euclaise/mathqa_programs huggingface dataset:
Problem: the ratio between the number of passengers travelling by i and ii class between the two railway stations is 1 : 50 , whereas the ratio of i and ii class fares between the same stations is 3 : 1 . if on a particular day rs . 1,325 were collected from the passengers travelling between these stations , then what was the amount collected from the ii class passengers ?
Options: a ) rs . 750 , b ) rs . 1000 , c ) rs . 850 , d ) rs . 1250 , e ) none of these
Rationale: let x be the number of passengers and y be the fare taken from passengers . 3 xy + 50 xy = 1325 = > xy = 25 amount collected from ii class passengers = 25 × 50 = rs . 1250 . answer : d
Answer: d
Python program:
a = 50 * 1
b = 10 * 100
c = 3 * 100
d = b + c 
e = 2 * 10
f = d + e 
g = 2 + 3 
h = f + g 
i = 1 * 3
j = 50 * 1
k = i + j 
l = h / k
m = a * l
Problem: a , b , c subscribe rs . 50,000 for a business . if a subscribes rs . 4000 more than b and b rs . 5000 more than c , out of a total profit of rs . 38,000 , what will be the amount a receives ?
Options: a ) 14700 , b ) 15960 , c ) 14900 , d ) 14300 , e ) 14000
Rationale: "total amount invested = 50000 assume that investment of c = x . then investment of b = 5000 + x , investment of a = 4000 + 5000 + x = 9000 + x x + 5000 + x + 9000 + x = 50000 ⇒ 3 x + 14000 = 50000 ⇒ 3 x = 50000 – 14000 = 36000 ⇒ x = 36000 / 3 = 12000 investment of c = x = 12000 investment of b = 5000 + x = 17000 investment of a = 9000 + x = 21000 ratio of the investment of a , b and c = 21000 : 17000 : 12000 = 21 : 17 : 12 share of a = total profit × 21 / 50 = 38000 × 21 / 50 = 15960 answer is b"
Answer: b
Python program:
a = 5000 * 10
b = 4000 + 5000 
c = b + 5000 
d = a - c
e = d / 3
f = 4000 + 5000 
g = e + f 
h = 3 * 12
i = h * 1000
j = 5000 * 10
k = i / j
l = g * k
Problem: ( ( - 1.9 ) ( 0.6 ) – ( 2.6 ) ( 1.2 ) ) / 4.0 = ?
Options: a ) 1.07 , b ) 1.0 , c ) - 1.065 , d ) 1.71 , e ) 2.71
Rationale: "dove straight into calculation but quickly realized that the sum of two negatives is a negative so there is only one option . - 1.065 answer c"
Answer: c
Python program:
a = 1 * 9
b = negate - (
c = 2 * 6
d = b / c
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 €  . 120 / 40 â € “ 30 * 20 - 5 = ?
Options: a ) 178.5 , b ) 156.6 , c ) 160.4 , d ) 163.6 , e ) 164.1
Rationale: "explanation : given : 120 / 40 â € “ 30 * 20 - 5 = ? substituting the coded symbols for mathematical operations , we get , 120 * 40 / 30 + 20 / 5 = ? 120 * 1.33 + 4 = ? 159.6 + 4 = 163.6 answer : d"
Answer: d
Python program:
a = 30 / 20
b = 120 / 40
c = a * b
d = c + 5
Problem: the hypotenuse of a right triangle is 2 centimeters more than the longer side of the triangle . the shorter side of the triangle is 7 centimeters less than the longer side . find the length of the hypotenuse .
Options: a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21
Rationale: let a and b be the two sides of the triangle such that a is longer than b . the statement ` ` the hypotenuse of a right triangle is 2 centimeters more than the longer side of the triangle ' ' may be fomulated by h = a + 2 or a = h - 2 the statement ` ` the shorter side of the triangle is 7 centimeters less than the longer side ' ' may be formulated . b = a - 7 or b = ( h - 2 ) - 7 = h - 9 we now use pythagora ' s theorem to write a third equation h 2 = a 2 + b 2 substitute a by h - 2 and b by h - 9 in the above equation to obtain an equation in one variable only . h 2 = ( h - 2 ) 2 + ( h - 9 ) 2 simplify and rewrite the above equation in standard form . h 2 - 22 h + 85 = 0 solve for h . h = 5 and h = 17 . only the solution h = 17 gives a and b positive and it is the length of the hypotenuse of the triangle . answer a
Answer: a
Python program:
a = 7 + 2 
b = a * 2
c = 7 + 2 
d = c * 2
e = d ** 2
f = 7 ** 2
g = 2 ** 2
h = f - g
i = h * 4
j = e - i
k = math.sqrt(j)
l = b + k 
m = l / 2
n = m + 2
Problem: how long does a train 120 m long running at the speed of 70 km / hr takes to cross a bridge 145 m length ?
Options: a ) 13.9 sec , b ) 12.1 sec , c ) 17.9 sec , d ) 13.9 sec , e ) 47.98 sec
Rationale: "speed = 70 * 5 / 18 = 19 m / sec total distance covered = 120 + 145 = 265 m . required time = 265 / 19 = 13.9 sec . answer : d"
Answer: d
Python program:
a = 120 + 145 
b = 70 * const_0_2778
c = a / b
Problem: if n is a positive integer and the product of all integers from 1 to n , inclusive , is a multiple of 650 , what is the least possible value of n ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "650 = 2 * 5 * 5 * 13 so the least value forncan be 13 . d"
Answer: d
Python program:
a = 650 / 2
b = a / 3
c = b / 4
d = 10 / 2
e = c / d
Problem: a rectangular field is to be fenced on three sides leaving a side of 30 feet uncovered . if the area of the field is 600 sq . ft , how many feet of fencing will be required ?
Options: a ) 70 feet , b ) 52 feet , c ) 32 feet , d ) 12 feet , e ) 55 feet
Rationale: "explanation : we are given with length and area , so we can find the breadth . as length * breadth = area = > 30 * breadth = 600 = > breadth = 20 feet area to be fenced = 2 b + l = 2 * 20 + 30 = 70 feet answer : option a"
Answer: a
Python program:
a = 600 / 30
b = a * 2
c = b + 30
Problem: two employees x and y are paid a total of rs . 560 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 . 254 , b ) s . 284 , c ) s . 290 , d ) s . 304 , e ) s . 380
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 560 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 560 ⇒ y [ 12 / 10 + 1 ] = 560 ⇒ 22 y / 10 = 560 ⇒ 22 y = 5600 ⇒ y = 5600 / 22 = rs . 254 ( approx ) a )"
Answer: a
Python program:
a = 1 + 4 
b = a * 2
c = 560 * b
d = 1 + 4 
e = d * 2
f = e + 1 
g = f * 2
h = c / g
Problem: calculate the sum of first 28 natural numbers .
Options: a ) 426 , b ) 406 , c ) 401 , d ) 409 , e ) 405
Rationale: "solution we know that ( 1 + 2 + 3 + . . . . . + 28 ) = n ( n + 1 ) / 2 therefore ( 1 + 2 + 3 + . . . . + 28 ) = ( 28 × 29 / 2 ) = 406 . answer b"
Answer: b
Python program:
a = 28 + 1 
b = 28 / 2
c = a * b
Problem: when tossed , a certain coin has equal probability of landing on either side . if the coin is tossed 4 times , what is the probability that it will land on the same side each time ?
Options: a ) 1 / 8 , b ) 1 / 4 , c ) 1 / 16 , d ) 1 / 2 , e ) 1 / 32
Rationale: "must be either 4 tails or 4 heads 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 + 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 1 / 16 + 1 / 16 = 1 / 8 answer : a"
Answer: a
Python program:
a = 2 ** 4
b = 1 / a
Problem: trapezoid jklm in the x - y plane has coordinates j = ( – 2 , – 3 ) , k = ( – 2 , 1 ) , l = ( 6 , 7 ) , and m = ( 6 , – 3 ) . what is its perimeter ?
Options: a ) 32 , b ) 36 , c ) 38 , d ) 40 , e ) ( f ) 42
Rationale: "jk = 4 lm = 10 kl = using distance formula 10 jm = using distance formula 8 sum of all is 32 a"
Answer: a
Python program:
a = 1 + 3 
b = 10 + a 
c = 2 + 6 
d = b + c 
e = 7 + 3 
f = d + e
Problem: the c . p of 8 books is equal to the s . p of 16 books . find his gain % or loss % ?
Options: a ) 60 % , b ) 50 % , c ) 70 % , d ) 90 % , e ) 55 %
Rationale: "explanation : 8 cp = 16 sp 16 - - - 8 cp loss 100 - - - ? = > 50 % loss answer : b"
Answer: b
Python program:
a = 8 / 16
b = 1 - a
c = b * 100
Problem: a & b started a partnership business . a ' s investment was thrice the investment of b and the period of his investment was two times the period of investments of b . if b received rs 5000 as profit , what is their total profit ?
Options: a ) 28000 , b ) 30000 , c ) 32000 , d ) 35000 , e ) none of these
Rationale: "explanation : suppose b ' s investment = x . then a ' s investment = 3 x suppose bs period of investment = y , then a ' s period of investment = 2 y a : b = 3 x * 2 y : xy = 6 : 1 total profit * 1 / 7 = 5000 = > total profit = 5000 * 7 = 35000 . answer : option d"
Answer: d
Python program:
a = 1 * 1
b = 3 * 2
c = 1 * 1
d = b + c 
e = a / d
f = 5000 / e
Problem: a can do a work in 6 days , b can do a work in 8 days and c can do it in 12 days . b left work after 1 day . for how many number of days should a and c should work together to complete the remaining work ?
Options: a ) 1 / 7 , b ) 2 / 7 , c ) 3 / 7 , d ) 4 / 7 , e ) 5 / 7
Rationale: b work 1 / 8 * 1 = 1 / 8 remaining work = 1 - 1 / 8 = 7 / 8 a and c work together = 1 / 6 + 1 / 12 = 3 / 12 = 1 / 4 take reciprocal 7 / 8 * remaining work = 8 / 7 * 1 / 4 = 2 / 7 answer : b
Answer: b
Python program:
a = 1 / 6
b = 1 / 8
c = a + b
Problem: the ratio by weight , measured in pounds , of books to clothes to electronics in a suitcase initially stands at 7 : 4 : 3 . someone removes 6 pounds of clothing from the suitcase , thereby doubling the ratio of books to clothes . how many pounds do the electronics in the suitcase weigh ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "the weights of the items in the suitcase are 7 k , 4 k , and 3 k . if removing 6 pounds of clothes doubles the ratio of books to clothes , then 6 pounds represents half the weight of the clothes . 2 k = 6 pounds and then k = 3 pounds . the electronics weigh 3 ( 3 ) = 9 pounds . the answer is e ."
Answer: e
Python program:
a = 7 + 4 
b = a + 3 
c = b * 6
d = negate / (
e = 7 + 4 
f = e + 3 
g = f * 2
h = 7 + 4 
i = h + 3 
j = i * 4
k = g - j
l = 3 * d
Problem: a bag consists of 50 marbles , of which 5 are blue , 9 are red , and the remainder are white . if lisa is to select a marble from the bag at random , what is the probability that the marble will be red or white ?
Options: a ) 3 / 4 , b ) 2 / 4 , c ) 1 / 4 , d ) 1 / 8 , e ) 9 / 10
Rationale: "bag consists of 50 marbles , of which 5 are blue , 9 are red remainder are white . so , white = 50 - 5 - 9 = 36 . probability that the marble will be red or white = probability that the marble will be red + probability that the marble will be white probability that the marble will be red or white = 9 / 50 + 36 / 50 = 45 / 50 = 9 / 10 hence , answer will be e ."
Answer: e
Python program:
a = 5 + 9 
b = 50 - a
c = b + 9 
d = c / 50
Problem: how many integers between 100 and 200 , inclusive , can not be evenly divided by 3 nor 5 ?
Options: a ) 46 , b ) 48 , c ) 50 , d ) 52 , e ) 54
Rationale: "the total numbers between 100 and 200 , inclusive , is 101 . 3 * 34 = 102 and 3 * 66 = 198 so the number of multiples of 3 is 33 . 5 * 20 = 100 and 5 * 40 = 200 so the number of multiples of 5 is 21 . however , the multiples of 15 have been counted twice . 15 * 7 = 105 and 15 * 13 = 195 so the number of multiples of 15 is 7 . thus the total number is 101 - 33 - 21 + 7 = 54 . the answer is e ."
Answer: e
Python program:
a = 2 * 100
b = 3 + 4 
c = b * 10
d = a + c 
e = d + 2 
f = 200 - e
Problem: for the positive integers x , x + 2 , x + 4 , x + 7 , and x + 22 , the mean is how much greater than the median ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 7
Rationale: mean = ( x + x + 2 + x + 4 + x + 7 + x + 22 ) / 5 = ( 5 x + 35 ) / 5 = x + 7 median = x + 4 thus mean - median = x + 7 - ( x + 4 ) = 3 answer = d
Answer: d
Python program:
a = 2 + 4 
b = a + 7 
c = b + 22 
d = 4 + 1 
e = c / d
f = e - 4
Problem: pavan travelled for 11 hours . he covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph . find the distance travelled by pavan ?
Options: a ) 398 km , b ) 892 km , c ) 387 km , d ) 300 km , e ) 230 km
Rationale: "let the distance travelled be x km . total time = ( x / 2 ) / 30 + ( x / 2 ) / 25 = 11 = > x / 60 + x / 50 = 11 = > ( 5 x + 6 x ) / 300 = 11 = > x = 300 km answer : d"
Answer: d
Python program:
a = 2 * 30
b = 1/(a)
c = 25 * 2
d = 1/(c)
e = b + d 
f = 1/(e)
g = f * 11
Problem: 3 / 4 of 1 / 2 of 2 / 5 of 5100 = ?
Options: a ) 392 , b ) 229 , c ) 765 , d ) 493 , e ) 540
Rationale: "c 765 ? = 5100 * ( 2 / 5 ) * ( 1 / 2 ) * ( 3 / 4 ) = 765"
Answer: c
Python program:
a = 3 / 4
b = 1 / 2
c = a * b
d = 2 / 5
e = c * d
f = e * 5100
Problem: in order to obtain an income of rs . 900 from 20 % stock at rs . 102 , one must make an investment of
Options: a ) rs . 6000 , b ) rs . 4590 , c ) rs . 4560 , d ) rs . 4500 , e ) rs . 4570
Rationale: "explanation : market value = rs . 102 . required income = rs . 900 . here face value is not given . take face value as rs . 100 if it is not given in the question to obtain rs . 20 ( ie , 20 % of the face value 100 ) , investment = rs . 102 to obtain rs . 900 , investment = 102 / 20 ã — 900 = rs . 4590 answer : option b"
Answer: b
Python program:
a = 102 / 20
b = a * 900
Problem: what is the value of ( p + q ) / ( p - q ) if p / q is 10 ?
Options: a ) 4 / 3 , b ) 2 / 3 , c ) 2 / 6 , d ) 11 / 9 , e ) 8 / 7
Rationale: "( p + q ) / ( p - q ) = [ ( p / q ) + 1 ] / [ ( p / q ) - 1 ] = ( 10 + 1 ) / ( 10 - 1 ) = 11 / 9 = 11 / 9 answer : d"
Answer: d
Python program:
a = 100 + const_60 
b = a + 1 
c = b * 10
d = c / 100
Problem: if the price of a certain bond on may 1 st was 1 / 2 the price of the bond on june 1 st and the price of the bond on july 1 st was 50 % greater than the price of the bond on may 1 st . then the price of the bond on june 1 st st was what percent of the average ( arithmetic mean ) price of the bond on may 1 st and july 1 st ?
Options: a ) 50 % , b ) 75 % , c ) 120 % , d ) 133 1 / 3 % , e ) 160 %
Rationale: "the price on june 1 st = 12 ( assume ) ; the price on may 1 st = 1 / 2 * 12 = 6 ; the price on july 1 st = 6 * 1.5 = 9 . the average price of the bond on may 1 st and july 1 st = ( 6 + 9 ) / 2 = 7.5 . the price of the bond on june 1 st ( 12 ) is 8 / 5 times ( 160 % ) the average price of the bond on may 1 st and july 1 st . answer : e ."
Answer: e
Python program:
a = 50 * const_0_33
b = 100 + const_0_33 
c = a + b
Problem: an investment compounds annually at an interest rate of 33.34 % what is the smallest investment period by which time the investment will more than triple in value ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 4
Rationale: "assume initial amount is x annual interest is 34.1 % so after 1 year the amount will become x * ( 100 + 33.34 ) / 100 = > x * 4 / 3 now we need to find n for x * ( 4 / 3 ) ^ n = 3 x or in other words n = 4 e"
Answer: e
Python program:
a = math.log(3)
b = 33 / 34
c = 1 + b 
d = math.log(c)
e = a / d
f = math.floor(e)
g = f + 1
Problem: a no . when divided by 220 gives a remainder 43 , what remainder will beobtained by dividingthe same no . 67 ?
Options: a ) 4 , b ) 6 , c ) 9 , d ) 11 , e ) 14
Rationale: "221 + 43 = 264 / 17 = 9 ( remainder ) c"
Answer: c
Python program:
a = 220 + 43 
b = a / 67
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 b ’ s salary ?
Options: a ) 777 , b ) 750 , c ) 789 , d ) 776 , e ) 881
Rationale: "( 5 / 100 ) a = ( 15 / 100 ) b a = 3 b a + b = 3000 4 b = 3000 = > b = 750 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: ritesh and co . generated revenue of rs . 1,700 in 2006 . this was 12.5 % of its gross revenue . in 2007 , the gross revenue grew by rs . 2,500 . what is the percentage increase in the revenue in 2007 ?
Options: a ) 18.38 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) none of these
Rationale: "explanation : given , ritesh and co . generated revenue of rs . 1,700 in 2006 and that this was 12.5 % of the gross revenue . hence , if 1700 is 12.5 % of the revenue , then 100 % ( gross revenue ) is : = > ( 100 / 12.5 ) × 1700 . = > 13,600 . hence , the total revenue by end of 2007 is rs . 13,600 . in 2006 , revenue grew by rs . 2500 . this is a growth of : = > ( 2500 / 13600 ) × 100 . = > 18.38 % . answer : a"
Answer: a
Python program:
a = 1 + 4 
b = 2 * a
c = b * 100
d = 2 * c
e = 1 + 4 
f = e * 100
g = d + f 
h = 1 + 4 
i = 2 * h
j = i * 100
k = 2 + 4 
l = k * 100
m = j + l 
n = 12 / 5
o = m / n
p = g / o
q = p * 100
Problem: find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 1120 ?
Options: a ) 1000 , b ) 3889 , c ) 8908 , d ) 3780 , e ) 2709
Rationale: "1120 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 1000 answer : a"
Answer: a
Python program:
a = 2 * 5
b = a + 2 
c = b / 5
d = c * 5
e = d / 100
f = e + 1 
g = 1120 / f
Problem: a man took a loan at rate of 12 % per annum simple interest . after 3 years he had to pay 5400 interest . the principal amount borrowed by him was .
Options: a ) rs 14000 , b ) rs 15000 , c ) rs 16000 , d ) rs 17000 , e ) none of these
Rationale: "explanation : s . i . = p ∗ r ∗ t / 100 = > p = s . i . ∗ 100 / r ∗ t = > p = 5400 ∗ 100 / 12 ∗ 3 = rs 15000 option b"
Answer: b
Python program:
a = 5400 * 100
b = 12 * 3
c = a / b
Problem: in a village there are 150 men and 90 women in present time . if in next year population will be p = ( a ^ 2 + b ^ 2 ) ^ 1 / 2 , and in every year men are reduces 12 % . what is population of after 2 year .
Options: a ) 139 , b ) 141 , c ) 142 , d ) 143 , e ) 144
Rationale: "next year total population = [ 150 ^ 2 + 90 ^ 2 ] ^ . 5 = 174.92 = 175 man decreased by 11 % so total man = 150 * . 88 = 132 women will be = 175 - 132 = 43 so population after two years = [ 135 ^ 2 + 43 ^ 2 ] ^ . 5 = 138.8 = 139 so population after two year = 139 answer : a"
Answer: a
Python program:
a = 1 / 12
b = 1 - a
c = b * 150
d = c ** 2
e = 150 ** 2
f = 90 ** 2
g = e + f 
h = 1 / 2
i = g ** h
j = 1 / 12
k = 1 - j
l = k * 150
m = i - l
n = m ** 2
o = d + n 
p = 1 / 2
q = o ** p
Problem: evaluate : 58 - 12 * 3 * 2 = ?
Options: a ) 42 , b ) 50 , c ) 62 , d ) 72 , e ) 82
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 58 - 12 * 3 * 2 = 58 - 8 = 50 correct answer b"
Answer: b
Python program:
a = 12 * 2
b = a * 2
c = 58 - b
Problem: jenny has recently moved house and is working out her optimal commute . she can take an indirect route which involves taking a bus for 1 mile and then walk 0.75 miles . or she can take a direct route and walk for 1.5 miles and this takes her 30 minutes . what is the most amount time that the bus journey can take for jenny to be indifferent between the two routes assuming travel time is her only concern ?
Options: a ) 5 minutes , b ) 10 minutes , c ) 15 minutes , d ) 20 minutes , e ) 25 minutes
Rationale: if jenny can walk 1.5 miles in 30 minutes , then she can talk 0.75 miles in half the time i . e . 15 minutes . for jenny to be indifferent between the two routes , the two journeys must have the same travel time . the direct route has a travel time of 30 minutes ( walking ) . the indirect route has a travel time of 15 minutes ( walking ) plus the bus journey . for the two routes to be the same the bus journey must take 15 minutes ( 30 - 15 ) . answer : c
Answer: c
Python program:
a = 1 / 5
b = 0 / 75
c = 30 - b
Problem: seller selling an apple for rs . 15 , a seller loses 1 / 6 th of what it costs him . the cp of the apple is ?
Options: a ) 10 , b ) 12 , c ) 16 , d ) 18 , e ) 20
Rationale: "sp = 15 loss = cp 16 loss = cp − sp = cp − 15 ⇒ cp 16 = cp − 15 ⇒ 15 cp 16 = 15 ⇒ cp 16 = 1 ⇒ cp = 16 c"
Answer: c
Python program:
a = 15 + 1
Problem: if the volume of a cube is x ^ 3 cubic units , what is the number of square units in the surface area of the cube ?
Options: a ) x ^ 2
b ) x ^ 3
c ) x ^ 6
d ) 6 x ^ 2
e ) 6 x ^ 3
Rationale: the question basically asks you to calculate the surface area of the cube . volume of the cube = x ^ 3 this means each side of the cube = x hence area of each side = x ^ 2 total surfaces in a cube = 6 total surface area = 6 * x 2 correct option : d
Answer: d
Python program:
a = 2 * 3
b = 1 * 1
c = a * b
Problem: the area of a square field is 28808 sq m . how long will a lady take to cross the field diagonally at the rate of 7.2 km / hr ?
Options: a ) 2.5 min , b ) 3 min , c ) 2 min , d ) 4 min , e ) 4.5 min
Rationale: "area of a square field = 28808 sq m let the side of square = a a ^ 2 = 28808 = > a = 169.73 diagonal = ( 2 ) ^ ( 1 / 2 ) * a = 1.414 * 169.73 = 240 speed of lady = 7.2 km / hour = 7200 m / hour = 120 m / min time taken by lady to cross the field diagonally = 240 / 120 = 2 min answer c"
Answer: c
Python program:
a = 7 * 2
b = 28808 / a
Problem: if a town of 35,000 people is growing at a rate of approx . 1 % per year , the population of the town in 5 years will be closest to ?
Options: a ) a . 36000 , b ) b . 37000 , c ) c . 38000 , d ) d . 39000 , e ) e . 40000
Rationale: 1 % is quite small and hence the answer is a )
Answer: a
Python program:
a = 3 + 4 
b = 5 * a
c = b * 100
d = 3 + 4 
e = d + 3 
f = c * e
Problem: there are 12 slate rocks , 17 pumice rocks , and 8 granite rocks randomly distributed in a certain field . if 2 rocks are chosen at random and without replacement , what is the probability that both rocks will be slate rocks ?
Options: a ) 5 / 36 , b ) 7 / 64 , c ) 9 / 83 , d ) 11 / 111 , e ) 13 / 135
Rationale: "12 / 37 * 11 / 36 = 11 / 111 the answer is d ."
Answer: d
Python program:
a = 12 + 17 
b = a + 8 
c = 12 / b
d = 12 - 1
e = 12 + 17 
f = e + 8 
g = f - 1
h = d / g
i = c * h
Problem: one day a car rental agency rented 3 / 4 of its cars , including 5 / 6 of its cars with cd players . if 3 / 5 of its cars have cd players , what percent of the cars that were not rented had cd players ?
Options: a ) 13 / 20 , b ) 11 / 15 , c ) 7 / 10 , d ) 4 / 7 , e ) 2 / 5
Rationale: "the cars with cd players which were not rented is ( 1 / 6 ) ( 3 / 5 ) = 1 / 10 of all the cars . the cars which were not rented is 1 / 4 of all the cars . the percent of non - rented cars which had cd players is ( 1 / 10 ) / ( 1 / 4 ) = 2 / 5 the answer is e ."
Answer: e
Python program:
a = 4 * 5
b = a * 6
c = 4 * b
d = c / 6
e = 4 * 5
f = e * 6
g = 4 * f
h = g / 6
i = h * 4
j = i / 5
k = d - j
l = 4 * 5
m = l * 6
n = 4 * 5
o = n * 6
p = 3 * o
q = p / 4
r = m - q
s = k / r
t = s * 100
Problem: how many words , with or without meaning , can be formed using all letters of the word red using each letter exactly once ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: the word red has exactly 3 letters which are all different . therefore the number of words that can be formed = number of permutations of 3 letters taken all at a time . = p ( 3 , 3 ) = 3 ! = 3 x 2 × 1 = 6 answer : a
Answer: a
Python program:
a = math.factorial(3)
Problem: of the 65 cars on a car lot , 30 have air - conditioning , 45 have air bag , and 12 have both air - conditioning and air bag . how many of the cars on the lot have neither air - conditioning nor air bag ?
Options: a ) 2 , b ) 8 , c ) 10 , d ) 15 , e ) 18
Rationale: "total - neither = all air conditioning + all air bags - both or 65 - neither = 30 + 45 - 12 = 63 . = > neither = 2 , hence c . answer : c"
Answer: c
Python program:
a = 30 + 45 
b = a - 12
c = 65 - b
Problem: a and b can do a piece of work in 2 days . with the help of c they finish the work in 1 days . c alone can do that piece of work in ?
Options: a ) 1.5 days , b ) 4 days , c ) 3 days , d ) 1 day , e ) 2 days
Rationale: c = 1 / 1 – 1 / 2 = 1 / 2 = > 2 days answer : e
Answer: e
Python program:
a = 1 / 2
b = 1 - a
c = 1/(b)
Problem: four machines , each working at the same constant rate , together can complete a certain job in 20 days . how many additional machines , each working at the same constant rate , will be needed to complete the job in 10 days ?
Options: a ) 5 , b ) 3 , c ) 4 , d ) 6 , e ) 1
Rationale: "rate of one machine = 1 job / ( 20 * 4 ) days let x = number of machines needed to complete the job in 10 days 1 / ( 4 * 20 ) * 10 * x = 1 job x = 8 8 - 4 = 4 answer : c"
Answer: c
Python program:
a = 4 + 1 
b = 20 * a
c = b / 10
d = 4 + 1 
e = c - d