euclaise/mathqa_programs huggingface dataset:
Problem: a bookstore has a shelf that contains biographies which normally sell for $ 20 each and mysteries that normally sell for $ 12 each . during a sale , the biographies and mysteries are discounted at different rates so that a customer saves a total of $ 19 from the normal price by buying 5 discounted biographies and 3 discounted mysteries . if the sum of the discount rates for the two types of books is 43 percent , what is the discount rate on mysteries ?
Options: a ) 24 % , b ) 25 % , c ) 30 % , d ) 37.5 % , e ) 40 %
Rationale: let b be the discount on biographies and m be the discount on mysteries so . , b + m = 0.435 - - - - - ( 1 ) and ( 20 * 5 + 12 * 3 ) - ( 20 * 5 * ( 1 - b ) + 12 * 3 * ( 1 - m ) ) = 19 - - > 100 ( 1 - ( 1 - b ) ) + 36 ( 1 - ( 1 - m ) = 19 100 b + 36 m = 19 - - - - - - ( 2 ) solving 12 . , we get m = 0.375 = 37.5 % d
Answer: d
Python program:
a = 20 * 2
b = 20 + 43 
c = b + 1 
d = a / c
e = 1 - d
f = e * 100
Problem: calculate the average of all the numbers between 15 and 55 which are divisible by 4 .
Options: a ) 39 , b ) 33 , c ) 34 , d ) 30 , e ) 36
Rationale: explanation : numbers divisible by 4 are 16,20 , 24,28 , 32,36 , 40,44 , 48,52 , , , average = ( 16 + 20 + 24 + 28 + 32 + 36 + 40 + 44 + 48 + 52 ) / 10 = 340 / 10 = 34 answer : c
Answer: c
Python program:
a = 15 / 4
b = math.floor(a)
c = b + 1 
d = 55 / 4
e = math.floor(d)
f = c + e 
g = f / 2
h = g * 4
Problem: what is the remainder when 9 ^ 1 + 9 ^ 2 + 9 ^ 3 + . . . + 9 ^ 9 is divided by 9 ?
Options: a ) 2 , b ) 3 , c ) 0 , d ) 5 , e ) none of the above
Rationale: "notice that in the brackets we have the sum of 9 odd multiples of 9 , which yields remainder of 0 upon division by 9 . answer : c"
Answer: c
Python program:
a = 9 ** 1
b = 9 ** 1
c = a - b
d = c / 9
Problem: by selling an article at rs . 800 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 25 % ?
Options: a ) rs . 488 , b ) rs . 480 , c ) rs . 482 , d ) rs . 487 , e ) rs . 481
Rationale: "sp = 800 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 800 * [ 100 / 125 ] = 640 loss = 25 % = 25 % of 640 = rs . 160 sp = cp - loss = 640 - 160 = rs . 480 answer : b"
Answer: b
Python program:
a = 800 * 100
b = 25 + 100 
c = a / b
d = 800 * 100
e = 25 + 100 
f = d / e
g = f * 25
h = g / 100
i = c - h
Problem: if ( a + b ) = 16 , ( b + c ) = 9 and ( c + d ) = 3 , what is the value of ( a + d ) ?
Options: a ) 10 . , b ) 8 . , c ) 7 . , d ) 2 . , e ) - 2 .
Rationale: "given a + b = 16 = > a = 16 - b - - > eq 1 b + c = 9 c + d = 3 = > d = 3 - c - - > eq 2 then eqs 1 + 2 = > a + d = 16 - b + 3 - c = > 19 - ( b + c ) = > 19 - 9 = 10 . option a . . ."
Answer: a
Python program:
a = 16 + 3 
b = a - 9
Problem: rs . 880 is divided amongst a , b , c so that 4 times a ' s share , 5 times b ' s share and 10 times c ' s share are all equal . find c ' s share ?
Options: a ) 177 , b ) 150 , c ) 817 , d ) 160 , e ) 616
Rationale: a + b + c = 880 4 a = 5 b = 10 c = x a : b : c = 1 / 4 : 1 / 5 : 1 / 10 = 5 : 4 : 2 2 / 11 * 880 = rs . 160 answer : d
Answer: d
Python program:
a = 10 / 4
b = 10 / 5
c = a + b 
d = c + 1 
e = 880 / d
Problem: divide $ 900 among a , b in the ratio 1 : 2 . how many $ that a get ?
Options: a ) $ 50 , b ) $ 300 , c ) $ 150 , d ) $ 250 , e ) $ 600
Rationale: "sum of ratio terms = 1 + 2 = 3 a = 900 * 1 / 3 = $ 300 answer is b"
Answer: b
Python program:
a = 900 / 1
Problem: a car is running at a speed of 96 kmph . what distance will it cover in 14 sec ?
Options: a ) 378 m , b ) 350 m , c ) 380 m , d ) 200 m , e ) 250 m
Rationale: "speed = 96 kmph = 96 * 5 / 18 = 27 m / s distance covered in 14 sec = 27 * 14 = 378 m answer is a"
Answer: a
Python program:
a = 96 / const_3_6
b = a * 14
Problem: in a certain aquarium , the number of red fish is 3 times the number of the green fish , and the number of blue fish is half the number of the red fish . if the ratio of green fish to red fish were to be doubled , and the ratio of red fish to blue fish were to be doubled , then the ratio of blue fish to green fish in that aquarium would be
Options: a ) 3 : 2 , b ) 1 : 1 , c ) 1 : 2 , d ) 3 : 4 , e ) 3 : 8
Rationale: lots of little places to make a mistake or panic here . = ) r = 3 g b = r / 2 g / r = 1 / 3 - - - - > doubled g / r = 2 / 3 r / b = 2 - - - - > doubled r / b = 4 b / g = ( b / r ) * ( r / g ) = ( 1 / 4 ) * ( 3 / 2 ) = 3 / 8 answer : e
Answer: e
Python program:
a = 2 * 2
b = 1/(a)
c = 1 / 3
d = 2 * c
e = 1/(d)
f = b * e
Problem: in what proportion must flour at $ 0.8 per pound be mixed with flour at $ 0.9 per pound so that the mixture costs $ 0.845 per pound ?
Options: a ) 1 : 3 , b ) 1 : 2 , c ) 1 : 1 , d ) 2 : 1 , e ) 5 : 4
Rationale: "using weighted average method : let x be the proportion in which the $ 0.8 per pound flour is mixed with $ 0.9 per pound flour . thus 0.8 * x + 0.9 * ( 1 - x ) = 0.845 0.9 – 0.1 x = 0.845 x = 0.55 thus ratio of both flours is 5 : 4 e"
Answer: e
Python program:
a = 0 + 8 
b = 0 / 845
Problem: a car drives 90 miles on local roads at 30 mph , and 75 miles on the highway at 60 mph , what is the average speed of the entire trip ?
Options: a ) 36 mph , b ) 40 mph , c ) 39 mph , d ) 42 mph , e ) 38 mph
Rationale: so the answer is plainly c . . . . we have a general relation for speed , time and distance : v ( velocity ) * t ( time ) = d ( distance ) for first part we have d = 90 miles , and v = 30 mph so we can obtain time : 30 * t = 90 or t = 90 / 30 = 3 hours the needed time to cover 90 miles in the same way we should divide 75 to 60 to find the needed time to cover 75 miles , so t = 1.25 hours so the total time for covering total distance would be 3 + 1.25 = 4.25 hours and total distance is 90 + 75 = 165 miles final stage : average speed is total distance divide to total time : 165 / 4.25 = 38.8 miles per hour rounded up to 39 mph . . . .
Answer: c
Python program:
a = 90 + 75 
b = 90 / 30
c = 75 / 60
d = b + c 
e = a / d
Problem: in a mixture of 45 litres the ratio of milk to water is 4 : 1 . additional 18 litres of water is added to the mixture . find the ratio of milk to water in the resulting mixture .
Options: a ) 2 / 1 , b ) 4 / 3 , c ) 2 / 3 , d ) 3 / 4 , e ) 3 / 2
Rationale: given that milk / water = 4 x / x and 4 x + x = 45 - - > x = 9 . thus milk = 4 x = 36 liters and water = x = 9 liters . new ratio = 36 / ( 9 + 18 ) = 36 / 27 = 4 / 3 . answer : b .
Answer: b
Python program:
a = 4 + 1 
b = 45 / a
c = 45 - b
d = 4 + 1 
e = 45 / d
f = e + 18 
g = c / f
Problem: a man sold 20 articles for $ 60 and gained 20 % . how many articles should he sell for $ 90 to incur a loss 20 % ?
Options: a ) 45 , b ) 36 , c ) 40 , d ) 50 , e ) 48
Rationale: "production cost per article : $ 60 * ( 100 % - 20 % ) / 20 = $ 2.40 required production costs for a loss of 20 % : $ 90 * ( 100 % + 20 % ) = $ 108 number of articles to be sold for $ 108 to incur a 20 % loss : $ 108 / $ 2.40 = 45 thus , solution a is correct ."
Answer: a
Python program:
a = original_price_before_loss / (
Problem: if x > 3000 , then the value of ( 3 x ) / ( 2 x ^ 1.21 - 1111 ^ 1.3 ) is closest to ?
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 10 / 21 , d ) 4 / 10 , e ) 3 / 2
Rationale: "assume x = 3002 ( 3 x ) / ( 2 x ^ 1.21 - 1111 ^ 1.3 ) = 9006 / ( 2 * ( 3002 ) ^ 1.21 - 1111 ^ 1.3 ) = 9006 / 23154 = = 4 / 10 d"
Answer: d
Python program:
a = 2 - 2
b = a * 2
Problem: john left home and drove at the rate of 55 mph for 2 hours . he stopped for lunch then drove for another 3 hours at the rate of 55 mph to reach his destination . how many miles did john drive ?
Options: a ) 235 miles . , b ) 245 miles . , c ) 255 miles . , d ) 265 miles . , e ) 275 miles .
Rationale: "the total distance d traveled by john is given by d = 55 * 2 + 3 * 55 = 275 miles . answer e"
Answer: e
Python program:
a = 55 * 2
b = 3 * 55
c = a + b
Problem: six bells commence tolling together and toll at intervals of 2 , 4,6 , 8,10 and 12 seconds respectively . in 30 m 9 nutes , how many times do they toll together ?
Options: a ) 4 , b ) 10 , c ) 15 , d ) 16 , e ) 17
Rationale: "solution l . c . m . of 2,4 , 6,8 , 10,12 is 120 . so , the bells will toll together after every 120 seconds , i . e . , 2 minutes in 30 minutes , they will toll together left [ ( 30 / 2 ) + 1 ] = 16 times . answer d"
Answer: d
Python program:
a = 2 + 3 
b = a * 2
c = b * 3
d = 2 * c
e = d * 2
f = e / 30
g = 30 / f
Problem: a man cycling along the road noticed that every 6 minutes a bus overtakes him and every 2 minutes he meets an oncoming bus . if all buses and the cyclist move at a constant speed , what is the time interval between consecutive buses ?
Options: a ) 3 minutes , b ) 6 minutes , c ) 8 minutes , d ) 9 minutes , e ) 10 minutes
Rationale: "let ' s say the distance between the buses is d . we want to determine interval = \ frac { d } { b } , where b is the speed of bus . let the speed of cyclist be c . every 6 minutes a bus overtakes cyclist : \ frac { d } { b - c } = 6 , d = 6 b - 6 c ; every 2 minutes cyclist meets an oncoming bus : \ frac { d } { b + c } = 2 , d = 2 b + 2 c ; d = 6 b - 6 c = 2 b + 2 c , - - > b = 2 c , - - > d = 6 b - 3 b = 3 b . interval = \ frac { d } { b } = \ frac { 3 b } { b } = 3 answer : a ( 3 minutes ) ."
Answer: a
Python program:
a = 2 + 6 
b = 6 - 2
c = a / b
d = 6 / c
e = 6 - d
f = e / 1
Problem: what is the area of a square field whose diagonal of length 30 m ?
Options: a ) 287 , b ) 269 , c ) 450 , d ) 200 , e ) 230
Rationale: "d 2 / 2 = ( 30 * 30 ) / 2 = 450 answer : c"
Answer: c
Python program:
a = square_area / (
Problem: what is the least number should be added to 1056 , so the sum of the number is completely divisible by 25 ?
Options: a ) 19 , b ) 20 , c ) 32 , d ) 41 , e ) 53
Rationale: "( 1056 / 25 ) gives remainder 6 19 + 6 = 23 , so we need to add 19 a"
Answer: a
Python program:
a = 1056 / 25
b = math.floor(a)
c = b + 1 
d = c * 25
e = d - 1056
Problem: a rectangular grassy plot 110 m . by 65 m has a gravel path 2.5 m wide all round it on the inside . find the cost of gravelling the path at 50 paise per sq . metre
Options: a ) s 425 , b ) s 780 , c ) s 880 , d ) s 480 , e ) s 980
Rationale: "area of the plot = 110 m * 65 m = 7150 sq . m area of plot excluding gravel = 105 m * 60 m = 6300 sq . m area of gravel = 7150 sq . m - 6300 sq . m = 850 sq . m cost of building it = 850 sq . m * 50 = 42500 p in rs = 42500 / 100 = rs 425 answer : a"
Answer: a
Python program:
a = 110 * 65
b = 2 * 5
c = 110 - b
d = 2 * 5
e = 65 - d
f = c * e
g = a - f
h = g * 50
i = h / 100
Problem: a man bought 40 shares of rs . 60 at 7 discount , the rate of dividend being 1212 % the rate of interest obtained is
Options: a ) 13.64 % , b ) 15.5 % , c ) 14 % , d ) 14.15 % , e ) 14.95 %
Rationale: "explanation : face value of a share = rs . 60 he bought each share at rs . 60 - rs . 7 = rs . 53 number of shares = 40 dividend = 12 1 / 2 % = 25 / 2 % dividend per share = 60 × 25 / 2 × 100 = rs . 7.5 total dividend = ( 40 × 7.5 ) ie , he got a dividend of ( 40 × 7.5 ) for an investment of rs . ( 40 × 53 ) interest obtained = 40 × 7.5 × 100 / 40 × 53 = 14.15 % answer : option d"
Answer: d
Python program:
a = 40 * 60
b = 1212 / 100
c = a * b
d = 60 - 7
e = 40 * d
f = c / e
Problem: if 853845 bars of chocolate need to be placed in little boxes and each box can contain at most 9 bars of chocolate . how many bars of chocolate will be in the last unfilled box ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 7
Rationale: the number of bars of chocolate that can be placed in the little boxes of 9 bars is the first number that is divisible by 9 that occurs before 853845 . in order to divide the sum in 9 parts , the amount must be divisible by 9 divisibility rule of 9 : the sum of the digits must be divisible by 9 sum of digits of 853845 = 33 and 27 is divisible by 9 . hence , we need to remove 6 to this number for it to be divisible by 9 correct option : d
Answer: d
Python program:
a = 853845 / 9
b = math.floor(a)
c = b * 9
d = 853845 - c
Problem: the length of a bridge in meters , which a train 110 - meters long and traveling at 45 km / hr can cross in 30 seconds is ?
Options: a ) 245 , b ) 265 , c ) 295 , d ) 325 , e ) 375
Rationale: "45 km / h = 45000 m / 3600 s = 12.5 m / s in 30 seconds , the train can go 30 ( 12.5 ) = 375 meters let x be the length of the bridge . x + 110 = 375 meters x = 265 meters the answer is b ."
Answer: b
Python program:
a = 45 * 1000
b = a / 3600
c = b * 30
d = c - 110
Problem: income and expenditure of a person are in the ratio 9 : 8 . if the income of the person is rs . 36000 , then find his savings ?
Options: a ) 2000 , b ) 3000 , c ) 4000 , d ) 5000 , e ) 6000
Rationale: "let the income and the expenditure of the person be rs . 9 x and rs . 7 x respectively . income , 9 x = 36000 = > x = 4000 savings = income - expenditure = 9 x - 8 x = x so , savings = rs . 4000 . answer : c"
Answer: c
Python program:
a = 8 / 9
b = a * 36000
c = 36000 - b
Problem: light glows for every 16 seconds . how many times did it between 1 : 57 : 58 and 3 : 20 : 47 am
Options: a ) 311 , b ) 322 , c ) 313 , d ) 314 , e ) 385
Rationale: "the diff in sec between 1 : 57 : 58 and 3 : 20 : 47 is 4969 sec , 4969 / 16 = 310 . so total 311 times light ll glow answer : a"
Answer: a
Python program:
a = 2 + 47 
b = 2 + const_60 
c = 20 + b 
d = c * const_60
e = a + d 
f = e / 16
Problem: the difference between c . i . and s . i . on an amount of rs . 15,000 for 2 years is rs . 294 . what is the rate of interest per annum ?
Options: a ) 18 , b ) 12 , c ) 9 , d ) 14 , e ) 16
Rationale: "explanation : [ 15000 * ( 1 + r / 100 ) 2 - 15000 ] - ( 15000 * r * 2 ) / 100 = 294 15000 [ ( 1 + r / 100 ) 2 - 1 - 2 r / 100 ] = 294 15000 [ ( 100 + r ) 2 - 10000 - 200 r ] / 10000 = 294 r 2 = ( 294 * 2 ) / 3 = 196 = > r = 14 rate = 14 % answer : option d"
Answer: d
Python program:
a = math.sqrt(294)
Problem: a thief goes away with a santro car at a speed of 30 kmph . the theft has been discovered after half an hour and the owner sets off in a bike at 60 kmph when will the owner over take the thief from the start ?
Options: a ) 1 hours , b ) 2 hours , c ) 2 / 3 hours , d ) 1 / 3 hours , e ) 2 / 5 hours
Rationale: "- - - - - - - - - - - 30 - - - - - - - - - - - - - - - - - - - - | 60 30 d = 30 rs = 60 â € “ 30 = 30 t = 30 / 30 = 1 hours answer : a"
Answer: a
Python program:
a = 1 / 2
b = a * 30
c = 60 - 30
d = b / c
e = 1 / 2
f = d - e
Problem: a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 10000 more than d , what is b ' s share ?
Options: a ) a ) 82390 , b ) b ) 29000 , c ) c ) 20005 , d ) d ) 23930 , e ) e ) 20000
Rationale: "let the shares of a , b , c and d be 5 x , 2 x , 4 x and 3 x rs . respectively . then , 4 x - 3 x = 1000 = > x = 10000 . b ' s share = rs . 2 x = 2 * 10000 = rs . 20000 . answer : e"
Answer: e
Python program:
a = 4 - 3
b = a * 10000
c = b * 3
Problem: one night a certain hotel rented 1 / 2 of its rooms , including 2 / 3 of their air conditioned rooms . if 3 / 5 of its rooms were air conditioned , what percent of the rooms that were not rented were air conditioned ?
Options: a ) 25 % , b ) 30 % , c ) 35 % , d ) 40 % , e ) 50 %
Rationale: "the rooms which were not rented is 1 / 2 the ac rooms which were not rented is ( 1 / 3 ) * ( 3 / 5 ) = 1 / 5 the percentage of unrented rooms which were ac rooms is ( 1 / 5 ) / ( 1 / 2 ) = 2 / 5 = 40 % the answer is d ."
Answer: d
Python program:
a = 2 / 0
b = 1 - a
c = 1 / 2
d = c * 100
e = b * d
f = 1 / 2
g = f * 100
h = 100 - g
i = e / h
j = i * 100
Problem: a class is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width . find the least number of square tiles of equal size required to cover the entire floor of the class room ?
Options: a ) 115 , b ) 117 , c ) 116 , d ) 114 , e ) 112
Rationale: explanation : length = 6 m 24 cm = 624 cm width = 4 m 32 cm = 432 cm hcf of 624 and 432 = 48 number of square tiles required = ( 624 x 432 ) / ( 48 x 48 ) = 13 x 9 = 117 . answer is b
Answer: b
Python program:
a = 6 * 100
b = a + 24 
c = 4 * 100
d = c + 32 
e = b * d
f = 24 + 24 
g = 24 + 24 
h = f * g
i = e / h
Problem: 128 % of 5 / 8 =
Options: a ) 0.2 , b ) 0.5 , c ) 0.6 , d ) 0.8 , e ) 1.0
Rationale: "should be simple . 1.28 * 5 / 8 = 6.4 / 8 = 0.8 correct option : d"
Answer: d
Python program:
a = 8 * 5
b = a / 100
c = b * 128
d = c / 100
Problem: mixture contains alcohol and water in the ratio 4 : 3 . if 4 liters of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture .
Options: a ) 20 , b ) 99 , c ) 27 , d ) 22 , e ) 29
Rationale: "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 16 x = 4 ( 3 x + 5 ) 4 x = 20 x = 5 quantity of alcohol = ( 4 x 5 ) litres = 20 litres . answer : a"
Answer: a
Python program:
a = 4 * 5
b = 4 * 4
c = 3 * 4
d = b - c
e = a / d
f = e * 4
Problem: the sum of the fourth and twelfth term of an arithmetic progression is 20 . what is the sum of the first 12 terms of the arithmetic progression ?
Options: a ) 300 , b ) 120 , c ) 150 , d ) 170 , e ) 270
Rationale: "n th term of a . p . is given by a + ( n - 1 ) d 4 th term = a + 3 d 12 th term = a + 11 d given a + 3 d + a + 11 d = 20 - - > 2 a + 14 d = 20 - - > a + 7 d = 10 sum of n term of a . p = n / 2 [ 2 a + ( n - 1 ) d ] subsitiuing n = 12 . . . we get 12 / 2 [ 2 a + 14 d ] = 15 [ a + 7 d ] = 12 * 10 = 120 . . . answer is b . . ."
Answer: b
Python program:
a = 20 * 12
b = a / 2
Problem: sonika bought a v . c . r . at the list price of 18,700 . if the rate of sales tax was 8 % , find the amount she had to pay for purchasing the v . c . r .
Options: a ) 20,196 , b ) 19,780 , c ) 19,680 , d ) 19,380 , e ) none of these
Rationale: "sol . list price of v . c . r . = 18,700 rate of sales tax = 8 % ∴ sales tax = 8 % of 18,700 = 8 ⁄ 100 × 18700 = 1496 so , total amount which sonika had to pay for purchasing the v . c . r . = 18,700 + 1496 = 20,196 . answer a"
Answer: a
Python program:
a = 1 + 4 
b = a * 2
c = b + 8 
d = c * 100
e = 1 + 4 
f = e * 2
g = d * f
h = 1 + 4 
i = h * 100
j = g + i 
k = 100 + 8 
l = j * k
m = l / 100
n = 1 + 4 
o = n * 100
p = o * 2
q = m / p
r = math.floor(q)
Problem: if the speed of a man is 54 km per hour , then what is the distance traveled by him in 25 seconds ?
Options: a ) 275 m , b ) 360 m , c ) 375 m , d ) 420 m , e ) 440 m
Rationale: the distance traveled in 25 sec = 54 * ( 5 / 18 ) * 25 = 375 m answer : c
Answer: c
Python program:
a = 54 * const_0_2778
b = a * 25
Problem: soja finished 2 / 3 of a book . she calculated that she finished 100 more pages than she has yet to read . how long is her book ?
Options: a ) a ) 300 , b ) b ) 150 , c ) c ) 130 , d ) d ) 90 , e ) e ) 210
Rationale: let x be the total number of pages in the book , then she finished 2 / 3 * x pages . then she has x − 2 / 3 * x = 1 / 3 * x pages left . 2 / 3 * x − 1 / 3 * x = 100 1 / 3 * x = 100 x = 300 so the book is 300 pages long . answer is a .
Answer: a
Python program:
a = 100 * 3
Problem: a monkey ascends a greased pole 18 metres high . he ascends 2 metres in first minute and slips down 1 metre in the alternate minute . in which minute , he reaches the top ?
Options: a ) 21 st , b ) 22 nd , c ) 33 rd , d ) 24 th , e ) none of these
Rationale: "in 2 minutes , he ascends = 1 metre â ˆ ´ 16 metres , he ascends in 32 minutes . â ˆ ´ he reaches the top in 33 rd minute . answer c"
Answer: c
Python program:
a = 2 * 18
b = a - 1
Problem: the average score of a cricketer in 10 matches is 60 and in other 15 matches is 70 . then find the average score in all the 25 matches ?
Options: a ) 50 , b ) 48 , c ) 65 , d ) 66 , e ) 72
Rationale: "average in 25 matches = ( 10 * 60 + 15 * 70 ) / 10 + 15 = 66 answer is d"
Answer: d
Python program:
a = 10 * 60
b = 15 * 70
c = a + b 
d = c / 25
Problem: one - third less than 30 % of 180 is equal to :
Options: a ) 15 , b ) 30 , c ) 36 , d ) 40 , e ) 45
Rationale: "lots of ways to tackle this . 30 % of 180 = 54 1 / 3 of 45 = 18 so , 1 / 3 less than 54 is equal to 54 - 18 = 36 answer : c"
Answer: c
Python program:
a = 30 / 100
b = a * 180
c = 1 / 3
d = 30 / 100
e = d * 180
f = c * e
g = b - f
Problem: the average of marks obtained by 120 boys was 35 . if the average of marks of passed boys was 39 and that of failed boys was 15 , the number of boys who passed the examination is ?
Options: a ) 100 , b ) 110 , c ) 120 , d ) 130 , e ) 140
Rationale: "let the number of boys who passed = x . then , 39 x x + 15 x ( 120 - x ) = 120 x 35 24 x = 4200 - 1800 = > x = 2400 / 24 x = 100 . hence , the number of boys passed = 100 . answer : a"
Answer: a
Python program:
a = 35 * 120
b = 120 * 15
c = a - b
d = 39 - 15
e = c / d
Problem: a whale goes on a feeding frenzy that lasts for 5 hours . for the first hour he catches and eats x kilos of plankton . in every hour after the first , it consumes 3 kilos of plankton more than it consumed in the previous hour . if by the end of the frenzy the whale will have consumed a whopping accumulated total 450 kilos of plankton , how many kilos did he consume on the third hour ?
Options: a ) 38 , b ) 47 , c ) 50 , d ) 53 , e ) 93
Rationale: "if you list the amount eaten each hour , you ' ll get an equally spaced list , increasing by 3 each hour . in any equally spaced list , the median equals the mean . here , the mean is 450 / 5 = 90 , so the median is also 90 , and that is the amount eaten in the 2 nd hour . we need to add 3 to find the total eaten in the next hour , so the answer is 93 option e"
Answer: e
Python program:
a = 450 / 5
b = a + 3
Problem: a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets $ 500 more than d , what is b ' s share ?
Options: a ) $ 500 , b ) $ 1000 , c ) $ 1500 , d ) $ 2000 , e ) $ 2500
Rationale: "let the shares of a , b , c and d be 5 x , 2 x , 4 x and 3 x respectively . then , 4 x - 3 x = 500 x = $ 500 b ' s share = 2 x = 2 * $ 500 = $ 1000 the answer is b ."
Answer: b
Python program:
a = 4 - 3
b = a * 500
c = b * 3
Problem: if 5 spiders make 5 webs in 5 days , then 1 spider will make 1 web in how many days ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "let the required number days be x . less spiders , more days ( indirect proportion ) less webs , less days ( direct proportion ) spiders 1 : 5 webs 5 : 1 1 x 5 x x = 5 x 1 x 5 = > x = 5 answer is c"
Answer: c
Python program:
a = 1 * 5
Problem: 10 camels cost as much as 24 horses , 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants . if the cost of 10 elephants is rs . 150000 , find the cost of a camel ?
Options: a ) s . 9800 , b ) s . 3800 , c ) s . 9800 , d ) s . 6000 , e ) s . 6880
Rationale: "cost of the camel = p 10 camels = 24 horses 16 horses = 4 oxen 6 oxen = 4 elephants 10 elephants = rs . 150000 p = rs . [ ( 24 * 4 * 4 * 150000 ) / ( 10 * 16 * 6 * 10 ) ] p = rs . ( 57600000 / 9600 ) = > p = rs . 6000 answer : d"
Answer: d
Python program:
a = 24 * 4
b = a * 4
c = b * 150000
d = 10 * 16
e = d * 6
f = e * 10
g = c / f
Problem: a candidate got 31 % of the votes polled and he lost to his rival by 2451 votes . how many votes were cast ?
Options: a ) 6150 , b ) 6250 , c ) 6350 , d ) 6450 , e ) 6550
Rationale: "let x be the total number of votes . 0.31 x + 2451 = 0.69 x 0.38 x = 2451 x = 2451 / 0.38 = 6450 the answer is d ."
Answer: d
Python program:
a = 31 / 100
b = 1 - a
c = 31 / 100
d = b - c
e = 2451 / d
Problem: find the simple interest on $ 2000 for 3 years at 10 % per annum ?
Options: a ) $ 250 , b ) $ 300 , c ) $ 500 , d ) $ 600 , e ) $ 1000
Rationale: "si = ptr / 100 = 2000 * 3 * 10 / 100 = $ 600 answer is d"
Answer: d
Python program:
a = 3 / 100
b = 2000 * a
Problem: an inspector rejects 10 % of the meters as defective . how many will he examine to reject 10 ?
Options: a ) 100 , b ) 120 , c ) 250 , d ) 200 , e ) 160
Rationale: "then , 10 % of x = 10 ( 10 / 100 ) x = 10 x = ( 10 * 100 * ) / 10 = 100 answer is a"
Answer: a
Python program:
a = 10 * 100
b = a / 10
Problem: the difference between the place value and the face value of 4 in the numeral 854973 is
Options: a ) 973 , b ) 6973 , c ) 3996 , d ) 6084 , e ) none of these
Rationale: "( place value of 4 ) - ( face value of 4 ) = ( 4000 - 4 ) = 3996 answer : option c"
Answer: c
Python program:
a = 10 * 4
b = a - 4