170 ) now time taken by p = time taken by q ( d - 340 ) + 170 / a = 340 + ( d - 170 ) / b ( d - 340 ) + 170 / 340 + ( d - 170 ) = a / b - - - - - - - - - ( 2 ) from 1 & 2 340 / ( d - 340 ) = ( d - 340 ) + 170 / 340 + ( d - 170 ) 340 / ( d - 340 ) = d - 170 / d + 170 340 d + 57800 = d ^ 2 - 340 d - 170 d + 57800 340 d = d ^ 2 - 510 d d ^ 2 - 850 d = 0 d ( d - 850 ) = 0 d = 0 ord = 850 so width of the river is 850 answer : b
Answer: b
Python program:
a = 340 + 170 
b = a + 170 
c = b + 170
Problem: if the number is decreased by 5 and divided by 7 the result is 7 . what would be the result if 34 is subtracted and divided by 10 ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 2 , e ) 3
Rationale: "explanation : let the number be x . then , ( x - 5 ) / 7 = 7 = > x - 5 = 49 x = 54 . : ( x - 34 ) / 10 = ( 54 - 34 ) / 10 = 2 answer : option d"
Answer: d
Python program:
a = 7 * 7
b = a + 5 
c = b - 34
d = c / 10
Problem: a 160 meter long train crosses a man standing on the platform in 9 sec . what is the speed of the train ?
Options: a ) 96 kmph , b ) 64 kmph , c ) 52 kmph , d ) 86 kmph , e ) 76 kmph
Rationale: "s = 160 / 9 * 18 / 5 = 64 kmph answer : b"
Answer: b
Python program:
a = 160 / 9
b = a * const_3_6
Problem: the difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4 % per annum is re . 1 . the sum ( in rs . ) is ?
Options: a ) 625 , b ) 827 , c ) 657 , d ) 726 , e ) 634
Rationale: "let the sum be rs . x . then , [ x ( 1 + 4 / 100 ) 2 - x ] = ( 676 / 625 x - x ) = 51 / 625 x s . i . = ( x * 4 * 2 ) / 100 = 2 x / 25 51 x / 625 - 2 x / 25 = 1 or x = 625 . answer : a"
Answer: a
Python program:
a = 4 / 100
b = a ** 2
c = b * 1
d = 1/(c)
Problem: how many pieces of 0.85 metres can be cut from a rod 42.5 metres long ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: "number of pieces = 42.5 / 0.85 = 42.50 / 0.85 = 4250 / 85 = 50 . answer : c"
Answer: c
Python program:
a = 42 / 5
Problem: 60 % of a number is added to 160 , the result is the same number . find the number ?
Options: a ) 300 , b ) 400 , c ) 266 , d ) 99 , e ) 121
Rationale: ": ( 60 / 100 ) * x + 160 = x 2 x = 800 x = 400 answer : b"
Answer: b
Python program:
a = 160 / 100
b = 160 / a
Problem: difference of 2 numbers is 1660 . if 7.5 % of one number is 12.5 % of the other number , find the 2 numbers ?
Options: a ) 125,150 , b ) 5124,4515 , c ) 4150,2490 , d ) 3250,4510 , e ) 1254,3210
Rationale: "let the numbers be x and y 7.5 % of x = 12.5 % of y x = 125 y / 75 = 5 y / 3 x - y = 1660 5 y / 3 - y = 1660 y = 2490 x = 5 y / 3 = 4150 answer is c"
Answer: c
Python program:
a = 1660 / 7
b = 1660 / 7
c = 1 - b
d = 2 / c
e = a * d
Problem: an optometrist charges $ 150 per pair for soft contact lenses and $ 85 per pair for hard contact lenses . last week she sold 5 more pairs of soft lenses than hard lenses . if her total sales for pairs of contact lenses last week were $ 2,395 , what was the total number of pairs of contact lenses that she sold ?
Options: a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 19
Rationale: "( x + 5 ) * 150 + x * 85 = 2395 = > x = 7 total lens = 7 + ( 7 + 5 ) = 19 answer e"
Answer: e
Python program:
a = 4 * 100
b = 5 * 10
c = a + b 
d = c + 5 
e = d + 1000 
f = 150 * 5
g = e - f
h = 150 + 85 
i = g / h
j = i * 2
k = j + 5
Problem: cole drove from home to work at an average speed of 75 kmh . he then returned home at an average speed of 105 kmh . if the round trip took a total of 1 hours , how many minutes did it take cole to drive to work ?
Options: a ) 35 , b ) 50 , c ) 62 , d ) 75 , e ) 78
Rationale: "first round distance travelled ( say ) = d speed = 75 k / h time taken , t 2 = d / 75 hr second round distance traveled = d ( same distance ) speed = 105 k / h time taken , t 2 = d / 105 hr total time taken = 1 hrs therefore , 1 = d / 75 + d / 105 lcm of 75 and 105 = 525 1 = d / 75 + d / 105 = > 1 = 7 d / 525 + 5 d / 525 = > d = 525 / 12 km therefore , t 1 = d / 75 = > t 1 = 525 / ( 12 x 75 ) = > t 1 = ( 7 x 60 ) / 12 - - in minutes = > t 1 = 35 minutes . a"
Answer: a
Python program:
a = 105 * 1
b = 75 + 105 
c = a / b
d = c * const_60
Problem: sum of the squares of 3 no . ' s is 179 and the sum of their products taken two at a time is 131 . find the sum ?
Options: a ) 20 , b ) 21 , c ) 26 , d ) 28 , e ) 30
Rationale: "( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 179 + 2 * 131 a + b + c = √ 441 = 21 b"
Answer: b
Python program:
a = 131 * 2
b = a + 179 
c = math.sqrt(b)
Problem: if 20 % of 30 is greater than 25 % of a number by 2 , the number is :
Options: a ) 16 , b ) 24 , c ) 20 , d ) 32 , e ) none of these
Rationale: explanation : = > 20 / 100 * 30 - 25 / 100 * x = 2 = > x / 4 = 4 so x = 16 answer : a
Answer: a
Python program:
a = 20 / 100
b = a * 30
c = b - 2
d = 25 / 100
e = c / d
Problem: how many positive integers less than 5000 are evenly divisible by neither 15 nor 23 ?
Options: a ) 4,514 , b ) 4,475 , c ) 4,521 , d ) 4,428 , e ) 4,349
Rationale: integers less than 5000 divisible by 15 5000 / 15 = 333 . something , so 333 integers less than 5000 divisible by 23 5000 / 23 = 238 . # # , so 238 we have double counted some , so take lcm of 15 and 23 = 105 and divide by 5000 , we get 47 . so all numbers divisible by 15 and 23 = 333 + 238 - 47 = 524 now subtract that from 4999 . 4999 - 524 = 4521 answer c .
Answer: c
Python program:
a = 5000 - 1
b = 5000 / 15
c = math.floor(b)
d = 5000 / 23
e = math.floor(d)
f = c + e 
g = math.lcm(15, 23)
h = 5000 / g
i = math.floor(h)
j = f - i
k = a - j
l = k / 1000
m = math.floor(l)
Problem: p alone can complete a job in 12 days . the work done by q alone in one day is equal to one - half of the work done by p alone in one day . in how many days can the work be completed if p and q work together ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "p ' s rate is 1 / 12 q ' s rate is 1 / 24 the combined rate is 1 / 12 + 1 / 24 = 1 / 8 if they work together , the job will take 8 days . the answer is d ."
Answer: d
Python program:
a = 1 / 12
b = 1 / 12
c = b / 3
d = a + c 
e = 1 / d
Problem: suzie ’ s discount footwear sells all pairs of shoes for one price and all pairs of boots for another price . on monday the store sold 22 pairs of shoes and 16 pairs of boots for $ 460 . on tuesday the store sold 8 pairs of shoes and 32 pairs of boots for $ 560 . how much more do pairs of boots cost than pairs of shoes at suzie ’ s discount footwear ?
Options: a ) 15 , b ) 18 , c ) 21 , d ) 23 , e ) 25
Rationale: let x be pair of shoes and y be pair of boots . 22 x + 16 y = 460 . . . eq 1 8 x + 32 y = 560 . . . . eq 2 . now multiply eq 1 by 2 and sub eq 2 . 44 x = 920 8 x = 560 . 36 x = 360 = > x = 10 . sub x in eq 2 . . . . we get 80 + 32 y = 560 . . . then we get 32 y = 480 then y = 25 differenece between x and y is 15 answer : a
Answer: a
Python program:
a = 460 * 2
b = a - 560
c = 22 * 2
d = c - 8
e = b / d
f = 22 * e
g = 460 - f
h = g / 16
Problem: if ( a + b ) = 4 , ( b + c ) = 9 and ( c + d ) = 3 , what is the value of ( a + d ) ?
Options: a ) 16 . , b ) 8 . , c ) 7 , d ) 2 . , e ) - 2
Rationale: "given a + b = 4 = > a = 4 - b - - > eq 1 b + c = 9 c + d = 3 = > d = 3 - c - - > eq 2 then eqs 1 + 2 = > a + d = 4 - b + 3 - c = > 7 - ( b + c ) = > 7 - 9 = - 2 . option e . . ."
Answer: e
Python program:
a = 4 + 3 
b = a - 9
Problem: the difference between a 8 digit number and the number formed by reversing its digit is not a multiple of
Options: a ) 3 , b ) 5 , c ) 296297 , d ) 888891 , e ) 2666673
Rationale: "another approach is to test a number . let ' s say the original number is 12000002 so , the reversed number is 20000021 the difference = 20000021 - 12000002 = 8000019 no check the answer choices 8000019 is a multiple of 3,296297 , 888891,2666673 5 is not a multiple of 8000019 answer ; b"
Answer: b
Python program:
a = 8 + 4 
b = a ** 4
Problem: a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 27 , then how old is b ?
Options: a ) 11 years , b ) 10 years , c ) 18 years , d ) 189 years , e ) 28 years
Rationale: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 27 5 x = 25 = > x = 5 hence , b ' s age = 2 x = 10 years . answer : b"
Answer: b
Python program:
a = 27 - 2
b = a * 2
c = 4 + 1 
d = b / c
Problem: 15 51 216 1100 ? 46452
Options: a ) 6630 , b ) 6650 , c ) 6560 , d ) 6530 , e ) none of these
Rationale: "the format of the series 15 * 3 + 6 = 51 51 * 4 + 12 = 216 216 * 5 + 20 = 1100 1100 * 6 + 30 = 6630 6630 * 7 + 42 = 46452 answer : a"
Answer: a
Python program:
a = 51 / 216
b = 15 + a 
c = b * 1100
d = c / 100
Problem: if a * b denotes the greatest common divisor of a and b , then ( ( 12 * 15 ) * ( 18 * 24 ) ) = ?
Options: a ) 24 , b ) 12 , c ) 6 , d ) 4 , e ) 3
Rationale: "the greatest common divisor of 12 and 15 is 3 . hence 12 * 15 = 3 ( note that * here denotes the function not multiplication ) . the greatest common divisor of 18 and 24 is 6 . hence 18 * 24 = 6 . hence ( ( 12 * 16 ) * ( 18 * 24 ) ) = 3 * 6 . the greatest common divisor of 3 and 6 is 3 . answer ; e ."
Answer: e
Python program:
a = 18 / 3
b = a / 3
Problem: what annual installment will discharge a debt of rs . 1260 due in 3 years at 12 % simple interest ?
Options: a ) 315 , b ) 345 , c ) 325 , d ) 375 , e ) none of them
Rationale: "let each installment be rs . x then , ( x + ( ( x * 12 * 1 ) / 100 ) ) + ( x + ( ( x * 12 * 2 ) / 100 ) ) + x = 1260 = ( ( 28 x / 25 ) + ( 31 x / 25 ) + x ) = 1260 ï ƒ › ( 28 x + 31 x + 25 x ) = ( 1260 * 25 ) x = ( 1260 * 25 ) / 84 = rs . 375 . therefore , each installment = rs . 375 . answer is d ."
Answer: d
Python program:
a = 12 / 1260
b = 100 * 0
c = b * 3
Problem: what is the sum of all even numbers from 1 to 801 ?
Options: a ) 160400 , b ) 281228 , c ) 281199 , d ) 122850 , e ) 128111
Rationale: "explanation : 800 / 2 = 400 400 * 401 = 160400 answer : a"
Answer: a
Python program:
a = 1 * 801
b = a / 4
Problem: there are 225 female managers in a certain company . find the total number of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .
Options: a ) 300 , b ) 400 , c ) 562.5 , d ) 600 , e ) none of these
Rationale: as per question stem 2 / 5 m ( portion of men employees who are managers ) + 225 ( portion of female employees who are managers ) = 2 / 5 t ( portion of total number of employees who are managers ) , thus we get that 2 / 5 m + 225 = 2 / 5 t , or 2 / 5 ( t - m ) = 225 , from here we get that t - m = 562.5 , that would be total number of female employees and the answer ( c )
Answer: c
Python program:
a = 2 / 5
b = 225 / a
Problem: if a randomly selected non - negative single digit integer is added to { 2 , 3 , 4 , 8 } . what is the probability that the median of the set will increase but the range still remains the same ?
Options: a ) 0.2 , b ) 0.3 , c ) 0.4 , d ) 0.5 , e ) 0.6
Rationale: "we are selecting from non - negative single digit integers , so from { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } . these 10 digits represent the total number of outcomes . hence , the total number of outcomes is 10 . we need to find the probability that the median of the set will increase but the range still remains the same . the median of the set is ( 3 + 4 ) / 2 = 3.5 , thus the number selected must be 4 or greater . for the range to remain the same , the number must be between 2 and 8 inclusive . to satisfy both conditions , the number selected must be 4 , 5 , 6 , 7 , or 8 . the probability is 5 / 10 = 0.5 the answer is d ."
Answer: d
Python program:
a = 4 / 10
Problem: a school has received 60 % of the amount it needs for a new building by receiving a donation of $ 300 each from people already solicited . people already solicited represent 40 % of the people from whom the school will solicit donations . how much average contribution is requited from the remaining targeted people to complete the fund raising exercise ?
Options: a ) $ 200 , b ) $ 177.78 , c ) $ 100 , d ) $ 277.78 , e ) $ 377.78
Rationale: "let the amount school needs = x let total people school plans to solicit = t school has received 60 % of x = > ( 3 / 5 ) x people already solicited = 40 % of t = > ( 2 / 5 ) t now , as per the information given in the question : ( 3 / 5 ) x = $ 400 . ( 2 / 5 ) . t - - - - - - - - - - - - - - - - - - - - - - - - - - - 1 remaning amount is 40 % i . e ( 2 / 5 ) x - - - - - - because school has already received 60 % and the remaining people are 60 % i . e ( 3 / 5 ) . t - - - - - because 40 % of the people are already solicited so , average contribution required from the remaining targeted people is ( 2 / 5 ) x = ( amount required ) . ( 3 / 5 ) . t - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2 divide eqn 1 by eqn 2 amount required = $ 177.78 b"
Answer: b
Python program:
a = 40 / 100
b = a * 300
c = 60 / 100
d = b / c
e = 40 / 100
f = d * e
g = 60 / 100
h = f / g
Problem: how many prime numbers are between 15 / 7 and 131 / 6 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "15 / 7 = 3 - 131 / 6 = 22 - prime numbers between 3 and 22 are 5 , 7 , 11 , 13 , 17 , and 19 - sign signifies that the number is marginally less . answer d"
Answer: d
Python program:
a = math.floor(2)
Problem: a can do a job in 18 days and b can do it in 30 days . a and b working together will finish twice the amount of work in days ?
Options: a ) 29 ½ days , b ) 22 ½ days , c ) 92 ½ days , d ) 28 ½ days , e ) 92 ½ days
Rationale: "1 / 18 + 1 / 30 = 8 / 90 = 4 / 45 45 / 4 = 11 ¼ * 2 = 22 ½ days answer : b"
Answer: b
Python program:
a = 1 / 18
b = 1 / 30
c = a + b
Problem: the cost of manufacturing a popular model car is made up of 3 items : cost of raw material , labour and overheads - in a year the cost of 3 items were in the ration of 4 : 3 : 2 . next year the cost of the raw material rose by 10 % , labour cost increased by 8 % but overhead reduced by 5 % . then % increase int the price of the car ?
Options: a ) 7.67 % , b ) 6 % , c ) 0.54 % , d ) 9.54 % , e ) 8.54 %
Rationale: before increase total cost = 4 + 3 + 2 = 9 , after increasing the cost = 9.54 so increase of . 54 over 9 , equal to 6 % answer : b
Answer: b
Python program:
a = 4 + 3 
b = a + 2 
c = 4 / b
d = 100 + 10 
e = c * d
f = 4 + 3 
g = f + 2 
h = 3 / g
i = 100 + 8 
j = h * i
k = e + j 
l = 4 + 3 
m = l + 2 
n = 2 / m
o = 100 - 5
p = n * o
q = k + p 
r = q - 100