euclaise/mathqa_programs huggingface dataset:
Problem: a , b and c invested rs . 8000 , rs . 4000 and rs . 8000 respectively in a business . a left after six months . if after eight months , there was a gain of rs . 4005 , then what will be the share of b ?
Options: a ) rs 690 , b ) rs 790 , c ) rs 890 , d ) rs 990 , e ) none of these
Rationale: "explanation : a : b : c = ( 8000 * 6 ) : ( 4000 * 8 ) : ( 8000 * 8 ) = 48 : 32 : 64 = 3 : 2 : 4 so b share = ( 2 / 9 ) * 4005 = rs 890 option c"
Answer: c
Python program:
a = 8000 + 4000 
b = a + 8000 
c = 8000 / b
d = c * 4005
Problem: two pumps are connected to an empty tank . pump x fills the tank with water at a constant rate , while pump y drains water out of the tank at a constant rate . the two pumps finish filling the tank in 6 times the duration it would take pump x alone to fill the tank . if pump y alone can empty a whole tank in 48 minutes , then how many minutes does it take pump x alone to fill the tank ?
Options: a ) 32 , b ) 34 , c ) 36 , d ) 38 , e ) 40
Rationale: let v be the volume of the tank . let r be the rate per minute that pump x fills the tank . let t be the time it takes pump x to fill the tank . the rate at which pump y empties the tank is v / 48 per minute . ( r - v / 48 ) * 6 t = v = rt . ( r - v / 48 ) * 6 = r 5 r = v / 8 . r = v / 40 . it takes pump x 40 minutes to fill the tank . the answer is e .
Answer: e
Python program:
a = 48 / 6
b = 48 - a
Problem: a man sells an article at a profit of 25 % . if he had bought it at 20 % less and sold it for rs . 16.80 less , he would have gained 30 % . find the cost of the article .
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 80
Rationale: "let c . p = 100 gain = 25 % s . p = 125 supposed c . p = 80 gain = 30 % s . p = ( 130 * 80 ) / 100 = 104 diff = ( 125 - 104 ) = 21 diff 21 when c . p = 100 then diff 16.80 when c . p = ( 100 * 16.80 ) / 21 = 50 answer : e"
Answer: e
Python program:
a = 16 * 80
b = 25 + 100 
c = 30 + 100 
d = 100 - 20
e = c * d
f = e / 100
g = b - f
h = a / g
Problem: given a two - digit number , the unit ' s digit exceeds its 10 ' s digit by 5 and the product of the given number and the sum of its digits is equal to 90 , which of the options is the number ?
Options: a ) 27 , b ) 16 , c ) 38 , d ) 61 , e ) 83
Rationale: using the elimination method the option that fits this description is 27 7 - 2 = 5 ( unit ' s digit that exceeds its ten ' s digit by 3 ) 27 * 9 = 243 ( the product of the given number and the sum of its digits is equal to 175 ) answer : a
Answer: a
Python program:
a = 2 * 10
b = 10 + 1 
c = 5 * b
d = c + 10 
e = 10 + 1 
f = 5 * e
g = f + 10 
h = d * g
i = 5 * 5
j = const_60 * 4
k = j + 3 
l = i - k
m = 10 + 1 
n = m * 2
o = l * n
p = o * 4
q = h - p
r = math.sqrt(q)
s = 10 + 1 
t = 5 * s
u = t + 10 
v = r - u
w = 10 + 1 
x = w * 2
y = x * 2
z = v / y
A = z + 5 
B = a + A
Problem: if â € œ * â €  is called â € œ + â €  , â € œ / â €  is called â € œ * â €  , â € œ - â €  is called â € œ / â €  , â € œ + â €  is called â € œ - â €  . 240 - 80 / 60 - 40 * 10 = ?
Options: a ) 14.5 , b ) 13.5 , c ) 12.5 , d ) 17.5 , e ) 11.5
Rationale: explanation : given : 240 - 80 / 60 - 40 * 10 = ? substituting the coded symbols for mathematical operations , we get , 240 / 80 * 60 / 40 + 10 = ? 3 * 1.5 + 10 = 14.5 answer : a
Answer: a
Python program:
a = 60 / 40
b = 240 / 80
c = a * b
d = c + 10
Problem: the least number which when increased by 3 each divisible by each one of 24 , 32 , 36 and 54 is :
Options: a ) 427 , b ) 859 , c ) 869 , d ) 861 , e ) none of these
Rationale: "solution required number = ( l . c . m . of 24 , 32 , 36 , 54 ) - 3 = 864 - 3 = 861 . answer d"
Answer: d
Python program:
a = math.lcm(24, 32)
b = math.lcm(a, 36)
c = math.lcm(b, 54)
d = c - 3
Problem: two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.10 km and 0.15 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
Options: a ) 65 sec , b ) 30 sec , c ) 48 sec , d ) 33 sec , e ) 12 sec
Rationale: "relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.10 + 0.15 = 1.25 km = 1250 m . required time = 1250 * 3 / 125 = 30 sec . answer : b"
Answer: b
Python program:
a = 1 * 10
b = 60 * 1000
c = b / 3600
d = a / c
e = 0 * 15
f = 90 * 1000
g = f / 3600
h = e / g
i = d - h
Problem: what is the compound interest on rs : 80,000 for 4 months at the rate of 5 % per annum
Options: a ) 1341.69 , b ) 1342.69 , c ) 1343.69 , d ) 1344.69 , e ) 1345.69
Rationale: "it is monthly compound rate = 5 / 12 % per month 80000 * ( 1 + 5 / 1200 ) ^ 4 - 80000 = 1341.69 answer : a"
Answer: a
Python program:
a = 3 * 100
b = a * 100
c = 4 * 3
d = 4 / c
e = 5 * d
f = b * e
g = f / 100
Problem: tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random . what is the probability that the ticket drawn has a number which is a multiple of 3 or 5 ?
Options: a ) 1 / 2 , b ) 1 / 2 , c ) 8 / 15 , d ) 9 / 20 , e ) 9 / 24
Rationale: "explanation : here , s = { 1 , 2 , 3 , 4 , . . . . , 19 , 20 } . let e = event of getting a multiple of 3 or 5 = { 3 , 6 , 9 , 12 , 15 , 18 , 5 , 10 , 20 } . p ( e ) = n ( e ) / n ( s ) = 9 / 20 answer : d"
Answer: d
Python program:
a = 3 / 10
Problem: the cross - section of a water channel is a trapezium in shape . if the channel is 14 meters wide at the top and 8 meters wide at the bottom and the area of cross - section is 770 square meters , what is the depth of the channel ( in meters ) ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "1 / 2 * d * ( 14 + 8 ) = 770 d = 70 the answer is c ."
Answer: c
Python program:
a = 14 + 8 
b = a / 2
c = 770 / b
Problem: what is the measure of the radius of the circle that circumscribes a triangle whose sides measure 5 , 12 and 13 ?
Options: a ) 2.5 , b ) 6.5 , c ) 5 , d ) 6.0 , e ) 7
Rationale: "some of pyhtagron triplets we need to keep it in mind . like { ( 2 , 3,5 ) , ( 5 , 12,13 ) , ( 7 , 24,25 ) , ( 11 , 60,61 ) . so now we know the triangle is an right angle triangle . the circle circumscribes the triangle . the circumraduis of the circle that circumscribes the right angle triangle = hypotanse / 2 = 13 / 2 = 6.5 ans . b"
Answer: b
Python program:
a = triangle_area_three_edges / (
Problem: the cost price of 20 articles is the same as the selling price of x articles . if the profit is 25 % then determine the value of x .
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: "explanation : let the cost price 1 article = re 1 cost price of x articles = x s . p of x articles = 20 gain = 20 - x = > 25 = ( 20 − x / x ∗ 100 ) = > 2000 − 100 x = 25 x = > x = 16 option c"
Answer: c
Python program:
a = 20 * 4
b = 4 + 1 
c = a / b
Problem: how many positive integers less than 260 are multiple of 4 but not multiples of 6 ?
Options: a ) 20 , b ) 31 , c ) 45 , d ) 53 , e ) 64
Rationale: "260 / 4 = 65 multiples of 4 which are a multiple of 6 will be of the form 2 * 2 * 3 = 12 n where n > 0 240 / 12 = 20 65 - 20 = 45 answer : c"
Answer: c
Python program:
a = 4 + 4 
b = a - 1
c = math.factorial(b)
d = math.factorial(4)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: the area of sector of a circle whose radius is 10 metro and whose angle at the center is 42 â ° is ?
Options: a ) 36.7 , b ) 52.9 , c ) 52.8 , d ) 52.1 , e ) 52.2
Rationale: "42 / 360 * 22 / 7 * 10 * 10 = 36.7 m 2 answer : a"
Answer: a
Python program:
a = 10 ** 2
b = 2 * 10
c = b + 2 
d = 4 + 3 
e = c / d
f = a * e
g = 3600 / 10
h = 42 / g
i = f * h
Problem: 120 is what percent of 80 ?
Options: a ) 0.2 % , b ) 2 % , c ) 5 % , d ) 150 % , e ) 500 %
Rationale: "120 = x * 80 / 100 x = 150 % ans ; d"
Answer: d
Python program:
a = 120 / 80
b = a * 100
Problem: a rectangular room has the rectangular shaped rug shown as above figure such that the rug ’ s area is 140 square feet and its length is 4 feet longer than its width . if the uniform width between the rug and room is 4 feet , what is the area of the region uncovered by the rug ( shaded region ) , in square feet ?
Options: a ) 32 , b ) 36 , c ) 40 , d ) 46 , e ) 256
Rationale: "rug ' s area = 140 which is ( x ) x ( 4 + x ) = 140 so x = 10 rug maintains a uniform distance of 4 feet so room has dimension 10 + 8 and 14 + 8 i . e . 18 and 22 area of room 18 x 22 = 396 area covered is 140 so uncovered area is 396 - 140 = 256 ( answer e )"
Answer: e
Python program:
a = 140 / 10
b = a - 2
c = b + 10 
d = 140 / 10
e = 140 / 10
f = e - 2
g = d + f 
h = c * g
i = h - 140
Problem: at a meeting , 25 attendants used a pencil and 15 attendants used a pen . if exactly 20 attendants used only one of the two types of writing tools , how many attendants wrote with both types of writing tools ?
Options: a ) 10 , b ) 6 , c ) 7 , d ) 4 , e ) 14
Rationale: say x attendants wrote with both writing tools . ( 25 - x ) + ( 15 - x ) = 20 - - > x = 10 . answer : a .
Answer: a
Python program:
a = 25 + 15 
b = a - 20
c = b / 2
Problem: working together , tim and tom can type 15 pages in one hour . if they would be able to type 18 pages in one hour if tom increases his typing speed by 60 % , what is the ratio of tom ' s normal typing speed to that of tim ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6
Rationale: "lets say tim types x pages an hour and tom types y pages an hour . we know that x + y = 15 tom increase speed by 60 % means he will type 1.6 y pages an hour . so we get x + 1.6 y = 18 we need to know the ratio of tom ' s speed to tim ' s speed . this is going to be proportional to the number of pages each can type in an hour , hence ( y / x ) . subtracting both : 0.6 y = 3 so y = 5 . . . so x = 10 ( y / x ) = 5 / 10 = 1 / 2 answer is ( a )"
Answer: a
Python program:
a = 18 - 15
b = 100 * 1
c = 60 / b
d = a / c
e = 18 - 15
f = 100 * 1
g = 60 / f
h = e / g
i = 15 - h
j = d / i
Problem: how many digits are in ( 12 × 10 ^ 14 ) ( 10 × 10 ^ 15 ) ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 32
Rationale: "the question simplfies to ( 12 × 10 ^ 14 ) ( 10 ^ 16 ) = > 12 * 10 ^ 30 = > will contain 30 zeros + 2 digit 12 = > 32 ans e"
Answer: e
Python program:
a = 3 + 4 
b = 10 + a
Problem: 20 men can complete a piece of work in 30 days . in how many days can 25 men complete that piece of work ?
Options: a ) 23 , b ) 27 , c ) 24 , d ) 27 , e ) 11
Rationale: "20 * 30 = 25 * x = > x = 24 days answer : c"
Answer: c
Python program:
a = 30 * 20
b = a / 25
Problem: a lamp is put on one corner of a square plot of side 50 m . it ' s light reaches 21 m . find the area of that plot that is lit by that lamp ?
Options: a ) 248
b ) 312.5
c ) 346.5
d ) 392.5
e ) 424
Rationale: area covered by lamp = pi * r ^ 2 / 4 ( here we divide by 4 because lamp is put in the corner of the plot and only 1 / 4 part lit is of the plot ) where r = 21 m = length of part lit so area = ( 22 / 7 ) * 21 * 21 / 4 = 346.5 sq m answer : c
Answer: c
Python program:
a = circle_area / (
Problem: what is 12.5 % of 4 / 12 of 600 ?
Options: a ) 25 , b ) 24 , c ) 30 , d ) 27 , e ) 28
Rationale: "12.5 % = 12.5 / 100 = 1 / 8 of 4 / 12 = 1 / 8 * 4 / 12 = 1 / 24 of 600 = 1 / 24 * 600 = 25 ans - a"
Answer: a
Python program:
a = 3 + 2 
b = a * 2
c = 3 * 4
d = c * 100
e = b * d
f = 3 + 4 
g = 3 + 2 
h = f * g
i = 3 + 2 
j = i * 2
k = h * j
l = e + k 
m = 3 + 3 
n = l + m 
o = 12 * 5
p = o / 100
Problem: find the slope of the line perpendicular to the line y = ( 1 / 6 ) x - 7
Options: a ) 1 , b ) 2 , c ) - 6 , d ) 4 , e ) 5
Rationale: "two lines are perpendicular if the product of their slopes is equal to - 1 . the slope of the given line is equal to 1 / 6 . if m is the slope of the line perpendicular to the given line , then m × ( 1 / 6 ) = - 1 solve for m m = - 6 correct answer c ) - 6"
Answer: c
Python program:
a = 1 / 6
Problem: find the mean proportional between 36 & 49 ?
Options: a ) a ) 42 , b ) b ) 61 , c ) c ) 63 , d ) d ) 65 , e ) e ) 67
Rationale: "formula = √ a × b a = 36 and b = 49 √ 36 × 49 = 6 × 7 = 42 a"
Answer: a
Python program:
a = 36 + 49 
b = a / 2
Problem: a , b and c play a cricket match . the ratio of the runs scored by them in the match is a : b = 1 : 3 and b : c = 1 : 5 . if the total runs scored by all of them are 95 , the runs scored by c are ?
Options: a ) 20.23 , b ) 20.13 , c ) 75 , d ) 20.93 , e ) 10.93
Rationale: a : b = 1 : 3 b : c = 1 : 5 a : b : c = 1 : 3 : 15 15 / 19 * 95 = 75 answer : c
Answer: c
Python program:
a = 1 / 3
b = 5 / 1
c = a + b 
d = c + 1 
e = 95 / d
f = e * 5
Problem: dacid obtained 61 , 65 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 29 , b ) 72 , c ) 39 , d ) 37 , e ) 75
Rationale: "average = ( 61 + 65 + 82 + 67 + 85 ) / 5 = 72 answer : b"
Answer: b
Python program:
a = 61 + 65 
b = a + 82 
c = b + 67 
d = c + 85 
e = 10 / 2
f = d / e
Problem: 7500 + ( 1250 / 50 )
Options: a ) 7500 , b ) 7525 , c ) 7550 , d ) 8000 , e ) none of these
Rationale: explanation : as per bodmas rule first we will solve the terms in the bracket then other . = 7500 + ( 25 ) = 7525 option b
Answer: b
Python program:
a = 1250 / 50
b = 7500 + a
Problem: the prices of tea and coffee per kg were the same in june . in july the price of coffee shot up by 20 % and that of tea dropped by 20 % . if in july , a mixture containing equal quantities of tea and coffee costs 50 / kg . how much did a kg of coffee cost in june ?
Options: a ) 50 , b ) 60 , c ) 80 , d ) 100 , e ) 120
Rationale: "let the price of tea and coffee be x per kg in june . price of tea in july = 1.2 x price of coffee in july = 0.8 x . in july the price of 1 / 2 kg ( 500 gm ) of tea and 1 / 2 kg ( 500 gm ) of coffee ( equal quantities ) = 50 1.2 x ( 1 / 2 ) + 0.8 x ( 1 / 2 ) = 50 = > x = 50 thus proved . . . option a ."
Answer: a
Python program:
a = 20 / 100
b = 1 - a
c = 20 / 100
d = c + 1 
e = b * d
f = 50 / e
Problem: in a certain town , the ratio of ny yankees fans to ny mets fans is 2 : 1 , and the ratio of ny mets fans to boston red sox fans is 3 : 7 . if there are 320 baseball fans in the town , each of whom is a fan of exactly one of those three teams , how many ny mets fans are there in this town ?
Options: a ) 48 , b ) 52 , c ) 56 , d ) 60 , e ) 64
Rationale: "the ratio of yankees : mets : red sox = 6 : 3 : 7 the mets fans are 3 / 16 of the population . ( 3 / 16 ) * 320 = 60 the answer is d ."
Answer: d
Python program:
a = 2 * 1
b = a + 3 
c = b + 7 
d = 320 / c
e = d * 3
Problem: solve below question 2 x + 1 = - 11
Options: a ) - 8 , b ) - 6 , c ) 9 , d ) 8 , e ) - 7
Rationale: "2 x + 1 = - 11 x = - 6 b"
Answer: b
Python program:
a = 11 + 1 
b = negate / (
Problem: if 7 / w + 7 / x = 7 / y and wx = y , then the average ( arithmetic mean ) of w and x is
Options: a ) 1 / 2 , b ) 1 , c ) 2 , d ) 4 , e ) 8
Rationale: given : 7 / w + 7 / x = 7 / ywx = y find : ( w + x ) / 2 = ? 7 ( 1 / w + 1 / x ) = 7 ( 1 / y ) - divide both sides by 7 ( 1 / w + 1 / x ) = 1 / y ( x + w ) / wx = 1 / wx - sub ' d in y = wx x + w - 1 = 0 x + w = 1 therefore ( w + x ) / 2 = 1 / 2 ans : a
Answer: a
Python program:
a = 7 + 7 
b = 7 / a
Problem: a man can row 10 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and black . how far is the place ?
Options: a ) 5.02 , b ) 4.92 , c ) 4.82 , d ) 4.72 , e ) 4.61
Rationale: "m = 10 s = 1.2 ds = 10 + 1.2 = 11.2 us = 10 - 1.2 = 8.8 x / 11.2 + x / 8.8 = 1 x = 4.92 . answer : b"
Answer: b
Python program:
a = 10 + 1 
b = 10 - 1
c = a * b
d = 10 + 1 
e = 10 - 1
f = d + e 
g = c / f
h = g * 2
Problem: a large field of 700 hectares is divided into two parts . the difference of the areas of the two parts is one – fifth of the average o fthe two areas . what is the area of the smaller part in hectares ?
Options: a ) 225 , b ) 280 , c ) 300 , d ) 385 , e ) none
Rationale: "solution let the areas of the two parts be x and ( 700 - x ) hectares = [ x - ( 700 - x ) ] = 1 / 5 x [ x + ( 700 - x ) / 2 ] = 2 x - 700 = 70 x = 385 . answer d"
Answer: d
Python program:
a = 700 / 2
b = 1 + 4 
c = 1 / b
d = a * c
e = 700 - d
f = e / 2
Problem: what is the least number of square tiles required to pave the floor of a room 13 m 44 cm long and 4 m 44 cm broad ?
Options: a ) 7724 , b ) 7804 , c ) 4144 , d ) 7844 , e ) none
Rationale: "solution length of largest tile = h . c . f . of 1344 cm & 444 cm = 12 cm . area of each tile = ( 12 x 12 ) cm 2 ∴ required number of tiles = [ 1344 x 444 / 12 x 12 ] = 4144 . answer c"
Answer: c
Python program:
a = 4 * 100
b = a + 44 
c = 13 * 100
d = b * c
e = 44 ** 2
f = d / e
Problem: micheal and adam can do together a piece of work in 20 days . after they have worked together for 16 days micheal stops and adam completes the remaining work in 10 days . in how many days micheal complete the work separately .
Options: a ) 80 days , b ) 100 / 3 days , c ) 120 days , d ) 110 days , e ) 90 days
Rationale: "rate of both = 1 / 20 together they do = 1 / 20 * 16 = 4 / 5 left work = 1 - 4 / 5 = 1 / 5 adam completes 1 / 5 work in 10 day so he took 10 * 5 = 50 days to complete the left work alone . thus the rate of adam is 1 / 50 rate of micheal = 1 / 20 - 1 / 50 = 1 / ( 100 / 3 ) thus micheal takes 100 / 3 days to complete the whole work . ans . b ."
Answer: b
Python program:
a = 1/(20)
b = 1/(20)
c = b * 16
d = 1 - c
e = 1/(d)
f = e * 10
g = 1/(f)
h = a - g
i = 1/(h)
Problem: a palindrome is a number that reads the same forward and backward , such as 171 . how many even , 6 - digit numbers are palindromes ?
Options: a ) 405 , b ) 450 , c ) 400 , d ) 900 , e ) 2500
Rationale: "first recognize you only need to consider the first three digits ( because the second three are just the first three flipped ) there are 900 possibilities for the first three digits of a 6 digit number , 100 - 999 inclusive . everything starting with a 2,4 , 6,8 will be even , which is 4 / 9 ths of the combinations . 4 / 9 * 900 = 400 answer : c"
Answer: c
Python program:
a = 6 / 2
b = 10 ** a
c = b / 2
Problem: of the 200 stamps in a collection , 90 are foreign and 50 are more than 10 years old . if 20 stamps are both foreign and more than 10 years old , how many stamps are neither foreign nor more than 10 years old ?
Options: a ) 30 , b ) 80 , c ) 100 , d ) 130 , e ) 150
Rationale: "20 stamps are both foreign and more than 10 years old . 70 stamps are foreign only . 30 stamps are 10 years old only . the number of remaining stamps is 200 - ( 20 + 70 + 30 ) = 80 the answer is b ."
Answer: b
Python program:
a = 90 + 50 
b = a - 20
c = 200 - b
Problem: after doing 3 / 5 of the biology homework on monday night , sanjay did 1 / 3 of the remaining homework on tuesday night . what fraction of the original homework would sanjay have to do on wednesday night to complete the biology assignment ?
Options: a ) 1 / 15 , b ) 2 / 15 , c ) 4 / 15 , d ) 2 / 5 , e ) none of these
Rationale: sol . ( c ) remaining homework on monday night = 1 - ( 3 / 5 ) = 2 / 5 work done on tuesday night = 1 / 3 of 2 / 5 = 2 / 15 remaining homework to complete the biology assignment = 2 / 5 - 2 / 15 = ( 6 - 2 ) / 15 = 4 / 15 answer c
Answer: c
Python program:
a = 3 / 5
b = 3 / 5
c = 1 - b
d = 1 / 3
e = c * d
f = a + e 
g = 1 - f
Problem: difference of two numbers is 1860 . if 7.5 % of the number is 12.5 % of the other number , find the number ?
Options: a ) 2660 , 1000 , b ) 3660 , 2000 , c ) 3000 , 4160 , d ) 2790 , 4650 , e ) 4660 , 3000
Rationale: "let the numbers be x and y . then , 7.5 % of x = 12.5 % of y x = 125 * y / 75 = 5 * y / 3 . now , x - y = 1860 5 * y / 3 – y = 1860 2 * y / 3 = 1860 y = [ ( 1860 * 3 ) / 2 ] = 2790 . one number = 2790 , second number = 5 * y / 3 = 4650 . answer d ."
Answer: d
Python program:
a = 7 / 5
b = 7 / 5
c = 1 - b
d = 1860 / c
e = a * d
Problem: a box contains 9 slips that are each labeled with one number : 1 , 2 , 3 , 5 , 8 , 13 , 21 , and 55 . two of the slips are drawn at random from the box without replacement . what is the probability that the sum of the numbers on the two slips is equal to one of the numbers left in the box ?
Options: a ) 7 / 72 , b ) 1 / 6 , c ) 7 / 36 , d ) 5 / 28 , e ) 21 / 36
Rationale: probability = no : of desired outcomes / total no : of outcomes . you are picking two slips out of 8 slips . so total no : of outcomes = 8 c 2 = 28 desired outcome : sum of the numbers on the two slips is equal to one of the numbers left in the box . how many such outcomes are there ? if you look at the numbers closely , you will see that the following pair of numbers will give you the desired outcome . ( 12 ) ( 23 ) ( 35 ) ( 58 ) ( 813 ) . there are 5 such pairs . if the two numbers which i pick is from any of these 5 pairs , then i get my desired outcome . so no : of desired outcomes = 5 probability = 5 / 28 answer : d
Answer: d
Python program:
a = 3 * 5
b = a + 10 
c = b + 3 
d = 5 / c
Problem: a shopkeeper sold an article offering a discount of 4 % and earned a profit of 26 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 24 , b ) 28 , c ) 31 , d ) 32 , e ) 34
Rationale: "let c . p . be rs . 100 . then , s . p . = rs . 126 let marked price be rs . x . then , 96 / 100 x = 126 x = 12600 / 96 = rs . 131.25 now , s . p . = rs . 131.25 , c . p . = rs . 100 profit % = 31 % . answer : c"
Answer: c
Python program:
a = 100 + 26 
b = a * 100
c = 100 - 4
d = b / c
e = d - 100
Problem: the reciprocal of the hcf and lcm of two are 1 / 17 and 1 / 312 . if one of the number is 24 then other no . is
Options: a ) 126 , b ) 136 , c ) 146 , d ) 221 , e ) 266
Rationale: "reciprocal of the hcf and lcm of two are 1 / 17 and 1 / 312 so , hcf = 17 , lcm = 312 lcm * hcf = product of two numbers = a * b = > b = lcm * hcf / a so , other = 17 * 312 / 24 = 221 answer : d"
Answer: d
Python program:
a = 17 * 312
b = a / 24
Problem: a man bought 10 crates of mangoes for $ 160 total . if he lost 2 of the crates , at what price would he have to sell each of the remaining crates in order to earn a total profit of 25 percent of the total cost ?
Options: a ) $ 35 , b ) $ 25 , c ) $ 45 , d ) $ 50 , e ) $ 55
Rationale: "as given , after lost , the remaining 8 crates total cost = $ 160 so , 1 crate cost = 160 / 8 = 20 to get 25 % profit , 1 crate cost should be = 20 + 20 * 25 / 100 = $ 25 answer : b"
Answer: b
Python program:
a = 25 / 100
b = 160 * a
c = 160 + b 
d = 10 - 2
e = c / d
Problem: the speed at which a man can row a boat in still water is 6.5 kmph . if he rows downstream , where the speed of current is 2.5 kmph , what time will he take to cover 90 metres ?
Options: a ) 90 seconds , b ) 36 seconds , c ) 26 seconds , d ) 18 seconds , e ) 6.5 seconds
Rationale: "speed of the boat downstream = 6.5 + 2.5 = 9 kmph = 9 * 5 / 18 = 2.5 m / s hence time taken to cover 90 m = 90 / 2.5 = 36 seconds . answer : b"
Answer: b
Python program:
a = 6 + 5 
b = a * const_0_2778
c = 90 / b
Problem: if x = 1 + √ 2 , then what is the value of x 4 - 4 x 3 + 4 x 2 + 4 ?
Options: a ) - 1 , b ) 0 , c ) 5 , d ) 2 , e ) 3
Rationale: answer x = 1 + √ 2 ∴ x 4 - 4 x 3 + 4 x 2 + 5 = x 2 ( x 2 - 4 x + 4 ) + 4 = x 2 ( x - 2 ) 2 + 4 = ( 1 + √ 2 ) 2 ( 1 + √ 2 - 2 ) 2 + 4 = ( √ 2 + 1 ) 2 ( √ 2 - 1 ) 2 + 4 = [ ( √ 2 ) 2 - ( 1 ) 2 ] 2 + 4 = ( 2 - 1 ) 2 = 1 + 4 = 5 correct option : c
Answer: c
Python program:
a = math.sqrt(2)
b = 1 + a 
c = b ** 2
d = math.sqrt(2)
e = 1 + d 
f = e - 2
g = f ** 2
h = c * g
i = h + 4
Problem: a cube of side 1.5 meter length is cut into small cubes of side 10 cm each . how many such small cubes can be obtained ?
Options: a ) 2878 , b ) 3375 , c ) 1000 , d ) 2997 , e ) 2701
Rationale: "along one edge , the number of small cubes that can be cut = 150 / 10 = 15 along each edge 10 cubes can be cut . ( along length , breadth and height ) . total number of small cubes that can be cut = 15 * 15 * 15 = 3375 answer : b"
Answer: b
Python program:
a = 1 ** 5
b = a ** 3
c = 1 ** 5
d = b / c
Problem: if the average ( arithmetic mean ) of a and b is 45 and the average of b and c is 70 , what is the value of c − a ?
Options: a ) 25 , b ) 50 , c ) 90 , d ) 140 , e ) it can not be determined from the information given
Rationale: "the arithmetic mean of a and b = ( a + b ) / 2 = 45 - - a + b = 90 - - 1 similarly for b + c = 140 - - 2 subtracting 1 from 2 we have c - a = 50 ; answer : b"
Answer: b
Python program:
a = 70 * 2
b = 45 * 2
c = a - b