euclaise/mathqa_programs huggingface dataset:
Problem: a worker ' s take - home pay last year was the same each month , and she saved the same fraction of her take - home pay each month . the total amount of money that she had saved at the end of the year was 6 times the amount of that portion of her monthly take - home pay that she did not save . if all the money that she saved last year was from her take - home pay , what fraction of her take - home pay did she save each month ?
Options: a ) 1 / 6 , b ) 1 / 5 , c ) 1 / 4 , d ) 1 / 3 , e ) 1 / 2
Rationale: "let x be the fraction of her take - home pay that the worker saved . let p be the monthly pay . 12 xp = 6 ( 1 - x ) p 12 xp = 6 p - 6 xp 18 xp = 6 p x = 1 / 3 the answer is d ."
Answer: d
Python program:
a = 12 / 6
b = a + 1 
c = 1/(b)
Problem: the product of two numbers is 4107 . if the h . c . f of these numbers is 37 , then the greater number is :
Options: a ) 101 , b ) 107 , c ) 111 , d ) 112 , e ) 113
Rationale: "let the numbers be 37 a and 37 b . then , 37 a * 37 b = 4107 = > ab = 3 now , co - primes with product 3 are ( 1 , 3 ) . so , the required numbers are ( 37 * 1 , 37 * 3 ) i . e . , ( 1 , 111 ) . greater number = 111 . answer : c"
Answer: c
Python program:
a = 2 * 4107
b = 37 - a
c = math.sqrt(b)
d = c ** 2
e = 4 * 4107
f = d + e 
g = math.sqrt(f)
Problem: marts income is 60 percent more than tims income and tims income is 40 percent less than juans income . what percentage of juans income is marts income
Options: a ) 124 % , b ) 120 % , c ) 96 % , d ) 80 % , e ) 64 %
Rationale: "tim = 100 mary ' s income is 60 percent more than tims income ; mary ' s income = t + 0.6 t = 1.6 t = 1.6 * 100 = 160 tims income is 40 percent less than juans income . 100 is 40 % less than juan ' s income 100 = j - 0.4 j 100 = 0.6 j j = 100 / 0.6 = 1000 / 6 what percentage of juans income is marts income ( 160 / ( 1000 / 6 ) ) * 100 = ( 160 * 6 * 100 ) / 1000 = 96 % answer : c"
Answer: c
Python program:
a = 100 + 60 
b = 100 - 40
c = 100 / b
d = c * 100
e = a / d
f = e * 100
Problem: on a trip , a cyclist averaged 8 miles per hour for the first 12 miles and 12 miles per hour for the remaining 24 miles . if the cyclist returned immediately via the same route and took a total of 7.5 hours for the round trip , what was the average speed ( in miles per hour ) for the return trip ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "the time to go 36 miles was 12 / 8 + 24 / 12 = 1.5 + 2 = 3.5 hours . the average speed for the return trip was 36 miles / 4 hours = 9 mph . the answer is a ."
Answer: a
Python program:
a = 12 + 24 
b = 12 / 8
c = 24 / 12
d = b + c 
e = 7 - 5
f = a / e
Problem: the price of a t . v . set worth rs . 20000 is to be paid in 20 installments of rs . 1000 each . if the rate of interest be 6 % per annum , and the first installment be paid at the time of purchase , then the value of the last installment covering the interest as well will be ?
Options: a ) 19002 , b ) 19028 , c ) 27788 , d ) 19000 , e ) 27711
Rationale: "money paid in cash = rs . 1000 balance payment = ( 20000 - 1000 ) = rs . 19000 answer : d"
Answer: d
Python program:
a = 20000 - 1000
Problem: working alone , pump a can empty a pool in 4 hours . working alone , pump b can empty the same pool in 6 hours . working together , how many minutes will it take pump a and pump b to empty the pool ?
Options: a ) 132 , b ) 138 , c ) 144 , d ) 150 , e ) 156
Rationale: pump a can empty ( 1 / 4 ) of the pool per hour . pump b can empty ( 1 / 6 ) of the pool per hour . together the pumps can empty 1 / 4 + 1 / 6 = 5 / 12 of the pool per hour . 1 pool / ( 5 / 12 ) pool per hour = 12 / 5 hours = 144 minutes . the answer is c .
Answer: c
Python program:
a = 1 / 4
b = 1 / 6
c = a + b 
d = 1/(c)
e = d * const_60
Problem: 1704 x 1704 = ?
Options: a ) a ) 3623216 , b ) b ) 2903616 , c ) c ) 3624316 , d ) d ) 3625116 , e ) e ) 3625216
Rationale: "1704 x 1704 = ( 1704 ) 2 = ( 1700 + 4 ) 2 = ( 1700 ) 2 + ( 4 ) 2 + ( 2 x 1700 x 4 ) = 2890000 + 16 + 13600 . = 2903616 . b )"
Answer: b
Python program:
a = 1704 / 1704
b = a * 100
Problem: the radius of a semi circle is 6.83 cm then its perimeter is ?
Options: a ) 32.52 , b ) 32.47 , c ) 34.97 , d ) 32.92 , e ) 32.33
Rationale: "36 / 7 r = 6.3 = 34.97 answer : c"
Answer: c
Python program:
a = circumface / (
b = a + 2
Problem: joan took out a mortgage from hel local bank . each monthly mortgage payment she makes must be triple the amount of the previous month ' s payment . if her first payment is $ 100 , and the total amount she must pay back is $ 109300 , how many months will it take joan to pay back her mortgage ?
Options: a ) 7 , b ) 8 , c ) 10 , d ) 11 , e ) 13
Rationale: "joan starts off with 100 $ . . which is to be tripled every month her monthly payments look like this : 100 , 300 , 900 , 2700 . . . . . . . . . upto 109300 this can be re written as : 100 x 1 , 100 x 3 , 100 x 9 , 100 x 27 . . . . . . 100 x 1093 so we have 1 , 3 , 9 , 27 . . . . . 109300 in gp we know that a = 1 , and r = 3 ( its easy to figure it out by looking at the question , but regardless of it being mentioned in the question we can still compute the value of r using the formula tn = a 3 ^ n - 1 . . . ) therefore to find the sum of n terms of a gp we use this formula : sn = a ( 1 - r ^ n ) / 1 - r using this and plugging in the information we get . . . 1093 = 1 - 3 ^ n / 1 - 3 ; 1 - 3 ^ n / - 2 cross multiplying we get 1093 x - 2 = 1 - 3 ^ n - 2186 = 1 - 3 ^ n - 2187 = - 3 ^ n 2187 = 3 ^ n ( negatives cancel out ) 2187 can also be re written as 3 ^ 7 therefore ; 3 ^ 7 = 3 ^ n thus n = 7 ( a )"
Answer: a
Python program:
a = 109300 * 2
b = a / 100
c = b + 1 
d = math.log(c)
e = math.log(3)
f = d / e
Problem: jerry began driving from home on a trip averaging 30 miles per hour . how many miles per hour must carla drive on average to catch up to him in exactly 3 hours if she leaves 30 minutes after jerry ?
Options: a ) 35 , b ) 55 , c ) 39 , d ) 40 , e ) 60
Rationale: carla starts 30 minutes later and it takes 3 hr for carla to meet jerry so jerry total time travelled = 3 hr + 30 minutes jerry distance = 30 * ( 3 1 / 2 ) = 105 so carla need to travle 105 to meet jerry in 3 hrs speed of carla = 105 / 3 = 35 miles per hour answer is a
Answer: a
Python program:
a = 30 / const_60
b = 3 + a 
c = 30 * b
d = c / 3
Problem: having scored 97 runs in the 19 th inning , a cricketer increases his average score by 4 . what will be his average score after 19 innings ?
Options: a ) 28 , b ) 27 , c ) 26 , d ) 22 , e ) 25
Rationale: "explanation : let the average score of the first 18 innings be n 18 n + 97 = 19 ( n + 4 ) = > n = 21 so , average score after 19 th innings = x + 4 = 25 . answer : e"
Answer: e
Python program:
a = 19 * 4
b = 97 - a
c = b + 4
Problem: find the area of a parallelogram with base 22 cm and height 21 cm ?
Options: a ) 462 cm 2 , b ) 478 cm 2 , c ) 490 cm 2 , d ) 268 cm 2 , e ) 668 cm 2
Rationale: "area of a parallelogram = base * height = 22 * 21 = 462 cm 2 answer : a"
Answer: a
Python program:
a = 22 * 21
Problem: the population of a town increased from 1 , 24,300 to 1 , 62,400 in a decade . the average percent increase of population per year is :
Options: a ) 4.37 % , b ) 4 % , c ) 2.3 % , d ) 3.75 % , e ) none
Rationale: "explanation : increase in 10 years = ( 162400 - 124300 ) = 87500 . increase % = ( 38100 / 162400 x 100 ) % = 23 % . required average = ( 23 / 10 ) % = 2.3 % . answer : option c"
Answer: c
Python program:
a = 10 * 1000
b = a * 10
c = b - 1000
d = c - 1000
e = 1 + 3 
f = e * 100
g = d - f
h = 3 + 4 
i = h * 10
j = 1 + 3 
k = i + j 
l = k * 1000
m = g / l
n = m - 1
o = n / 10
p = o * 100
q = p + 4
Problem: a boatman goes 4 km against the current of the stream in 4 hour and goes 1 km along the current in 20 minutes . how long will it take to go 6 km in stationary water ?
Options: a ) 5 hours , b ) 1 hours , c ) 3 hours , d ) 2 hours , e ) 4 hours
Rationale: speed upstream = 4 / 4 = 1 km / hr speed downstream = 1 / ( 20 / 60 ) = 3 km / hr speed in still water = 1 / 2 ( 3 + 1 ) = 2 km / hr time taken to travel 6 km in still water = 6 / 2 = 3 hours answer : c
Answer: c
Python program:
a = 1 / 20
b = a * const_60
c = 4 / 4
d = b + c 
e = d / 2
f = 6 / e
Problem: if z is a multiple of 7899 , what is the remainder when z ^ 2 is divided by 9 ?
Options: a ) 0 , b ) 2 , c ) 3 , d ) 6 , e ) 7
Rationale: the sum of the digits is 7 + 8 + 9 + 9 = 33 . thus 3 is a factor of 7899 , so 3 is a factor of z . then 3 ^ 3 = 9 is a factor of z ^ 2 . then the remainder when z ^ 2 is divided by 9 is 0 . the answer is a .
Answer: a
Python program:
a = 7899 / 3
b = a ** 2
c = b / 9
d = 9 - 2
e = 1000 * d
f = e * 100
g = 9 - 2
h = 1000 * g
i = h * 10
j = f + i 
k = 2 * 100
l = j + k 
m = 100 - 2
n = l + m 
o = c - n
p = o * 9
Problem: working alone , printers x , y , and z can do a certain printing job , consisting of a large number of pages , in 12 , 10 , and 20 hours , respectively . what is the ratio of the time it takes printer x to do the job , working alone at its rate , to the time it takes printers y and z to do the job , working together at their individual rates ?
Options: a ) 5 / 3 , b ) 7 / 4 , c ) 9 / 5 , d ) 11 / 6 , e ) 13 / 7
Rationale: "the time it takes printer x is 12 hours . the combined rate of y and z is 1 / 10 + 1 / 20 = 3 / 20 the time it takes y and z is 20 / 3 the ratio of times is 12 / ( 20 / 3 ) = 3 * 12 / 20 = 9 / 5 the answer is c ."
Answer: c
Python program:
a = 1 / 10
b = 1 / 20
c = a + b 
d = 1 / c
e = 12 / d
Problem: the width of a rectangular hall is ½ of its length . if the area of the hall is 288 sq . m , what is the difference between its length and breadth ?
Options: a ) 8 m , b ) 10 m , c ) 12 m , d ) 15 m , e ) 17 m
Rationale: "let the length of the hall be x m breadth of the hall = 1 x / 2 m area of the hall = length * breadth 288 = x * 1 x / 2 x ² = 576 x = 24 difference between the length and breadth of the hall = x - 1 x / 2 = x / 2 = 24 / 2 = 12 m answer : c"
Answer: c
Python program:
a = 1 / 2
b = 288 / a
c = math.sqrt(b)
d = c / 2
Problem: a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 9 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter of liquid a was contained by the can initially ?
Options: a ) 10 , b ) 20 , c ) 21 , d ) 25 , e ) 27
Rationale: using the values here might be the most straightforward way for this question . as a : b : : 7 : 5 - - - > only option c is a multiple of 7 and hence it is a good place to start . also a : b : : 7 : 5 means that , a = ( 712 ) * total and b = ( 5 / 12 ) * total if a = 21 , b = 15 - - - > remove 9 litres - - - > you remove ( 7 / 12 ) * 9 of a - - - > a remaining = 21 - ( 7 / 12 ) * 9 = 63 / 4 similarly , for b , you remove ( 5 / 12 ) * 9 - - - > b remaining = 15 - ( 5 / 12 ) * 9 = 45 / 4 and then add 9 more litres of b - - - > 9 + 45 / 4 = 81 / 4 thus a / b ( final ratio ) = ( 45 / 4 ) / ( 81 / 4 ) = 7 : 9 , the same as the final ratio mentioned in the question . hence c is the correct answer . fyi , the algebraic equations will become : a / b = 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) , where 7 x and 5 x are initial quantities of a and b respectively . thus , 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) - - - > giving you x = 3 . thus a ( original ) = 7 * 3 = 21 . answer : c
Answer: c
Python program:
a = 7 + 9 
b = 7 + 5 
c = 5 / b
d = c * 9
e = 9 - d
f = a * e
g = 9 * 7
h = 7 * 5
i = g - h
j = f / i
k = 7 * j
Problem: bert and rebecca were looking at the price of a condominium . the price of the condominium was 25 % more than bert had in savings , and separately , the same price was also 50 % more than rebecca had in savings . what is the ratio of what bert has in savings to what rebecca has in savings .
Options: a ) 1 : 5 , b ) 2 : 5 , c ) 3 : 5 , d ) 4 : 5 , e ) 1 : 1
Rationale: "suppose bert had 100 so price becomes 125 , this 125 = 1.5 times r ' s saving . . so r ' s saving becomes 250 so required ratio is 100 : 250 = 2 : 5 answer : b"
Answer: b
Python program:
a = 100 + 25 
b = 100 / a
c = 100 + 50 
d = 100 / c
e = b / d
Problem: a and b can do a piece of work in 45 days and 40 days respectively . they began to do the work together but a leaves after some days and then b completed the remaining work in 23 days . the number of days after which a left the work was
Options: a ) 5 days , b ) 6 days , c ) 7 days , d ) 9 days , e ) 8 days
Rationale: "does the job in 40 days = 1 / 40 a & b together completes the job = ? after a leaves , b completes the remaining job in 23 days . i . e b ' s part of job in 23 days = 23 / 40 remaining part 17 / 40 is done by a & b together in x no . of days . i . e ( x / 45 ) + ( x / 40 ) = 17 / 40 = > x = 9 days answer : d"
Answer: d
Python program:
a = 23 / 40
b = 1 - a
c = 1 / 45
d = 1 / 40
e = c + d 
f = b / e
Problem: virginia , adrienne , and dennis have taught history for a combined total of 75 years . if virginia has taught for 9 more years than adrienne and for 9 fewer years than dennis , for how many years has dennis taught ?
Options: a ) 23 , b ) 34 , c ) 35 , d ) 41 , e ) 44
Rationale: "let number of years taught by virginia = v number of years taught by adrienne = a number of years taught by dennis = d v + a + d = 75 v = a + 9 = > a = v - 9 v = d - 9 = > a = ( d - 9 ) - 9 = d - 18 d - 9 + d - 18 + d = 96 = > 3 d = 75 + 27 = 102 = > d = 34 answer b"
Answer: b
Python program:
a = 9 + 9 
b = a + 9 
c = 75 - b
d = c / 3
e = 9 + 9 
f = d + e
Problem: a big container is 40 % full with water . if 28 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container in liters ?
Options: a ) 68 , b ) 72 , c ) 76 , d ) 80 , e ) 84
Rationale: "28 liters is 35 % of the capacity c . 28 = 0.35 c c = 28 / 0.35 = 80 liters . the answer is d ."
Answer: d
Python program:
a = 3 / 4
b = 40 / 100
c = a - b
d = 28 / c
Problem: x starts a business with rs . 54000 . y joins in the business after 9 months with rs . 27000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 1 : 2 , b ) 2 : 1 , c ) 8 : 3 , d ) 3 : 5 , e ) 8 : 1
Rationale: "explanation : ratio in which they should share the profit = ratio of the investments multiplied by the time period = 54000 * 12 : 27000 * 3 = 54 * 12 : 27 * 3 = 2 * 4 : 1 = 8 : 1 . answer : option e"
Answer: e
Python program:
a = 54000 * 12
b = 4 + 3 
c = 27000 * b
d = a / c
Problem: at an international conference , “ red ” world countries and “ blue ” world countries are the only participants . the ratio of “ red ” world participants to “ blue ” world participants is 2 : 1 . if one - third of “ red ” world participants are left - handed and two - thirds of “ blue ” world participants are left - handed , then what is the fraction of the participants who are left - handed ?
Options: a ) 2 / 3 , b ) 4 / 5 , c ) 6 / 2 , d ) 5 / 2 , e ) 4 / 9
Rationale: "red : blue = 2 : 1 let red = 2 x and blue = 1 x 1 / 3 of red are left handed = > 1 / 3 * 2 x = 2 x / 3 red left handed 2 / 3 of blue are left handed = > 2 / 3 * 1 x = 2 x / 3 blue left handed fraction of participants who are left handed = total left handed / total participants = ( red left handed + blue left handed ) / total participants = ( 2 x / 3 + 2 x / 3 ) / ( 2 x + 1 x ) = 4 / 9 answer : e"
Answer: e
Python program:
a = 2 * const_0_33
b = 2 / 3
c = 1 * b
d = a + c 
e = 2 + 1 
f = d / e
Problem: if 4 men can colour 48 m long cloth in 2 days , then 6 men can colour 72 m long cloth in
Options: a ) 1 day , b ) 2 days , c ) 3 days , d ) 4 days , e ) 5 days
Rationale: "the length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m no . of days required to paint 36 m cloth by 6 men = 72 / 6 × 6 = 2 day . b"
Answer: b
Python program:
a = 4 * 2
b = 48 / a
c = b * 6
d = 72 / c
Problem: how many 4 digit even numbers do not use any digit more than once
Options: a ) 1720 , b ) 2160 , c ) 2240 , d ) 2460 , e ) 2520
Rationale: "a b c d ( thousand , hundreds , tens , units ) d can be 0 2 4 6 8 ( any of the 5 digits ) a can be anything except ( d or 0 ) so 8 possibilities c can be anything except a and b so 8 possibilities b can be anything except ( a d c ) so 7 possibilities total ways are 8 * 7 * 8 * 5 = 2240 ans : c"
Answer: c
Python program:
a = 1000 - 10
b = 4 * 4
c = 10 * b
d = 4 * 2
e = c * d
f = a - e
g = f + 10
Problem: calculate the speed of a boat in still water ( in km / hr ) if in one hour , the boat goes 10 km / hr downstream and 4 km / hr upstream .
Options: a ) 7 kmph , b ) 8 kmph , c ) 9 kmph , d ) 7 kmph , e ) 6 kmph
Rationale: speed in still water = ( 10 + 4 ) 1 / 2 kmph = 7 kmph . answer : a
Answer: a
Python program:
a = 10 + 4 
b = a / 2
Problem: how many times digit 10 is used while writing numbers from 100 to 1000 ?
Options: a ) 100 , b ) 90 , c ) 85 , d ) 110 , e ) 120
Rationale: "in 100 to 300 there are 20 ten ' s in 300 to 500 there are 20 ten ' s in 500 to 700 there are 20 ten ' s in 700 t 0 900 there are 20 ten ' s in 900 to 1000 there are 10 ten ' s so total is 90 ten ' s correct option : b"
Answer: b
Python program:
a = 1000 - 100
b = a / 10
c = 10 + 1 
d = 10 + 1 
e = c * d
f = b + e 
g = 10 * 2
h = f + g
Problem: jacob is 10 years old . he is 5 times as old as his brother . how old will jacob be when he is twice as old ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: "j = 10 ; j = 5 b ; b = 10 / 5 = 2 ; twice as old so b = 2 ( now ) + ( 2 ) = 4 ; jacob is 10 + 4 = 14 answer : b"
Answer: b
Python program:
a = 10 * 5
Problem: the cash difference between the selling prices of an article at a profit of 4 % and 6 % 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 = 104 % of x / 106 % of x = 104 / 106 = 52 / 53 = 52 : 53 option b"
Answer: b
Python program:
a = 100 + 4 
b = 100 + 6 
c = a / b
Problem: a steel vessel has a base of length 60 cm and breadth 30 cm . water is poured in the vessel . a cubical steel box having edge of 30 cm is immersed completely in the vessel . how much will the water rise ?
Options: a ) 7.5 cm rise
b ) 10 cm rise
c ) 15 cm rise
d ) 30 cm rise
e ) none of these
Rationale: explanation : volume of cube = a 3 = a * a * a 60 cm * 30 cm * h = 30 cm * 30 cm * 30 cm h = 15 cm answer is c
Answer: c
Python program:
a = 30 ** 3
b = 60 * 30
c = a / b
Problem: a 3 - digit number 4 a 3 is added to another 3 - digit number 984 to give a 4 - digit number 13 b 7 , which is divisible by 11 . then , ( a + b ) = ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 15 , e ) 16
Rationale: 4 a 3 | 9 8 4 } = = > a + 8 = b = = > b - a = 8 13 b 7 | also , 13 b 7 is divisible by 11 = > ( 7 + 3 ) – ( b + 1 ) = ( 9 – b ) ( 9 – b ) = 0 b = 9 ( b = 9 and a = 1 ) = > ( a + b ) = 10 . answer a
Answer: a
Python program:
a = 3 * 3
b = a + 1
Problem: if 3 ^ x * 4 ^ y = 19,683 and x – y = 9 , then x = ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: since 19,683 is an odd number , it is not a multiple of 4 . this means that y must equal zero . since x - y = 9 and y = 0 , then x = 9 . the answer is b .
Answer: b
Python program:
a = 9 * 1
Problem: in what time will a railway train 64 m long moving at the rate of 46 kmph pass a telegraph post on its way ?
Options: a ) 3 , b ) 5 , c ) 4 , d ) 6 , e ) 7
Rationale: "t = 64 / 46 * 18 / 5 = 5 sec answer : b"
Answer: b
Python program:
a = 46 * const_0_2778
b = 64 / a
Problem: matt gets a $ 1,600 commission on a big sale . this commission alone raises his average commission by $ 150 . if matt ' s new average commission is $ 400 , how many sales has matt made ?
Options: a ) 9 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let , average commission = x no . of items sold = y total commission = xy new commission = xy + 1600 new average = ( xy + 1600 ) / ( y + 1 ) = 150 + x i . e . ( xy + 1600 ) = ( y + 1 ) * ( 150 + x ) i . e . ( xy + 1600 ) = ( xy + x + 150 y + 150 ) i . e . ( 1450 ) = ( x + 150 y ) new commission = 400 = 150 + x i . e . x = 250 i . e . y = 8 new sales = y + 1 = 9 answer : option a"
Answer: a
Python program:
a = 1 - 600
b = 400 - 150
c = 400 - b
d = a / c
Problem: if the sides of a triangle are 30 cm , 28 cm and 14 cm , what is its area ?
Options: a ) 196 cm 2 , b ) 187 cm 2 , c ) 178 cm 2 , d ) 189 cm 2 , e ) 176 cm 2
Rationale: "the triangle with sides 30 cm , 28 cm and 14 cm is right angled , where the hypotenuse is 30 cm . area of the triangle = 1 / 2 * 28 * 14 = 196 cm 2 answer : a"
Answer: a
Python program:
a = 28 * 14
b = a / 2
Problem: find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 1232 ?
Options: a ) 1000 , b ) 2217 , c ) 1100 , d ) 2777 , e ) 2991
Rationale: "1232 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 1100 answer : c"
Answer: c
Python program:
a = 2 * 5
b = a + 2 
c = b / 5
d = c * 5
e = d / 100
f = e + 1 
g = 1232 / f
Problem: a group of students was interviewed for that if it was asked whether or not they speak french and / or english . among those who speak french , 30 speak english well , while 40 of them do not speak english . if 86 % of students do not speak french , how many students were surveyed ?
Options: a ) 500 , b ) 450 , c ) 250 , d ) 350 , e ) 525
Rationale: "number of students who speak french are 30 + 40 = 70 of total students , the percentage of students who do not speak french was 86 % - - > percentage of who do is 14 % 70 - - - - - - - 14 % x - - - - - - - 100 % x = 70 * 100 / 14 = 500 = number of all students answer is a"
Answer: a
Python program:
a = 30 + 40 
b = 100 - 86
c = b / 100
d = a / c
Problem: the parameter of a square is equal to the perimeter of a rectangle of length 4 cm and breadth 2 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places ) ?
Options: a ) 4.51 , b ) 4.71 , c ) 4.32 , d ) 4.21 , e ) 4.68
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 4 + 2 ) = 12 cm parameter of the square = 12 cm i . e . 4 a = 12 a = 3 diameter of the semicircle = 3 cm circimference of the semicircle = 1 / 2 ( â ˆ  ) ( 3 ) = 1 / 2 ( 22 / 7 ) ( 3 ) = 66 / 14 = 4.71 cm to two decimal places answer : b"
Answer: b
Python program:
a = square_edge_by_perimeter / (
b = circumface / (
Problem: 15 different biology books and 8 different chemistry books lie on a shelf . in how many ways can a student pick 2 books of each type ?
Options: a ) 80 , b ) 160 , c ) 720 , d ) 2100 , e ) 2940
Rationale: "no . of ways of picking 2 biology books ( from 15 books ) = 15 c 2 = ( 15 * 14 ) / 2 = 105 no . of ways of picking 2 chemistry books ( from 8 books ) = 8 c 2 = ( 8 * 7 ) / 2 = 28 total ways of picking 2 books of each type = 105 * 28 = 2940 ( option e )"
Answer: e
Python program:
a = math.factorial(15)
b = 15 - 2
c = math.factorial(b)
d = a / c
e = d / 2
f = math.factorial(8)
g = 8 - 2
h = math.factorial(g)
i = f / h
j = i / 2
k = e * j
Problem: a and b can do a piece of work in 10 days . with the help of c they finish the work in 5 days . c alone can do that piece of work in ?
Options: a ) 33 , b ) 878 , c ) 30 , d ) 10 , e ) 11
Rationale: "c = 1 / 5 â € “ 1 / 10 = 1 / 10 = > 10 days answer : d"
Answer: d
Python program:
a = 5 / 10
b = 5 - a
c = 1/(b)
Problem: a computer factory produces 6048 computers per month at a constant rate , how many computers are built every 30 minutes assuming that there are 28 days in one month ?
Options: a ) 2.25 . , b ) 3.125 . , c ) 4.5 . , d ) 5.225 . , e ) 6.25 .
Rationale: "number of hours in 28 days = 28 * 24 number of 30 mins in 28 days = 28 * 24 * 2 number of computers built every 30 mins = 6048 / ( 28 * 24 * 2 ) = 4.5 answer c"
Answer: c
Python program:
a = 6048 / 28
b = 28 - 4
c = b * 2
d = a / c
Problem: find the greatest number which on dividing 1428 and 2206 , leaves a reminder of 9 and 13 respectively
Options: a ) 125 , b ) 127 , c ) 129 , d ) 131 , e ) 141
Rationale: "explanation : in this type of question , its obvious we need to calculate the hcf , trick is hcf of ( 1428 - 9 ) and ( 2206 - 13 ) = hcf ( 1419 , 2193 ) = 129 option c"
Answer: c
Python program:
a = 1428 - 9
b = 2206 - 13
c = math.gcd(a, b)