euclaise/mathqa_programs huggingface dataset:
Problem: what is remainder of the division ( 1225 * 1227 * 1229 ) / 12 ?
Options: a ) 1 , b ) 0 , c ) 3 , d ) 2 , e ) 4
Rationale: "remainder will be number / 100 here as the divisor is two digit number = 12 . hence checking for the last two digits = 5 * 7 * 9 = 15 thus remainder = 3 . answer : c"
Answer: c
Python program:
a = 1225 * 1227
b = a * 1229
c = 1225 * 1227
d = c * 1229
e = d - 3
f = b - e
Problem: the sum of three consecutive multiples of 3 is 99 . what is the largest number ?
Options: a ) 36 , b ) 33 , c ) 30 , d ) 27 , e ) 24
Rationale: "let the numbers be 3 x , 3 x + 3 and 3 x + 6 . then , 3 x + ( 3 x + 3 ) + ( 3 x + 6 ) = 99 9 x = 90 x = 10 largest number = 3 x + 6 = 36 answer : a"
Answer: a
Python program:
a = 3 - 10
b = a - 2
c = b / 4
d = c + 2 
e = d + 2 
f = e ** 2
g = 3 - 10
h = g - 2
i = h / 4
j = i + 2 
k = j + 2 
l = k + 2 
m = l ** 2
n = f + m 
o = 3 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 3 - 10
t = s - 2
u = t / 4
v = u + 2 
w = v ** 2
x = r + w 
y = n + x
Problem: what number should replace the question mark ? 2 , 16 , 4 , 14 , 6 , 12 , - - - ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: answer : a 2 , 16 , 4 , 14 , 6 , 12 , 8 ? there are two alternate sequences : + 2 and - 2 .
Answer: a
Python program:
a = 2 + 2 
b = a + 2 
c = b + 2
Problem: a garrison of 400 men had a provision for 31 days . after 28 days 280 persons re - enforcement leave the garrison . find the number of days for which the remaining ration will be sufficient ?
Options: a ) 65 days , b ) 45 days , c ) 10 days , d ) 16 days , e ) 18 days
Rationale: "400 - - - 31 400 - - - 3 120 - - - ? 400 * 3 = 120 * x = > x = 10 days . answer : c"
Answer: c
Python program:
a = 31 - 28
b = a * 400
c = b / 280
Problem: a father said his son , ` ` i was as old as you are at present at the time of your birth . ` ` if the father age is 62 now , the son age 5 years back was
Options: a ) 14 , b ) 17 , c ) 11 , d ) 19 , e ) 26
Rationale: "let the son ' s present age be x years . then , ( 62 - x ) = x x = 31 . son ' s age 5 years back = ( 31 - 5 ) = 26 years answer : e"
Answer: e
Python program:
a = 62 / 2
b = a - 5
Problem: calculate the average of all the numbers between 7 and 49 which are divisible by 6 .
Options: a ) 20 , b ) 18 , c ) 19 , d ) 15 , e ) 30
Rationale: "explanation : numbers divisible by 6 are 12 , 18,24 , 30,36 , 42,48 , average = ( 12 + 18 + 24 + 30 + 36 + 42 + 48 , ) / 7 = 210 / 7 = 30 answer : e"
Answer: e
Python program:
a = 7 / 6
b = math.floor(a)
c = b + 1 
d = 49 / 6
e = math.floor(d)
f = c + e 
g = f / 2
h = g * 6
Problem: a certain sum of money is divided among a , b and c such that a gets one - third of what b and c together get and b gets two - seventh of what a and c together get . if the amount received by a is $ 35 more than that received by b , find the total amount shared by a , b and c .
Options: a ) $ 1360 , b ) $ 1250 , c ) $ 1260 , d ) $ 1270 , e ) $ 1280
Rationale: "a = 1 / 3 ( b + c ) = > c = 3 a - b - - - ( 1 ) b = 2 / 7 ( a + c ) = > c = 3.5 b - a - - ( b ) a - b = $ 35 a = 35 + b ( 1 ) = = = > c = 105 + 3 b - b = 2 b + 105 = = > 2 b - c = - 105 - - - ( 3 ) ( 2 ) = = = > c = 3.5 b - b - 35 = 2.5 b - 35 = = > 2.5 b - c = 35 - - - ( 4 ) from ( 4 ) and ( 3 ) 0.5 b = 140 b = $ 280 a = $ 315 c = 945 - 280 = $ 665 total amount = 315 + 280 + 665 = $ 1260 answer : c"
Answer: c
Python program:
a = 3 * 35
b = a * 2
c = 2 * 35
d = b + c 
e = 3 * 35
f = e * 2
g = 2 * 35
h = f + g 
i = h + 35 
j = d + i 
k = 3 * 35
l = k * 2
m = 2 * 35
n = l + m 
o = n + 35 
p = o * 3
q = 3 * 35
r = q * 2
s = 2 * 35
t = r + s 
u = p - t
v = j + u
Problem: a train 125 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ?
Options: a ) 45 kmph , b ) 25 kmph , c ) 30 kmph , d ) 50 kmph , e ) none of these
Rationale: "explanation : speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) x ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be ' s ' km / hr . then , relative speed = ( s - 5 ) km / hr . s - 5 = 45 = > s = 50 km / hr . answer is d"
Answer: d
Python program:
a = 5 * const_0_2778
b = a * 5
c = 125 - b
d = c / 5
e = d / const_0_2778
Problem: the number which exceeds 16 % of it by 21 is :
Options: a ) 25 , b ) 52 , c ) 58 , d ) 60 , e ) 62
Rationale: "solution solution let the number be x . x - 16 % of x = 21 x - 16 / 100 x = 21 x - 4 / 25 x = 21 21 / 25 x = 21 x = ( 21 x 25 / 21 ) = 25 answer a"
Answer: a
Python program:
a = 21 * 100
b = 100 - 16
c = a / b
Problem: excluding stoppages , the speed of a bus is 60 kmph and including stoppages , it is 50 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 10 min , b ) 15 min , c ) 12 min , d ) 8 min , e ) 16 min
Rationale: "due to stoppages , it covers 10 km less . time taken to cover 10 km = ( 10 / 60 x 60 ) min = 10 min answer : a"
Answer: a
Python program:
a = 60 - 50
b = a / 60
c = const_60 * b
Problem: if 4 ( p ' s capital ) = 6 ( q ' s capital ) = 10 ( r ' s capital ) , then out of the total profit of rs 4960 , r will receive
Options: a ) 600 , b ) 700 , c ) 800 , d ) 960 , e ) none of these
Rationale: "explanation : let p ' s capital = p , q ' s capital = q and r ' s capital = r then 4 p = 6 q = 10 r = > 2 p = 3 q = 5 r = > q = 2 p / 3 r = 2 p / 5 p : q : r = p : 2 p / 3 : 2 p / 5 = 15 : 10 : 6 r ' s share = 4960 * ( 6 / 31 ) = 160 * 6 = 960 . answer : option d"
Answer: d
Python program:
a = 4 + 1 
b = 10 + a 
c = b + 10 
d = c + 6 
e = 6 / d
f = 4960 * e
Problem: an isosceles triangle those sides are 13 cm , 13 cm , 10 cm long inscribed in a circle . find the radius of the circle
Options: a ) 8 cm
b ) 9 cm
c ) 10 cm
d ) 11 cm
e ) 7 cm
Rationale: a , b , c are sides of triangle , ad is the median , ad ^ 2 = ab ^ 2 - bd ^ 2 then ad = 12 , the centriod median divides into 2 : 1 ratio so 12 will be divide into 2 : 1 ratio so 8 is radius . so ans is 8 cm answer : a
Answer: a
Python program:
a = 13 ** 2
b = 10 / 2
c = b ** 2
d = a - c
e = 10 / 2
f = e ** 2
g = d + f 
h = 13 ** 2
i = 10 / 2
j = i ** 2
k = h - j
l = math.sqrt(k)
m = l * 2
n = g / m
o = n + 1
Problem: n is an 80 - digit positive integer ( in the decimal scale ) . all digits except the 44 th digit ( from the left ) are 2 . if n is divisible by 13 , find the 26 th digit ?
Options: a ) 5 , b ) 6 , c ) 1 , d ) 2 , e ) 3
Rationale: detailed solution to begin with , the question should read ` ` find the 44 th digit ' ' . any number of the form abcabc is a multiple of 1001 . 1001 is 7 * 11 * 13 . so , any number of the form abcabc is a multiple of 13 . so , a number comprising 42 2 ' s would be a multiple of 13 , so would a number comprising 36 2 ' s . so , in effect , we are left with a two digit number 2 a , where a is the 44 th digit . 26 is a multiple of 13 , so the 44 th digit should be 6 . correct answer b
Answer: b
Python program:
a = 12 / 2
b = a / 1
Problem: 60 boys can complete a work in 40 days . how many men need to complete twice the work in 20 days
Options: a ) 160 , b ) 170 , c ) 180 , d ) 190 , e ) 240
Rationale: "one man can complete the work in 40 * 60 = 2400 days = one time work to complete the work twice it will be completed in let m be the no . of worker assign for this therefore the eqn becomes m * 20 = 2 * 2400 m = 240 workers answer : e"
Answer: e
Python program:
a = 40 * 2
b = 60 * a
c = b / 20
Problem: an outlet pipe empties a tank which is full in 8 hours . if the inlet pipe is kept open , which lets water in at the rate of 8 litres / min then outlet pipe would take 4 hours longer . find the capacity of the tank .
Options: a ) 8600 litres , b ) 200 litres , c ) 12800 litres , d ) 11520 litres , e ) 13200 litres
Rationale: "let the rate of outlet pipe be x liters / hour ; rate of inlet pipe is 8 litres / min , or 8 * 60 = 480 liters / hour ; net outflow rate when both pipes operate would be x - 480 liters / hour . capacity of the tank = x * 8 hours = ( x - 480 ) * ( 8 + 4 ) hours 8 x = ( x - 480 ) * 12 - - > x = 1440 - - > capacity = 8 x = 11520 liters . answer : d ."
Answer: d
Python program:
a = 8 * const_60
b = 8 + 4 
c = a * b
d = c / 4
e = d * 8
Problem: how should we mix two rice packets to get one 1 kg packet priced at rs 8 when the prices of 1 kg packets of the two types are rs 7.1 and rs 9.2 .
Options: a ) 4 : 3 , b ) 4 : 7 , c ) 4 : 9 , d ) 4 : 2 , e ) 4 : 1
Rationale: explanation : no explanation is available for this question ! answer : a
Answer: a
Python program:
a = 9 - 2
b = 8 - 7
c = a / b
Problem: car a runs at the speed of 35 km / hr & reaches its destination in 9 hr . car b runs at the speed of 43 km / h & reaches its destination in 10 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 65 : 69 , b ) 56 : 45 , c ) 89 : 71 , d ) 68 : 23 , e ) 63 : 86
Rationale: "sol . distance travelled by car a = 35 × 9 = 315 km distance travelled by car b = 43 × 10 = 430 km ratio = 315 / 430 = 63 : 86 e"
Answer: e
Python program:
a = 35 * 9
b = 43 * 10
c = a / b
Problem: a and b ’ s salaries together amount to rs . 3,000 . a spends 95 % of his salary and b spends 85 % of his . if now their savings are the same , what is a ’ s salary ?
Options: a ) 2777 , b ) 2250 , c ) 2789 , d ) 2776 , e ) 2881
Rationale: "( 5 / 100 ) a = ( 15 / 100 ) b a = 3 b a + b = 3000 4 b = 3000 = > b = 750 a = 2250 answer b"
Answer: b
Python program:
a = 2 + 3 
b = 4 * a
c = 2 * b
d = c * 100
e = 85 / 100
f = 1 - e
g = d * f
h = 95 / 100
i = 1 - h
j = 85 / 100
k = 1 - j
l = i + k 
m = g / l
Problem: the average weight of 3 packets a , b and c is 84 kg . another packet d added into the group and the average now becomes 80 kg . if another packet e , whose weight is 3 kg more than that of d , replaces a then the average weight of b , c , d and e becomes 79 kg . the weight of a is :
Options: a ) 70 kg , b ) 72 kg , c ) 75 kg , d ) 80 kg , e ) none of these
Rationale: explanation : a + b + c = ( 84 x 3 ) = 252 kg , a + b + c + d = ( 80 x 4 ) = 320 kg . d = ( 320 - 252 ) = 68 , e = ( 68 + 3 ) = 7 l . b + c + d + e = ( 79 x 4 ) = 316 . ( a + b + c + d ) - ( b + c + d + e ) = ( 320 - 316 ) kg = 4 kg . a - e = 4 = a = ( 4 + e ) = 75 kg answer : c
Answer: c
Python program:
a = 3 * 84
b = 4 * 79
c = 4 * 80
d = 3 * 84
e = c - d
f = 4 * 80
g = 3 * 84
h = f - g
i = h + 3 
j = e + i 
k = b - j
l = a - k
Problem: the consumption of diesel per hour of a bus varies directly as square of its speed . when the bus is travelling at 60 kmph its consumption is 1 litre per hour . if each litre costs $ 30 and other expenses per hous is $ 20 , then what would be the minimum expenditure required to cover a distance of 600 km ?
Options: a ) 500 , b ) 450 , c ) 600 , d ) 650 , e ) 750
Rationale: 60 kmph consumption is 1 lt / hr so 600 km will take 10 hrs and the consumption is 10 lt for entire distance . 1 lt costs $ 30 so 10 lt costs $ 300 extra expenses for 1 hr - $ 20 10 hrs - $ 200 total expense - $ 300 + $ 200 = $ 500 answer : a
Answer: a
Python program:
a = 600 / 60
b = a * 30
c = 600 / 60
d = c * 20
e = b + d
Problem: if the average of 10 consecutive integers is 19.5 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 = 19 , integer 6 = 20 . counting up to the tenth integer we get 24 . answer : d"
Answer: d
Python program:
a = 10 * 2
b = 10 * 2
c = 19 - 5
d = c * 10
e = a + d
Problem: on the first day of her vacation , louisa traveled 100 miles . on the second day , traveling at the same average speed , she traveled 175 miles . if the 100 - mile trip took 3 hours less than the 175 - mile trip , what was the average speed , in miles per hour ?
Options: a ) 27 , b ) 28 , c ) 25 , d ) 30 , e ) 35
Rationale: "( time ) * ( rate ) = ( distance ) - - > ( rate ) = ( distance ) / ( time ) - - > given : ( rate ) = 100 / t = 175 / ( t + 3 ) - - > 4 / t = 7 / ( t + 3 ) - - > 4 t + 12 = 7 t - - - - > 3 t = 12 . t = 4 - - - - > ( rate ) = 100 / 4 = 25 answer : c"
Answer: c
Python program:
a = 175 - 100
b = a / 3
Problem: at a certain paint store forest green is made by mixing 4 parts blue paint with 3 parts yellow paint . verdant green is made by mixing 4 parts yellow paint with 3 parts blue paint . how many liters of yellow paint must be added to 28 liters of forest green to change it to verdant green ?
Options: a ) 28 / 3 , b ) 13 / 6 , c ) 3 , d ) 4 , e ) 14 / 3
Rationale: "28 liter of forset green have 16 liter of blue and 12 liter of yellow suppose we add x liter of yellow to make it a verdant green so the ratio of blue to yellow in verdant green is ¾ so the equation is blue / yellow = 16 / ( 12 + x ) = ¾ 36 + 3 x = 64 = > x = 28 / 3 answer : a"
Answer: a
Python program:
a = 4 / 3
b = a * 4
c = b - 3
Problem: in a office work is distribute between p persons . if 1 / 5 members are absent then work increased for each person is ?
Options: a ) 13.28 % , b ) 14.28 % , c ) 15.28 % , d ) 16.28 % , e ) 25 %
Rationale: "let total % of work is 100 % total person = p 1 / 5 person are absent of total person . so absent person is 1 / 5 p ie p / 5 . left person is , p - p / 5 = 4 p / 5 . p person do the work 100 % 1 person do the work 100 * p % 4 p / 5 person do the work ( 100 * p * 5 ) / 4 p % = 125 % work increased for each person is = ( 125 - 100 ) % = 25 % answer : e"
Answer: e
Python program:
a = 100 * 5
b = 5 - 1
c = a / b
d = c - 100
Problem: what could be the range of a set consisting of odd multiples of 5 ?
Options: a ) 21 , b ) 24 , c ) 35 , d ) 62 , e ) 60
Rationale: "range = the difference between the greatest and the smallest numbers in the sequence . our sequence is odd and is a multiple of 7 . every number in that sequence can be represented like this : 5 * ( 2 n + 1 ) where n is any positive integer . range = 5 * ( 2 m + 1 ) - 5 * ( 2 n + 1 ) = 5 * 2 * ( m - n ) = 10 * ( m - n ) . m , n - any positive integers the answer must be divisible by 10 , which is only 60 . the correct answer is e ."
Answer: e
Python program:
a = 5 * 4
Problem: a book is bought for $ 60 and sold for $ 75 . what is the profit in percentage ?
Options: a ) 12 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: "75 / 60 = 1.25 the answer is d ."
Answer: d
Python program:
a = 75 - 60
b = a / 60
c = b * 100
Problem: how many multiples of 5 are there between 5 to 85 ?
Options: a ) 15 , b ) 18 , c ) 17 , d ) none of these , e ) can not be determined
Rationale: "explanation : as you know , multiples of 5 are integers having 0 or 5 in the digit to the extreme right ( i . e . the units place ) . so the numbers are 10 , 15 , 20 , 25 , 30 , 35 , 40 , 45 , 50 , 55 , 60 , 65 , 70 , 75 , 80 . answer : a"
Answer: a
Python program:
a = 85 - 5
b = a / 5
c = b + 1
Problem: the difference between a number and its two - fifth is 510 . what is 10 % of that number ?
Options: a ) 12.75 , b ) 85 , c ) 204 , d ) 250 , e ) none of these
Rationale: "explanation : let the number be x . then , x - 2 / 5 x = 510 x = ( 510 * 5 ) / 3 = 850 10 % of 850 = 85 . answer is b"
Answer: b
Python program:
a = 4 + 1 
b = 510 * a
c = 1 + 2 
d = b / c
Problem: in a recent election , james received 0.5 percent of the 2,000 votes cast . to win the election , a candidate needed to receive more than 45 percent of the vote . how many additional votes would james have needed to win the election ?
Options: a ) 901 , b ) 989 , c ) 990 , d ) 891 , e ) 1,001
Rationale: "james = ( 0.5 / 100 ) * 2000 = 10 votes to win = ( 45 / 100 ) * total votes + 1 = ( 45 / 100 ) * 2000 + 1 = 901 remaining voted needed to win election = 901 - 10 = 891 answer : option d"
Answer: d
Python program:
a = 1000 + 1000 
b = 1000 + 1000 
c = b * 0
d = a - c
Problem: the value of a machine depreciates at 23 % per annum . if its present value is $ 1 , 50,000 , at what price should it be sold after two years such that a profit of $ 24,000 is made ?
Options: a ) $ 252935 , b ) $ 432935 , c ) $ 122935 , d ) $ 112935 , e ) $ 152935
Rationale: "the value of the machine after two years = 0.77 * 0.77 * 1 , 50,000 = $ 88,935 sp such that a profit of $ 24,000 is made = 88,935 + 24,000 = $ 1 , 12,935 d"
Answer: d
Python program:
a = 23 / 100
b = 1 - a
c = 23 / 100
d = 1 - c
e = b * d
f = 100 * 100
g = math.sqrt(100)
h = f * g
i = math.sqrt(100)
j = i / 2
k = j * 100
l = k * 100
m = h + l 
n = e * m
o = 23 + 2 
p = o * 100
q = math.sqrt(100)
r = p * q
s = n + r
Problem: a train travels 240 km in 3 hours and 450 km in 5 hours . find the average speed of train .
Options: a ) 80 kmph , b ) 60 kmph , c ) 86 kmph , d ) 90 kmph , e ) none of these
Rationale: "as we know that speed = distance / time for average speed = total distance / total time taken thus , total distance = 240 + 450 = 690 km thus , total speed = 8 hrs or , average speed = 690 / 8 or , 86 kmph . answer : c"
Answer: c
Python program:
a = 240 + 450 
b = 3 + 5 
c = a / b
Problem: a gambler bought $ 3,000 worth of chips at a casino in denominations of $ 20 and $ 100 . that evening , the gambler lost 16 chips , and then cashed in the remainder . if the number of $ 20 chips lost was 2 more or 2 less than the number of $ 100 chips lost , what is the largest amount of money that the gambler could have received back ?
Options: a ) $ 2,040 , b ) $ 2,120 , c ) $ 1,960 , d ) $ 1,920 , e ) $ 1,400
Rationale: in order to maximize the amount of money that the gambler kept , we should maximize # of $ 20 chips lost and minimize # of $ 100 chips lost , which means that # of $ 20 chips lost must be 2 more than # of $ 100 chips lost . so , if # of $ 20 chips lost is x then # of $ 100 chips lost should be x - 2 . now , given that total # of chips lost is 16 : x + x - 2 = 16 - - > x = 9 : 9 $ 20 chips were lost and 9 - 2 = 7 $ 100 chips were lost . total worth of chips lost is 9 * 20 + 7 * 100 = $ 880 , so the gambler kept $ 3,000 - $ 880 = $ 2,120 . answer : b .
Answer: b
Python program:
a = 3 * 1000
b = 16 + 2 
c = b / 2
d = c * 20
e = 16 + 2 
f = e / 2
g = f - 2
h = g * 100
i = d + h 
j = a - i
Problem: a train running at the speed of 60 km / hr crosses a pole in 12 seconds . find the length of the train ?
Options: a ) 150 meter , b ) 200 meter , c ) 156 meter , d ) 168 meter , e ) 154 meter
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 12 = 200 meter answer : b"
Answer: b
Python program:
a = 60 * 1000
b = a / 3600
c = b * 12
Problem: two trains of equal lengths take 12 sec and 24 sec respectively to cross a telegraph post . if the length of each train be 120 m , in what time will they cross other travelling in opposite direction ?
Options: a ) 18 sec , b ) 12 sec , c ) 17 sec , d ) 21 sec , e ) 16 sec
Rationale: "speed of the first train = 120 / 12 = 10 m / sec . speed of the second train = 120 / 24 = 5 m / sec . relative speed = 10 + 5 = 15 m / sec . required time = ( 120 + 120 ) / 15 = 16 sec . answer : e"
Answer: e
Python program:
a = 120 * 2
b = speed + ( 
c = a / b
Problem: set a contains 4 different positive odd integers and 6 different positive even integers . set b contains two different positive odd integers and 3 different positive even integers . if one integer from set a and one integer from set b are chosen at random , what is the probability that the product of the chosen integers is even ?
Options: a ) 3 / 5 , b ) 4 / 5 , c ) 17 / 25 , d ) 21 / 25 , e ) 43 / 50
Rationale: there can be an odd product only if both integers are odd . p ( odd product ) = 4 / 10 * 2 / 5 = 4 / 25 p ( even product ) = 1 - 4 / 25 = 21 / 25 the answer is d .
Answer: d
Python program:
a = 2 + 3 
b = 2 / a
c = 4 + 6 
d = 4 / c
e = b * d
f = 1 - e
Problem: a and b can do a piece of work in 16 days , b and c in 24 days , c and a in 12 days . how long will c take to do it ?
Options: a ) 16 days , b ) 55 days , c ) 24 days , d ) 32 days , e ) 22 days
Rationale: "2 c = 1 / 24 + 1 / 12 – 1 / 16 = 1 / 16 c = 1 / 32 = > 32 days answer : d"
Answer: d
Python program:
a = 16 * 3
b = 16 * 3
c = b / 12
d = 16 * 3
e = d / 16
f = 16 * 3
g = f / 24
h = e + g 
i = c + h 
j = i / 2
k = 16 * 3
l = k / 16
m = j - l
n = a / m
Problem: population of a city in 20004 was 1000000 . if in 2005 there isan increment of 15 % , in 2006 there is a decrement of 35 % and in 2007 there is an increment of 45 % , then find the population of city at theend of the year 2007
Options: a ) 2456789 , b ) 3458009 , c ) 3890043 , d ) 3455048 , e ) 1083875
Rationale: "required population = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) ( 1 + r 3 / 100 ) = p ( 1 + 15 / 100 ) ( 1 - 35 / 100 ) ( 1 + 45 / 100 ) = 1083875 e"
Answer: e
Python program:
a = 15 / 100
b = 1 + a 
c = 35 / 100
d = 1 - c
e = b * d
f = 35 / 100
g = 1 + f 
h = e * g
i = 1000000 * h
Problem: a searchlight on top of the watch - tower makes 3 revolutions per minute . what is the probability that a man appearing near the tower will stay in the dark for at least 5 seconds ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4
Rationale: "3 revolutions per minute = 1 revolution every 20 seconds so no matter what anybody appearing at the tower can not stay in the dark for more than 20 seconds . this will be our total number of possibilities i . e the denominator . p ( man in dark for at least 5 seconds ) = 1 - p ( man in dark for max of 5 seconds ) = 1 - 5 / 20 = 1 - 1 / 4 = 3 / 4 or the other way would be : p ( man in dark for at least 5 seconds ) is like saying he can be in dark for 5 , 6,7 . . . all the way to 20 seconds because that is the max . in this approach it would be 15 / 20 seconds = 3 / 4 ."
Answer: e
Python program:
a = const_60 * 1
b = a / 3
c = 5 / b
d = 1 - c
Problem: in the first 10 overs of a cricket game , the run rate was only 4.8 . what should be the run rate in the remaining 40 overs to reach the target of 282 runs ?
Options: a ) 4.25 , b ) 5.85 , c ) 6.25 , d ) 7 , e ) 7.5
Rationale: "required run rate = 282 - ( 4.8 x 10 ) = 234 234 / 40 = 5.85 b )"
Answer: b
Python program:
a = 10 * 4
b = 282 - a
c = b / 40
Problem: the timing of a college is from 12 p . m to 4.20 p . m . six lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students . find the duration of each lecture .
Options: a ) 52 minutes , b ) 45 minutes , c ) 30 minutes , d ) 39 minutes , e ) 44 minutes
Rationale: "explanation : total time a student spends in college = 4 hours 20 minutes = 260 minutes as there are 6 lectures , the number of breaks between lectures is 5 . total time of the break = 25 minutes hence , the duration of each lecture is = ( 260 â € “ 25 ) / 6 = 39 minutes answer d"
Answer: d
Python program:
a = 4 * 20
b = a / 5
Problem: a man rows his boat 75 km downstream and 45 km upstream , taking 2 1 / 2 hours each time . find the speed of the stream ?
Options: a ) 6 , b ) 7 , c ) 5 , d ) 8 , e ) 9
Rationale: "speed downstream = d / t = 75 / ( 2 1 / 2 ) = 30 kmph speed upstream = d / t = 45 / ( 2 1 / 2 ) = 18 kmph the speed of the stream = ( 30 - 18 ) / 2 = 6 kmph answer : a"
Answer: a
Python program:
a = 75 / 2
b = 45 / 2
c = a - b
d = c / 2
Problem: in the land of oz only one or two - letter words are used . the local language has 66 different letters . the parliament decided to forbid the use of the seventh letter . how many words have the people of oz lost because of the prohibition ?
Options: a ) 65 , b ) 66 , c ) 67 , d ) 131 , e ) 132
Rationale: "the seventh letter ( let it be @ ) can be used with other 65 in two type of arrangents one when seventh letter is in 1 st slot @ _ ( 65 ways ) another , when seventh letter is in 2 nd slot _ @ ( 65 ways ) seventh letter ( @ ) itself lost words = 1 + 65 + 65 = 131 answer : d"
Answer: d
Python program:
a = 1 + 66 
b = a + 66
Problem: the sum of the first 100 numbers , 1 to 100 is always divisible by
Options: a ) 2 , b ) 2 and 4 , c ) 2 , 4 and 8 , d ) 2 , 4 and 9 , e ) none of these
Rationale: explanation : the sum of the first 100 natural numbers = ( 100 x 101 ) / 2 = ( 50 x 101 ) as 101 is an odd number and 50 is divisible by 2 , so the sum is always divisible by 2 . answer : option a
Answer: a
Python program:
a = 100 / 2
b = 100 + 1 
c = a * b
d = 100 / 2
e = 100 + 1 
f = d * e
g = f / 2
h = c / g