euclaise/mathqa_programs huggingface dataset:
Problem: the sale price sarees listed for rs . 400 after successive discount is 15 % and 5 % is ?
Options: a ) 297 , b ) 879 , c ) 323 , d ) 762 , e ) 269
Rationale: "400 * ( 85 / 100 ) * ( 95 / 100 ) = 323 answer : c"
Answer: c
Python program:
a = 400 * 15
b = a / 100
c = 400 - b
d = 400 * 15
e = d / 100
f = 400 - e
g = f * 5
h = g / 100
i = c - h
Problem: efrida and frazer who live 15 miles apart , meet at a restaurant that is directly north of efrida ' s home and directly east of frazer ' s home . if the restaurant is two miles closer to efrida ' s home , than to frazer ' s home , how many miles is the restaurant from frazer ' s home ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 10 , e ) 13
Rationale: it ' s a simple geometry problem . look at the diagram below : answer : e .
Answer: e
Python program:
a = 15 ** 2
b = 2 ** 2
c = a - b
d = c / 2
e = math.sqrt(d)
f = e + 2
Problem: the sum of two consecutive integers is 15 . find the numbers .
Options: a ) 17 , 18 , b ) 7 , 8 , c ) 5 , 6 , d ) 1 , 2 , e ) 8 , 9
Rationale: "n + ( n + 1 ) = 15 2 n + 1 = 15 2 n = 14 n = 7 answer : b"
Answer: b
Python program:
a = 15 - 10
b = a - 2
c = b / 4
d = c + 2 
e = d + 2 
f = e ** 2
g = 15 - 10
h = g - 2
i = h / 4
j = i + 2 
k = j + 2 
l = k + 2 
m = l ** 2
n = f + m 
o = 15 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 15 - 10
t = s - 2
u = t / 4
v = u + 2 
w = v ** 2
x = r + w 
y = n + x
Problem: a and b are two partially filled buckets of water . if 3 liters are transferred from a to b , then a would contain one - third of the amount of water in b . alternatively , if 5 liters are transferred from b to a , b would contain one - half of the amount of water in a . bucket a contains how many liters of water ?
Options: a ) 11 , b ) 13 , c ) 39 / 5 , d ) 21 , e ) 23
Rationale: "let a contains a , b contains b liters so , ( a - 3 ) / ( b + 3 ) = 1 / 3 . . . . . . . ( 1 ) again , ( b - 5 ) / ( a + 5 ) = 1 / 2 . . . . . . . . . . ( 2 ) from ( 1 ) ( 2 ) we find a = 39 / 5 ans : ( c )"
Answer: c
Python program:
a = 3 + 3 
b = a + 2 
c = 3 / 2
d = b * c
e = 1 / 2
f = 2 + e 
g = d / f
Problem: a space shuttle orbits the earth at about 2 kilometers per second . this speed is equal to how many kilometers per hour ?
Options: a ) 7,200 , b ) 8,880 , c ) 10,800 , d ) 28,800 , e ) 48,000
Rationale: "seconds in 1 hours : 60 s in 1 min 60 min in 1 hr 60 * 60 = 3600 sec in 1 hr 2 * 3600 = 28,800 answer : a"
Answer: a
Python program:
a = 2 * 3600
Problem: a train 220 m long is running with a speed of 59 kmph . . in what will it pass a man who is running at 7 kmph in the direction opposite to that in which the train is going
Options: a ) 8 sec , b ) 10 sec , c ) 12 sec , d ) 14 sec , e ) 15 sec
Rationale: "explanation : speed of the train relative to man = ( 59 + 7 ) kmph = 66 × 5 / 18 m / sec = 55 / 3 m / sec . time taken by the train to cross the man = time taken by it to cover 220 m at ( 55 / 3 ) m / sec = ( 220 × 3 / 55 ) sec = 12 sec answer : option c"
Answer: c
Python program:
a = 220 / 1000
b = 59 - 7
c = a / b
d = c * 3600
Problem: each week , harry is paid x dollars per hour for the first 35 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 41 hours if harry and james were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 35 , b ) 36 , c ) 34 , d ) 38 , e ) 39
Rationale: "james worked for 41 hours hence he earned 40 * x + 1 * 2 x = 42 x dollars ; we know that harry also earned the same 42 x dollars , out of which he earned 35 x dollars for thefirst 35 hoursplus 7 x additional dollars . since for each additional hour he gets 1.5 x dollars then he worked for 7 x / 1.5 x = 4 additional hours , so harry worked for total of 30 + 4 = 34 hours . answer : c ."
Answer: c
Python program:
a = 40 + 2 
b = a - 35
c = b / 1
d = c + 35
Problem: in what time will a railway train 80 m long moving at the rate of 36 kmph pass a telegraph post on its way ?
Options: a ) 4 sec , b ) 7 sec , c ) 2 sec , d ) 6 sec , e ) 8 sec
Rationale: "t = 80 / 36 * 18 / 5 = 8 sec answer : e"
Answer: e
Python program:
a = 36 * const_0_2778
b = 80 / a
Problem: two equilateral triangles of side 12 cm are placed one on top of another , such that a 6 pointed star is formed . if the six verticals lie on a circle what is the area of the circle not enclosed by the star ?
Options: a ) 68
b ) 83
c ) 57
d ) 61
e ) 62
Rationale: area of star = √ 3 / 4 * ( 12 ) ^ 2 + 3 * √ 3 / 4 * ( 12 / 3 ) ^ 2 = 48 √ 3 if r be radius of circle then r = 6 / cos 30 = > r = 12 / √ 3 = > r ^ 2 = 48 area of circle = pi * 48 area of the circle not enclosed by the star = 48 * pi - 48 √ 3 = 48 ( 3.14 - 1.732 ) = 68 ( approax ) answer : a
Answer: a
Python program:
a = math.sqrt(3)
b = a / 2
c = b * 12
d = c * 2
e = d / 3
f = circle_area - (
Problem: jaclyn buys $ 30 000 worth of debentures in a company . she earns 9.5 % p . a . simple interest , paid to her quarterly ( that is , every 3 months ) . if the agreed period of the debenture was 18 months : calculate the amount of interest jaclyn will earn for each quarter
Options: a ) 712.5 , b ) 1234 , c ) 1289 , d ) 1345 , e ) none of these
Rationale: "explanation : i = ( p x r x t ) / 100 = 30000 * 9.5 / 100 * ( 18 / 12 ) ^ 1 / 6 = 712.50 answer : a"
Answer: a
Python program:
a = 100 * 100
b = a * 9
c = b / 100
d = c / 4
Problem: the average of 6 observations is 12 . a new seventh observation is included and the new average is decreased by 1 . the seventh observation is :
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 8
Rationale: "explanation : seventh observation = ( 7 × × 11 - 6 × × 12 ) = 5 correct option : c"
Answer: c
Python program:
a = 12 - 1
b = 6 + 1 
c = a * b
d = 12 * 6
e = c - d
Problem: for a certain art exhibit , a museum sold admission tickets to a group of 30 people every 5 minutes from 9 : 00 in the morning to 5 : 55 in the afternoon , inclusive . the price of a regular admission ticket was $ 10 and the price of a student ticket was $ 5 . if on one day 3 times as many regular admission tickets were sold as student tickets , what was the total revenue from ticket sales that day ?
Options: a ) $ 24960 , b ) $ 25920 , c ) $ 28080 , d ) $ 28350 , e ) $ 29160
Rationale: "from 9 : 00 in the morning to 5 : 55 in the afternoon , inclusive there are 9 * 12 = 108 five - minute intervals , thus total of 108 * 30 tickets were sold . say x student and 3 x regular tickets were sold , then x + 3 x = 108 * 30 - - > x = 27 * 30 and 3 x = 3 * ( 27 * 30 ) = 27 * 90 . therefore , the total revenue from ticket sales that day was 27 * 30 * 5 + 27 * 90 * 10 = $ 28,350 . answer : d ."
Answer: d
Python program:
a = 12 + 5 
b = a - 9
c = b + 1 
d = c * 12
e = d * 30
f = 3 + 1 
g = e / f
h = g * 3
i = h * 10
j = 12 + 5 
k = j - 9
l = k + 1 
m = l * 12
n = m * 30
o = 3 + 1 
p = n / o
q = p * 5
r = i + q
Problem: how many factors of 880 are odd numbers greater than 1 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: when factorized , 880 has 6 prime factors . of these prime factors 2 are odd and 4 are even . hence total number of odd factors is 2 * 2 ( 4 ) , which includes 4 . the total number of odd factors greater than 1 are 3 . ( option a )
Answer: a
Python program:
a = 10 * 2
b = const_60 / 0
Problem: how many multiples of 9 are there between 18 and 270 ?
Options: a ) 12 , b ) 27 , c ) 42 , d ) 61 , e ) 60
Rationale: "it should be mentioned whether 18 and 270 are inclusive . if 18 and 270 are inclusive , then the answer is ( 270 - 18 ) / 9 + 1 = 29 . if 18 and 270 are not inclusive , then the answer is ( 261 - 27 ) / 9 + 1 = 27 . since oa is b , then we have not inclusive case ."
Answer: b
Python program:
a = 270 - 18
b = a / 9
c = b + 1
Problem: if it takes 30 construction workers 70 days to build a skyscraper , how long would it take 50 workers ?
Options: a ) 52 days , b ) 47 days , c ) 42 days , d ) 37 days , e ) 32 days
Rationale: 30 * 70 = 50 * x x = 42 answer : c
Answer: c
Python program:
a = 70 * 30
b = a / 50
Problem: there are thirty - 4 lines that are tangent to a circle , and these lines create regions in the plane . can you tell how many of these regions are not enclosed ?
Options: a ) 50 , b ) 74 , c ) 37 , d ) 77 , e ) 68
Rationale: e 68 68 regions . each new tangent increases the non - enclosed areas by two
Answer: e
Python program:
a = 4 * 10
b = 2 * 10
c = a + b 
d = 4 * 2
e = c + d
Problem: 2 cow ’ s and 8 goats are brought for rs . 1400 . if the average price of a goat be rs . 60 . what is the average price of a cow .
Options: a ) rs . 480 , b ) rs . 960 , c ) rs . 960 , d ) rs . 460 , e ) rs . 560
Rationale: explanation : average price of a goat = rs . 60 total price of 8 goats = 8 * 60 = rs . 480 but total price of 2 cows and 8 goats = rs . 1400 total price of 2 cows is = 1400 - 480 = 980 average price of a cow = 980 / 2 = rs . 460 answer : option d
Answer: d
Python program:
a = 8 * 60
b = 1400 - a
c = b / 2
Problem: 1 = 6,2 = 36,3 = 363,4 = 364,5 = 365 , then 36 = ?
Options: a ) 1 , b ) 2 , c ) 345 , d ) 445 , e ) 235
Rationale: 1 = 6,2 = 36,3 = 363,4 = 364,5 = 365 , then 36 = ? 36 = 2 check the second eqn . answer : b
Answer: b
Python program:
a = 4 + 2 
b = 4 + 2 
c = a * b
d = c * 10
e = 365 - d
f = e - 1
g = f / 2
Problem: p alone can complete a job in 6 days . the work done by q alone in one day is equal to one - fifth 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 ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "p ' s rate is 1 / 6 q ' s rate is 1 / 30 the combined rate is 1 / 6 + 1 / 30 = 1 / 5 if they work together , the job will take 5 days . the answer is e ."
Answer: e
Python program:
a = 1 / 6
b = 1 / 6
c = b / 3
d = a + c 
e = 1 / d
Problem: 60 % of a number is added to 150 , the result is the same number . find the number ?
Options: a ) 375 , b ) 277 , c ) 266 , d ) 99 , e ) 121
Rationale: ": ( 60 / 100 ) * x + 150 = x 2 x = 750 x = 375 answer : a"
Answer: a
Python program:
a = 150 / 100
b = 150 / a
Problem: x , y , and z are different prime numbers . the product x ^ 3 * y ^ 2 * z ^ 2 is divisible by how many different positive numbers ?
Options: a ) 24 , b ) 36 , c ) 48 , d ) 60 , e ) 72
Rationale: "the exponents of x ^ 3 * y ^ 2 * z ^ 2 are 3 , 2 , and 2 . the number of factors is ( 3 + 1 ) ( 2 + 1 ) ( 2 + 1 ) = 36 the answer is b ."
Answer: b
Python program:
a = 3 ** 4
b = a - 4
Problem: what is the smallest integer that is multiple of 87 and 20
Options: a ) 141 , b ) 180 , c ) 130 , d ) 122 , e ) 280
Rationale: correct answer : e it is the lcm of 8,7 and 20 which is 280
Answer: e
Python program:
a = math.lcm(87, 20)
b = a / 12
c = b * 2
Problem: two employees x and y are paid a total of rs . 600 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
Options: a ) s . 200.72 , b ) s . 250.72 , c ) s . 272.72 , d ) s . 300.72 , e ) s . 310.72
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 600 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 600 ⇒ y [ 12 / 10 + 1 ] = 600 ⇒ 22 y / 10 = 600 ⇒ 22 y = 6000 ⇒ y = 6000 / 22 = rs . 272.72 c"
Answer: c
Python program:
a = 1 + 4 
b = a * 2
c = 600 * b
d = 1 + 4 
e = d * 2
f = e + 1 
g = f * 2
h = c / g
Problem: a reduction of 20 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 800 , what is the reduced price for kg ?
Options: a ) s . 42 , b ) s . 46 , c ) s . 40 , d ) s . 41 , e ) s . 32
Rationale: "800 * ( 20 / 100 ) = 160 - - - - 5 ? - - - - 1 = > rs . 32 answer : e"
Answer: e
Python program:
a = 800 * 20
b = a / 100
c = b / 5
Problem: mary ' s income is 40 percent more than tim ' s income , and tim ' s income is 40 percent less than juan ' s income . what percent of juan ' s income is mary ' s income ?
Options: a ) 124 % , b ) 120 % , c ) 96 % , d ) 80 % , e ) 84 %
Rationale: "juan ' s income = 100 ( assume ) ; tim ' s income = 60 ( 40 percent less than juan ' s income ) ; mary ' s income = 84 ( 40 percent more than tim ' s income ) . thus , mary ' s income ( 84 ) is 84 % of juan ' s income ( 100 ) . answer : e ."
Answer: e
Python program:
a = 40 / 100
b = 1 - a
c = 40 / 100
d = 1 + c 
e = b * d
f = e * 100
Problem: kim has 40 percent more money than sal and sal has 20 percent less money than phil . if sal and phil have a combined total of $ 1.80 , how much money does kim have ?
Options: a ) $ 1.00 , b ) $ 1.12 , c ) $ 1.20 , d ) $ 1.32 , e ) $ 1.40
Rationale: phil = x sal = 0.8 x kim = ( 1.4 ) * 0.8 x = 1.12 x x + 0.8 x = 1.8 - - > x = 1 kim = 1.12 answer : b
Answer: b
Python program:
a = 100 - 20
b = 100 + a 
c = 1 / 8
d = 100 - 20
e = 100 + 40 
f = d * e
g = f / 100
h = c * g
Problem: a gambler bought $ 3,000 worth of chips at a casino in denominations of $ 20 and $ 100 . that evening , the gambler lost 14 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 ) $ 2,240 , 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 14 : x + x - 2 = 14 - - > x = 8 : 8 $ 20 chips were lost and 8 - 2 = 6 $ 100 chips were lost . total worth of chips lost is 8 * 20 + 6 * 100 = $ 760 , so the gambler kept $ 3,000 - $ 760 = $ 2,240 . answer : a ."
Answer: a
Python program:
a = 3 * 1000
b = 14 + 2 
c = b / 2
d = c * 20
e = 14 + 2 
f = e / 2
g = f - 2
h = g * 100
i = d + h 
j = a - i
Problem: a dress on sale in a shop is marked at $ d . during the discount sale its price is reduced by 35 % . staff are allowed a further 30 % reduction on the discounted price . if a staff member buys the dress what will she have to pay in terms of d ?
Options: a ) 0.555 d , b ) 0.765 d , c ) 0.455 d , d ) 0.785 d , e ) 0.805 d
Rationale: "effective discount = a + b + ab / 100 = - 35 - 30 + ( - 35 ) ( - 30 ) / 100 = - 54.5 sale price = d * ( 1 - 54.5 / 100 ) sale price = . 455 * d answer ( c )"
Answer: c
Python program:
a = 100 - 35
b = a / 100
c = 100 - 35
d = c / 100
e = 30 / 100
f = d * e
g = b - f
Problem: the number of boxes in a warehouse can be divided evenly into 6 equal shipments by boat or 28 equal shipments by truck . what is the smallest number of boxes that could be in the warehouse ?
Options: a ) 27 , b ) 33 , c ) 84 , d ) 81 , e ) 162
Rationale: "answer is the lcm of 6 and 28 = 84 answer c"
Answer: c
Python program:
a = 2 * 2
b = a * 2
c = b * 3
d = c * 6
Problem: if k ^ 3 is divisible by 336 , what is the least possible value of integer k ?
Options: a ) 56 , b ) 70 , c ) 84 , d ) 96 , e ) 120
Rationale: "k ^ 3 = 336 * x = 2 ^ 4 * 3 * 7 * x the factors of k must at minimum include 2 ^ 2 * 3 * 7 = 84 . the answer is c ."
Answer: c
Python program:
a = 336 / 2
b = a / 2
Problem: there are 6 boxes numbered 1 , 2 , . . . 6 . each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered . the total number of ways in which this can be done is
Options: a ) 5 , b ) 21 , c ) 33 , d ) 60 , e ) 40
Rationale: given the constraints of this question , we have to consider 6 possible outcomes . . . 1 green ball : 6 options grrrrr rgrrrr rrgrrr rrrgrr rrrrgr rrrrrg 2 green balls : 5 options ggrrrr rggrrr rrggrr rrrggr rrrrgg 3 green balls : 4 options gggrrr rgggrr rrgggr rrrggg 4 green balls : 3 options ggggrr rggggr rrgggg 5 green balls : 2 options gggggr rggggg 6 green balls : 1 option gggggg 6 + 5 + 4 + 3 + 2 + 1 = 21 options . b
Answer: b
Python program:
a = 6 - 1
b = 6 + a 
c = 6 - 1
d = c - 1
e = b + d 
f = 6 - 1
g = f - 1
h = g - 1
i = e + h 
j = i + 2
Problem: a man walked diagonally across a square lot . approximately , what was the percent saved by not walking along the edges ?
Options: a ) 20 %
b ) 30 %
c ) 40 %
d ) 50 %
e ) 55 %
Rationale: let the side of the square ( abcd ) be x metres . then , ab + bc = 2 x metres . ac = 2 x = ( 1.41 x ) m . saving on 2 x metres = ( 0.59 x ) m . saving % = ( 0.59 x ) / 2 x x 100 % = 30 % ( approx . ) b )
Answer: b
Python program:
a = 1 ** 2
b = 1 ** 2
c = a + b 
d = 1 ** 2
e = 1 ** 2
f = d + e 
g = math.sqrt(f)
h = c - g
i = h * 100
j = 1 ** 2
k = 1 ** 2
l = j + k 
m = i / l
Problem: rs . 500 amounts to rs . 670 in 5 years at simple interest . if the interest is increased by 2 % , it would amount to how much ?
Options: a ) 150 , b ) 550 , c ) 760 , d ) 450 , e ) 260
Rationale: ( 500 * 5 * 2 ) / 100 = 50 500 + 50 = 550 answer : b
Answer: b
Python program:
a = 2 / 100
b = 1 + a 
c = b ** 5
d = c * 500
Problem: the lcm and hcf of two numbers are 10000 and 1000 respectively . find the larger of the two numbers if their sum is 11000 .
Options: a ) 10000 , b ) 562 , c ) 352 , d ) 576 , e ) 594
Rationale: "there are 2 approaches in solving this . methode 1 . hcf * lcm = the actual number . 10000 * 1000 = 10000000 so the answer which we are looking for has to be a factor of 10000000 . so among the options shortlist the answers by eliminating those numbers which is not divisible by 10000000 . and then take the highest number as the answer as the question asks abt the highest number . answer is a"
Answer: a
Python program:
a = 10000 * 1000
b = a / 11000
Problem: a cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 10 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 4.3 hrs , b ) 8.9 hrs , c ) 2.9 hrs , d ) 7.2 hrs , e ) 8.6 hrs
Rationale: "net part filled in 1 hour = ( 1 / 3 - 1 / 10 ) = 7 / 30 the cistern will be filled in 30 / 7 hrs i . e . , 4.3 hrs . answer : a"
Answer: a
Python program:
a = 1 / 3
b = 1 / 10
c = a - b
d = 1 / c
Problem: a software engineer starts from home at 3 pm for every walk on a route which has level road for some distance and a then a hillock . he walks speed of 4 kmph on level ground and then at a speed of 3 kmph on the uphill and then down the hill at a speed of 6 kmph to the level ground and then at a speed of 4 kmph to the home if he reaches home at 9 pm . what is the distance one way of his route ?
Options: a ) 12 km , b ) 15 km , c ) 18 km , d ) 24 km , e ) data inadequate
Rationale: time = distance / speed so , let the distance to the level road from home be x km and the distance to the hillock from the level road be y km so , ( x / 4 + y / 3 ) + ( y / 6 + x / 4 ) = 6 x + y = 12 km . answer : a
Answer: a
Python program:
a = 9 - 3
b = 6 + 4 
c = 4 + 3 
d = b + c 
e = d / 4
f = e - const_0_25
g = a * f
h = g / 2
Problem: a box contains either blue or red flags . the total number of flags in the box is an even number . a group of children are asked to pick up two flags each . if all the flags are used up in the process such that 60 % of the children have blue flags , and 60 % have red flags , what percentage of children have flags of both the colors ?
Options: a ) 5 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) it can not be determined
Rationale: "solution : let the total number of flags be 100 ( even number ) let the total number of ' blue ' flags alone be ' a ' let the total number of ' red ' flags alone be ' b ' let the total number of ' both ' flags be ' c ' we have given , total number of blue flags = 60 % = 60 = a + c total number of red flags = 55 % = 55 = b + c total number of flags = a + b + c = 100 ( since all the flags have been utilized ) so , substituting for c in the third equation , we have , 60 - c + c + 60 - c = 100 c = 20 option d ."
Answer: d
Python program:
a = 60 + 60 
b = a - 100
Problem: there are 30 balls which are red , blue or green . if 11 balls are green and the sum of red balls and green balls is less than 25 , at most how many red balls are there ?
Options: a ) 14 , b ) 13 , c ) 16 , d ) 17 , e ) 8
Rationale: "r + g + b = 30 g = 11 r + g < 25 = > r + 11 < 25 = > r < 14 = > at most 13 red balls answer : b"
Answer: b
Python program:
a = 11 - 1
Problem: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 3000 resolutions ?
Options: a ) 2187 m , b ) 3704 m , c ) 4179 m , d ) 4224 m , e ) 4297 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 3000 resolutions . = 3000 * 2 * 22 / 7 * 22.4 = 422400 cm = 4224 m answer : d"
Answer: d
Python program:
a = 3 + 4 
b = a * 3
c = b + 1 
d = 3 + 4 
e = c / d
f = e * 22
g = f * 2
h = g * 3000
i = h / 100
Problem: half a number plus 6 is 11 . what is the number ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: let x be the number . always replace ` ` is ' ' with an equal sign ( 1 / 2 ) x + 6 = 11 ( 1 / 2 ) x = 11 - 6 ( 1 / 2 ) x = 5 x = 10 correct answer is c
Answer: c
Python program:
a = 11 - 6
b = a * 2
Problem: n ^ ( n / 2 ) = 6 is true when n = 6 in the same way what is the value of n if n ^ ( n / 2 ) = 10 ?
Options: a ) 8 , b ) 12 , c ) 10 , d ) 16 , e ) 18
Rationale: n ^ ( n / 2 ) = 10 apply log n / 2 logn = log 10 nlogn = 2 log 10 = log 10 ^ 2 = log 100 logn = log 100 now apply antilog n = 100 / n now n = 10 . answer : c
Answer: c
Python program:
a = 10 ** 2
b = a / 10
Problem: the average age of 11 boys is 50 , if the average age of first 6 boys is 49 and that of the last 6 is 52 . find the boy age ?
Options: a ) 48 , b ) 50 , c ) 56 , d ) 62 , e ) 64
Rationale: 1 to 11 = 11 * 50 = 550 1 to 6 = 6 * 49 = 294 6 to 11 = 6 * 52 = 312 6 th = 294 + 312 – 550 = 56 c
Answer: c
Python program:
a = 6 * 52
b = 11 * 50
c = 6 * 49
d = b - c
e = a - d
Problem: after successive discounts of 20 % , 10 % and 5 % a certain good is sold for rs . 6840 . find the actual price of the good .
Options: a ) rs . 6000 , b ) rs . 9000 , c ) rs . 10800 , d ) rs . 10000 , e ) rs . 9980
Rationale: "let actual price was 100 . after three successive discount this will become , 100 = = 20 % discount = > 80 = = 10 % discount = > 72 = = 5 % discount = 68.4 now compare , 68.4 = 6840 1 = 6840 / 68.4 100 = ( 6840 * 100 ) / 68.4 = rs . 10,000 . answer : option d"
Answer: d
Python program:
a = 6840 * 100
b = 100 - 20
c = 100 - 20
d = c * 10
e = d / 100
f = b - e
g = 100 - 20
h = 100 - 20
i = h * 10
j = i / 100
k = g - j
l = k * 5
m = l / 100
n = f - m
o = a / n
Problem: a rope of which a calf is tied is increased from 9 m to 23 m , how much additional grassy ground shall it graze ?
Options: a ) 1218 , b ) 1212 , c ) 1408 , d ) 2707 , e ) 2591
Rationale: "π ( 232 – 92 ) = 1408 answer : c"
Answer: c
Python program:
a = 23 ** 2
b = 10 ** 2
c = a - b
d = 9 * 2
e = d + 2 
f = 4 + 3 
g = e / f
h = c * g
Problem: what is the value of 3 x ^ 2 − 1.6 x + 0.3 for x = 0.8 ?
Options: a ) − 0.3 , b ) 0 , c ) 0.3 , d ) 0.94 , e ) 2.46
Rationale: "3 x ^ 2 - 1.6 x + 0.3 for x = 0.6 = 3 ( 0.8 * 0.8 ) - 2 * 0.8 * ( 0.8 ) + 0.3 = 0.8 * 0.8 + 0.3 = 0.94 correct option : d"
Answer: d
Python program:
a = 3 ** 2
b = 1 ** 6
c = a - b
d = c / 1000
e = d / 1000
f = e * 3
g = 3 ** 2
h = 1 ** 6
i = g - h
j = i / 1000
k = j / 1000
l = f - k
Problem: in a school of 900 students , 44 % wear blue shirts , 28 % wear red shirts , 10 % wear green shirts , and the remaining students wear other colors . how many students wear other colors ( not blue , not red , not green ) ?
Options: a ) 144 , b ) 153 , c ) 162 , d ) 171 , e ) 180
Rationale: "44 + 28 + 10 = 82 % 100 – 82 = 18 % 900 * 18 / 100 = 162 the answer is c ."
Answer: c
Python program:
a = 44 / 100
b = a * 900
c = 28 / 100
d = c * 900
e = b + d 
f = 10 / 100
g = f * 900
h = e + g 
i = 900 - h
Problem: if c is 14 % of a and 40 % of b , what percent of a is b ?
Options: a ) 2.5 % , b ) 15 % , c ) 25 % , d ) 35 % , e ) 250 %
Rationale: "answer = d 14 a / 100 = 40 b / 100 b = 14 a / 40 = 35 a / 100 = 35 %"
Answer: d
Python program:
a = 14 / 100
b = 40 / 100
c = a / b
d = c * 100