euclaise/mathqa_programs huggingface dataset:
Problem: what is the lowest positive integer that is divisible by 4 through 7 , inclusive ?
Options: a ) 77 , b ) 270 , c ) 1600 , d ) 840 , e ) 980
Rationale: "the integer should be divisible by : 4 , 5 , 6 and 7 . the least common multiple of these integers is lcm = 4 * 5 * 6 * 7 = 840 answer : d"
Answer: d
Python program:
a = math.lcm(4, 7)
Problem: of the people who responded to a market survey , 60 preferred brand x and the rest preferred brand y . if the respondents indicated a preference for brand x over brand y by ratio of 3 to 1 , how many people responded to the survey ?
Options: a ) 80 , b ) 150 , c ) 240 , d ) 360 , e ) 480
Rationale: "ratio = 3 : 1 = > 3 x respondents preferred brand x and x preferred brand y since , no . of respondents who preferred brand x = 60 = > 3 x = 60 = > x = 20 hence total no . of respondents = 60 + 20 = 80 hence a is the answer ."
Answer: a
Python program:
a = 60 / 3
b = a + 60
Problem: the average of 50 numbers id 38 . if two numbers , namely 45 and 55 are discarded , the average of the remaining numbers is :
Options: a ) 22.3 , b ) 33.2 , c ) 22.2 , d ) 11.3 , e ) 37.5
Rationale: "explanation : total of 50 numbers = ( 50 × 38 ) = 1900 ( 50 × 38 ) = 1900 total of 48 numbers = ( 1900 - ( 45 + 55 ) ] = 1800 required average = 180048 = 2256 = 37.5 answer : e"
Answer: e
Python program:
a = 50 * 38
b = 45 + 55 
c = a - b
d = 50 - 2
e = c / d
Problem: when fair coin is tossed 9 times find the probability of getting head at least once .
Options: a ) 1 / 512 , b ) 511 / 512 , c ) 9 / 512 , d ) 503 / 51 , e ) 503 / 510
Rationale: 1 - 1 / 2 ^ 9 = 1 - 1 / 512 = 511 / 512 answer : b
Answer: b
Python program:
a = 1 / 2
b = a ** 9
c = 1 - b
Problem: an outlet pipe empties a tank which is full in 10 hours . if the inlet pipe is kept open , which lets water in at the rate of 16 litres / min then outlet pipe would take 8 hours longer . find the capacity of the tank .
Options: a ) 8600 litres , b ) 200 litres , c ) 21600 litres , d ) 11200 litres , e ) 13200 litres
Rationale: "let the rate of outlet pipe be x liters / hour ; rate of inlet pipe is 16 litres / min , or 16 * 60 = 960 liters / hour ; net outflow rate when both pipes operate would be x - 960 liters / hour . capacity of the tank = x * 10 hours = ( x - 960 ) * ( 10 + 8 ) hours 10 x = ( x - 960 ) * 18 - - > x = 2160 - - > capacity = 10 x = 21600 liters . answer : c ."
Answer: c
Python program:
a = 16 * const_60
b = 10 + 8 
c = a * b
d = c / 8
e = d * 10
Problem: in a certain company , a third of the workers do not have a retirement plan . 50 % of the workers who do not have a retirement plan are women , and 40 % of the workers who do have a retirement plan are men . if 120 of the workers of that company are men , how many of the workers are women ?
Options: a ) 80 , b ) 95 , c ) 105 , d ) 156 , e ) 210
Rationale: "set up equation : x = total number of workers 120 = 0,4 * 2 / 3 * x + 0,5 * 1 / 3 * x 120 = 13 / 30 x x = 276 276 - 120 = 156 answer d"
Answer: d
Python program:
a = 1 / 3
b = 1 / 3
c = 50 / 100
d = b * c
e = a - d
f = 1 / 3
g = 1 - f
h = 40 / 100
i = g * h
j = e + i 
k = 120 / j
l = 1 / 3
m = 50 / 100
n = l * m
o = 1 / 3
p = 1 - o
q = 1 / 3
r = 1 - q
s = 40 / 100
t = r * s
u = p - t
v = n + u 
w = k * v
Problem: which number need to add to 1782452 to get a number exactly divisible by 92 ?
Options: a ) 44 , b ) 43 , c ) 42 , d ) 41 , e ) 48
Rationale: "1782452 / 92 = 19374 and reminder = 44 . 92 - 44 = 48 so , the next number divisible by 92 is 48 places in front of 1782452 which means 48 + 1782452 = 1782500 48 should be added to 1782452 e"
Answer: e
Python program:
a = 1782452 / 92
b = math.floor(a)
c = b + 1 
d = 1782452 / 92
e = c - d
f = 92 * e
Problem: a boat takes 19 hours for travelling downstream fro poin a to point b and coming back to a point c midway between a and b . if the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph , what is the distance between a and b ?
Options: a ) 180 km , b ) 190 km , c ) 220 km , d ) 230 km , e ) none
Rationale: sol . speed downstream = ( 14 + 4 ) km / hr = 18 km / hr ; speed upstream = ( 14 - 4 ) km / hr = 10 km / hr . let the distance between a and b be x km . then , x / 18 + ( x / 2 ) / 10 = 19 ⇔ x / 18 + x / 20 = 19 ⇒ x = 180 km . answer a
Answer: a
Python program:
a = 14 - 4
b = a * 2
c = 1/(b)
d = 4 + 14 
e = 1/(d)
f = c + e 
g = 19 / f
Problem: city x has a population 7 times as great as the population of city y , which has a population twice as great as the population of city z . what is the ratio of the population of city x to the population of city z ?
Options: a ) 1 : 8 , b ) 1 : 4 , c ) 2 : 1 , d ) 14 : 1 , e ) 18 : 1
Rationale: x = 7 y , y = 2 * z x : y , y : z 7 : 1 , 2 : 1 14 : 2 , 2 : 1 so , x : z = 14 : 1 ( d )
Answer: d
Python program:
a = 7 * 2
Problem: in a certain supermarket , a triangular display of cans is arranged in 10 rows , numbered 1 through 10 from top to bottom . each successively numbered row contains 3 more cans than the row immediately above it . if there are fewer than 150 cans in the entire display , how many cans are in the sixth row ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
Rationale: "let x be the number of cans in row 1 . the total number of cans is x + ( x + 3 ) + . . . + ( x + 27 ) = 10 x + 3 ( 1 + 2 + . . . + 9 ) = 10 x + 3 ( 9 ) ( 10 ) / 2 = 10 x + 135 since the total is less than 150 , x must equal 1 . the number of cans in the 6 th row is 1 + 3 ( 5 ) = 16 the answer is b ."
Answer: b
Python program:
a = 3 + 3 
b = a * 3
c = 10 - 1
d = 3 * c
e = d / 2
f = e * 10
g = 150 - f
h = g / 10
i = math.floor(h)
j = b + i
Problem: in a new housing development , trees are to be planted along the sidewalk of a certain street . each tree takes up one square foot of sidewalk space , and there are to be 20 feet between each tree . how many trees can be planted if the road is 148 feet long ?
Options: a ) 8
b ) 9
c ) 10
d ) 11
e ) 16
Rationale: let t be the number of trees . then the length required for trees on the sidewalk will be 1 * t = t to maximize the number of trees , the number of 20 feet spaces between trees should be 1 less than total number of trees . for example , if there are 3 trees , then there should be 2 spaces between them . so the number of 20 feet spaces will be t - 1 . then , the length of sidewalk required for 20 feet spaces will be 20 * ( t - 1 ) it is given that total length of sidewalk is 148 feet . or 20 ( t - 1 ) + t = 148 or 20 t - 20 + t = 148 or 21 t = 168 or t = 8 answer : - a
Answer: a
Python program:
a = 148 - 1
b = 20 + 1 
c = a / b
d = c + 1
Problem: 20 balls are numbered 1 to 20 . a ball is drawn and then another ball is drawn without replacement . what is the probability that both balls have even numbers ?
Options: a ) 7 / 30 , b ) 3 / 14 , c ) 9 / 38 , d ) 4 / 21 , e ) 5 / 26
Rationale: "p ( 1 st ball is even ) = 10 / 20 p ( 2 nd ball is also even ) = 9 / 19 p ( both balls are even ) = 10 / 20 * 9 / 19 = 9 / 38 the answer is c ."
Answer: c
Python program:
a = 4 + 4 
b = a / 20
c = 4 + 4 
d = c - 1
e = 20 - 1
f = d / e
g = b * f
Problem: how long does a train 120 m long travelling at 60 kmph takes to cross a bridge of 170 m in length ?
Options: a ) 15.8 sec , b ) 14.9 sec , c ) 12.4 sec , d ) 16.8 sec , e ) 17.4 sec
Rationale: "e 17.4 sec d = 120 + 170 = 290 m s = 60 * 5 / 18 = 50 / 3 t = 290 * 3 / 50 = 17.4 sec answer is e"
Answer: e
Python program:
a = 120 + 170 
b = 60 * const_0_2778
c = a / b
Problem: the probability that a number selected at random from first 50 natural numbers is a composite number is
Options: a ) 21 / 25 , b ) 17 / 25 , c ) 4 / 25 , d ) 8 / 25 , e ) 10 / 25
Rationale: "the number of exhaustive events = 50 c 1 = 50 . we have 15 primes from 1 to 50 . number of favourable cases are 34 . therefore , required probability = 34 / 50 = 17 / 25 . answer : b"
Answer: b
Python program:
a = 6 * 3
b = a - 1
c = b * 2
d = c / 50
Problem: the speed of a train is 90 kmph . what is the distance covered by it in 15 minutes ?
Options: a ) 15 , b ) 66 , c ) 22.5 , d ) 52 , e ) 42
Rationale: "90 * 15 / 60 = 22.5 kmph answer : c"
Answer: c
Python program:
a = 15 / const_60
b = a * 90
Problem: 225 , or 15 ^ 2 , is the first perfect square that begins with two 2 s . what is the sum of the digits of the next perfect square to begin with two 2 s ?
Options: a ) 9 , b ) 12 , c ) 13 , d ) 14 , e ) 17
Rationale: because 16 ^ 2 = 256 , y the next perfect square to begin with two 2 s can not be 3 - digit . let ' s try 4 - digit . 40 ^ 2 = 1600 and 50 ^ 2 = 2500 . so , if there is a 4 - digit perfect square to begin with two 2 s it must be between 41 ^ 2 and 49 ^ 2 . test the middle number 45 ^ 2 = 2025 . test larger number : 46 ^ 2 = 2116 . test next number : 47 ^ 2 = 2209 . bingo ! the sum of the digits = 2 + 2 + 0 + 9 = 13 . answer : c .
Answer: c
Python program:
a = 2 + 2 
b = 12 * 4
c = b - 1
d = c ** 2
e = 12 - 2
f = 12 - 2
g = 12 - 2
h = f * g
i = e * h
j = 2 * i
k = 12 - 2
l = 12 - 2
m = k * l
n = 2 * m
o = j + n 
p = d - o
q = a + p
Problem: what is the angle between the two hands of a clock when time is 8 : 30
Options: a ) 15 degree , b ) 45 degree , c ) 55 degree , d ) 75 degree , e ) 65 degree
Rationale: "use the formula i . e 1 / 2 ( 60 h - 11 m ) / / h - hour and m - minute 1 / 2 ( 60 * 8 - 11 * 30 ) 1 / 2 ( 150 ) 75 degree answer : d"
Answer: d
Python program:
a = 3 * 2
b = 30 * a
c = b - 8
Problem: two trains are moving at 80 kmph and 70 kmph in opposite directions . their lengths are 150 m and 100 m respectively . the time they will take to pass each other completely is ?
Options: a ) 6 sec , b ) 7 sec , c ) 7 2 / 2 sec , d ) 8 sec , e ) 9 sec
Rationale: 70 + 80 = 150 * 5 / 18 = 125 / 3 mps d = 150 + 100 = 250 m t = 250 * 3 / 125 = 6 sec answer : a
Answer: a
Python program:
a = 150 + 100 
b = 80 + 70 
c = b * const_0_2778
d = a / c
Problem: if x > 0 , x / 50 + x / 25 is what percent of x ?
Options: a ) 6 % , b ) 25 % , c ) 37 1 / 2 % , d ) 60 % , e ) 75 %
Rationale: just plug and chug . since the question asks for percents , pick 100 . ( but any number will do . ) 100 / 50 + 100 / 25 = 2 + 4 = 6 6 is 6 % of 100 . answer : a
Answer: a
Python program:
a = 1 / 50
b = 1 / 25
c = a + b 
d = c * 100
Problem: the price of commodity p increases by 40 paise every year , while the price of commodity q increases by 15 paise every year . if in 2001 , the price of commodity p was rs . 4.20 and that of q was rs . 6.30 , in which year commodity p will cost 40 paise more than the commodity q ?
Options: a ) 2008 , b ) 2009 , c ) 2010 , d ) 2011 , e ) 2012
Rationale: let the commodity p costs 40 paise more than the commodity q after n years . price of the commodity p in 2001 = rs . 4.20 since the price of the commodity p increases by rs 0.40 every year , price of the commodity p after n years from 2001 = rs . 4.20 + ( n × . 40 ) price of the commodity q in 2001 = rs . 6.30 since the price of the commodity q increases by rs 0.15 every year , price of the commodity q after n years from 2001 = rs . 6.30 + ( n × . 15 ) since the commodity p costs rs . 0.40 more that the commodity q after n years from 2001 , 4.20 + ( n × . 40 ) = 6.30 + ( n × . 15 ) + 0.40 = > ( 40 n - . 15 n ) = 6.30 - 4.20 + 0.40 = 2.5 = > . 25 n = 2.5 = > n = 2.5 / . 25 = 10 = > commodity p costs rs . 0.40 more that the commodity q after 10 years from 2001 . i . e . , in 2011 answer : d
Answer: d
Python program:
a = 2001 + 10
Problem: a train 110 m long running at 52 kmph crosses a platform in 30 sec . what is the length of the platform ?
Options: a ) 287 , b ) 398 , c ) 323 , d ) 245 , e ) 267
Rationale: "d = 52 * 5 / 18 = 30 = 433 â € “ 110 = 323 answer : c"
Answer: c
Python program:
a = 52 * const_0_2778
b = 30 * a
c = b - 110
Problem: when magnified 1,000 times by an electron microscope , the image of a certain circular piece of tissue has a diameter of 1 centimeter . the actual diameter of the tissue , in centimeters , is
Options: a ) 0.005 , b ) 0.002 , c ) 0.001 , d ) 0.0005 , e ) 0.0002
Rationale: "it is very easy if x is the diameter , then the magnified length is 1000 x . ince 1000 x = 1 then x = 1 / 1000 = 0.001 . the answer is c"
Answer: c
Python program:
a = 1 / 1
Problem: the distance from city a to city b is 120 miles . while driving from city a to city b , cara drives at a constant speed of 30 miles per hour . dan leaves city a 90 minutes after cara . what is the minimum constant speed in miles per hour that dan must exceed in order to arrive in city b before cara ?
Options: a ) 42 , b ) 44 , c ) 46 , d ) 48 , e ) 50
Rationale: "the time it takes cara to drive to city b is 120 / 30 = 4 hours . dan needs to take less than 2.5 hours for the trip . dan needs to exceed a constant speed of 120 / 2.5 = 48 miles per hour . the answer is d ."
Answer: d
Python program:
a = 120 / 30
b = 90 / const_60
c = a - b
d = 120 / c
Problem: a and b began business with rs . 2000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000 more . at the end of the year , their profits amounted to rs . 630 find the share of a .
Options: a ) 175 , b ) 288 , c ) 277 , d ) 877 , e ) 361
Rationale: "( 2 * 8 + 1 * 4 ) : ( 4 * 8 + 5 * 4 ) 5 : 13 5 / 18 * 630 = 175 answer : a"
Answer: a
Python program:
a = 2000 * 8
b = 2000 - 1000
c = 12 - 8
d = b * c
e = a + d 
f = 4000 * 8
g = 4000 + 1000 
h = 12 - 8
i = g * h
j = f + i 
k = e + j 
l = 630 / k
m = 2000 * 8
n = 2000 - 1000
o = 12 - 8
p = n * o
q = m + p 
r = l * q
Problem: a fair coin is tossed 9 times . what is the probability of getting more heads than tails in 9 tosses ?
Options: a ) 1 / 2 , b ) 63 / 128 , c ) 4 / 7 , d ) 61 / 256 , e ) 63 / 64
Rationale: "on each toss , the probability of getting a head is 1 / 2 and the probability of getting a tail is 1 / 2 . there is no way to get the same number of heads and tails on an odd number of tosses . there will either be more heads or more tails . then there must be more heads on half of the possible outcomes and more tails on half of the possible outcomes . p ( more heads ) = 1 / 2 the answer is a ."
Answer: a
Python program:
a = math.comb(9, 2)
b = math.comb(9, 3)
c = a + b 
d = math.comb(9, 4)
e = c + d 
f = math.comb(9, 9)
g = e + f 
h = 2 ** 9
i = g / h
Problem: if 18 bindres bind 900 books in 10 days , how many binders will be required to bind 660 books in 12 days ?
Options: a ) 71 , b ) 12 , c ) 18 , d ) 11 , e ) 29
Rationale: explanation : let the required no of binders be x . less books , less binders ( direct proportion ) more days , less binders ( indirect proportion ) \ inline \ fn _ jvn \ left . \ begin { matrix } books \ : 900 : 600 \ \ days \ : \ : 12 : 10 \ end { matrix } \ right \ } : : 18 : x \ inline \ fn _ jvn \ therefore \ inline \ fn _ jvn ( 900 \ times 12 \ times x ) = ( 600 \ times 10 \ times 18 ) \ inline \ fn _ jvn \ leftrightarrow x = \ inline \ fn _ jvn \ frac { 600 \ times 10 \ times 18 } { 900 \ times 12 } = 11 answer : d
Answer: d
Python program:
a = 660 * 10
b = a * 18
c = 900 * 12
d = b / c
Problem: if a ã — b = 2 a - 3 b + ab , then 1 ã — 2 + 2 ã — 1 is equal to :
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: explanation : 1 ã — 2 + 2 ã — 1 = ( 2 ã — 1 - 3 ã — 2 + 1 ã — 2 ) + ( 2 ã — 2 - 3 ã — 1 + 2 ã — 1 ) = ( 2 - 6 + 2 + 4 - 3 + 2 ) = 1 . answer : a
Answer: a
Python program:
a = 2 * 1
b = 3 * 2
c = a - b
d = 1 * 2
e = c + d 
f = 2 * 2
g = 3 * 1
h = f - g
i = 2 * 1
j = h + i 
k = e + j
Problem: when a train travels at a speed of 80 kmph , it reaches the destination on time . when the same train travels at a speed of 50 kmph , it reaches its destination 15 min late . what is the length of journey ?
Options: a ) 25 km , b ) 50 km , c ) 60 km , d ) 85 km , e ) 95 km
Rationale: "let x be the time reached with the speed 80 km / h 50 km / h - - - - > x + 15 distance is equal so 80 ( km / h ) × xhr = 50 ( km / h ) × ( x + 15 ) hr so 80 x = 50 x + 750 so the would be in km and x = 25 answer : a"
Answer: a
Python program:
a = 15 / const_60
b = a * 50
c = b / 50
d = const_60 * c
Problem: a train running at the speed of 60 km / hr crosses a pole in 4 seconds . find the length of the train .
Options: a ) 66.67 , b ) 882 , c ) 772 , d ) 252 , e ) 121
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 4 = 66.67 meter . answer : a"
Answer: a
Python program:
a = 60 * 1000
b = a / 3600
c = b * 4
Problem: the average marks of a class of 30 students is 40 and that of another class of 50 students is 60 . find the average marks of all the students ?
Options: a ) 82.5 , b ) 52.9 , c ) 52.2 , d ) 52.5 , e ) 52.7
Rationale: "sum of the marks for the class of 30 students = 30 * 40 = 1200 sum of the marks for the class of 50 students = 50 * 60 = 3000 sum of the marks for the class of 80 students = 1200 + 3000 = 4200 average marks of all the students = 4200 / 80 = 52.5 answer : d"
Answer: d
Python program:
a = 30 * 40
b = 50 * 60
c = a + b 
d = 30 + 50 
e = c / d
Problem: 75 men working 8 hours per day dig 50 m deep . how many extra men should be put to dig to a depth of 70 m working 6 hours per day ?
Options: a ) 75 , b ) 45 , c ) 55 , d ) 65 , e ) 35
Rationale: ( 75 * 8 ) / 50 = ( x * 6 ) / 70 = > x = 140 140 â € “ 65 = 65 answer : d
Answer: d
Python program:
a = 75 * 8
b = a / 50
c = b * 70
d = c / 6
e = d - 75
Problem: on a certain date , pat invested $ 5,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 12 years will be $ 20,000 , in how many years , the total value of the investment plus interest will increase to $ 30,000 ?
Options: a ) 15 , b ) 16 , c ) 18 , d ) 20 , e ) 24
Rationale: if i were to choose during the test , would go for 18 or 20 . probably 18 cuz it wont take too long to get the value doubled . . . . i found a method : rule of 72 . given an x % return , it takes 5,000 to quadralope 12 years . so according to the rule : 72 / x is the no of years 5 , 000.00 took to double 10 , 000.00 . again , 10 , 000.00 took to double 20 , 000.00 same ( 72 / x ) no of years . 72 / x + 72 / x = 12 x = 12 % ( though rate here is not very much required ) . again , 20 , 000.00 takes the same ( 72 / x ) no of years to double 30 , 000.00 . 72 / x = 6 years . so altogather : 5,000 - 10,000 = 6 years 10,000 - 20,000 = 6 years 20,000 - 30,000 = 3 years answer a 15 years .
Answer: a
Python program:
a = 3 * 10
b = 4 + 1 
c = a / b
d = math.log(c)
e = 2 * 10
f = 4 + 1 
g = e / f
h = 1 / 12
i = g ** h
j = math.log(i)
k = d / j
Problem: a clock store sold a certain clock to a collector for 20 percent more than the store had originally paid for the clock . when the collector tried to resell the clock to the store , the store bought it back at 50 percent of what the collector had paid . the shop then sold the clock again at a profit of 80 percent on its buy - back price . if the difference between the clock ' s original cost to the shop and the clock ' s buy - back price was $ 100 , for how much did the shop sell the clock the second time ?
Options: a ) $ 270 , b ) $ 250 , c ) $ 240 , d ) $ 220 , e ) $ 200
Rationale: original price = x sold to collector at 1.2 x re - buy price = 1.2 x * 0.5 = 0.6 x therefore , x - 0.6 x = 100 ; x = 250 second selling price = 1.8 * 0.6 * 250 = 270 answer : a
Answer: a
Python program:
a = 100 + 80 
b = 100 + 20 
c = b / 2
d = a * c
e = d / 100
f = 100 * e
g = 100 + 20 
h = g / 2
i = h - 20
j = f / i
Problem: the average of first six prime numbers greater than 3 is ?
Options: a ) 16 , b ) 10 , c ) 12 , d ) 19 , e ) 17.8
Rationale: "5 + 7 + 11 + 13 + 17 + 19 = 72 / 6 = 12 answer : c"
Answer: c
Python program:
a = 3 + 1
Problem: positive integer y is 50 percent of 50 percent of positive integer x , and 2 y percent of x equals 100 . what is the value of x ?
Options: a ) 50 , b ) 100 , c ) 140 , d ) 1,000 , e ) 2,000
Rationale: "y = 50 % of 50 % 0 f x = x / 4 and 2 y / 100 of x = 100 2 y / 100 * 4 y = 5000 y = 35 and x = 140 answer - c"
Answer: c
Python program:
a = 50 / 2
b = 50 / 2
c = a * b
d = c * 1000
Problem: nhai employs 100 men to build a highway of 2 km in 50 days working 8 hours a day . if in 25 days they completed 1 / 3 part of work . than how many more employees should nhai hire to finish it in time working 10 hours a day ?
Options: a ) 22 , b ) 60 , c ) 28 , d ) 11 , e ) 218
Rationale: "here 2 km is immaterial . the given problem can be written in a tabular form like below . we can apply chain rule now . total men required to complete the remaining work = 100 × 2525 × 810 × 2313100 × 2525 × 810 × 2313 = 160 so additional men required = 160 - 100 = 60 answer : b"
Answer: b
Python program:
a = 100 * 25
b = a * 8
c = 2 * b
d = 25 * 10
e = c / d
f = e - 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 . 1680 ?
Options: a ) 1500 , b ) 2777 , c ) 2889 , d ) 27670 , e ) 2771
Rationale: "1680 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 1500 . 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 = 1680 / f
Problem: if x : y = 1 : 2 , find the value of ( 2 x + 3 y ) : ( x + 4 y )
Options: a ) 5 : 6 , b ) 7 : 8 , c ) 8 : 9 , d ) 9 : 10 , e ) 11 : 12
Rationale: "x : y = 1 : 2 means x / y = 1 / 2 now , ( 2 x + 3 y ) : ( x + 4 y ) = ( 2 x + 3 y ) / ( x + 4 y ) [ divide numerator and denominator by y . ] = [ ( 2 x + 3 y ) / y ] / [ ( x + 4 y ) / 2 ] = [ 2 ( x / y ) + 3 ] / [ ( x / y ) + 4 ] , put x / y = 1 / 2 we get = [ 2 ( 1 / 2 ) + 3 ) / ( 1 / 2 + 4 ) = ( 1 + 3 ) / [ ( 1 + 8 ) / 2 ] = 4 / ( 9 / 2 ) = 4 / 1 × 2 / 9 = 8 / 9 therefore the value of ( 2 x + 3 y ) : ( x + 4 y ) = 8 : 9 answer is c"
Answer: c
Python program:
a = 2 ** 3
b = a + 3 
c = 1 + 2 
d = c + 3 
e = b / d
Problem: what number has a 5 : 1 ratio to the number 13 ?
Options: a ) 22 , b ) 50 , c ) 88 , d ) 65 , e ) 12
Rationale: "5 : 1 = x : 13 x = 65 answer : d"
Answer: d
Python program:
a = 13 * 5
Problem: a train 490 m long , running with a speed of 63 km / hr will pass a tree in ?
Options: a ) 15 sec , b ) 16 sec , c ) 28 sec , d ) 20 sec , e ) 25 sec
Rationale: "speed = 63 * 5 / 18 = 35 / 2 m / sec time taken = 490 * 2 / 35 = 28 sec answer : c"
Answer: c
Python program:
a = 63 * 1000
b = 490 / a
c = b * 3600
Problem: the dimensions of a field are 20 m by 5 m . a pit 10 m long , 4 m wide and 3 m deep is dug in one corner of the field and the earth removed has been evenly spread over the remaining area of the field . what will be the rise in the height of field as a result of this operation ?
Options: a ) 1 m , b ) 5 m , c ) 4 m , d ) 2 m , e ) 3 m
Rationale: "the volume of the earth removed is 10 * 4 * 3 = 120 m ^ 3 . the remaining area of the field is 20 * 5 - 10 * 4 = 60 m ^ 2 . 120 m ^ 3 of the earth evenly spread over the area of 60 m ^ 2 will rise the height by ( height ) = ( volume ) / ( area ) = 120 / 60 = 2 m . answer : d"
Answer: d
Python program:
a = 5 * 10
b = rectangle_area - (
c = a / b
Problem: george does 3 / 5 th of a piece of work in 9 days . he then calls in paul , and they finish the work in 4 days . how long would paul take to do the work by himself ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: 100 % work will be done by george in 15 days ( 1 / 15 ) 9 + ( 1 / 15 + 1 / x ) 4 = 1 solving this eqn . we get x = 30 hence paul take to do the work in 30 days answer : a
Answer: a
Python program:
a = 3 / 5
b = 1 - a
c = 5 * 3
d = 1 / c
e = 4 * d
f = b - e
g = f / 4
h = 1/(g)
Problem: a boat sails 15 km of a river towards upstream in 5 hours . how long will it take to cover the same distance downstream , if the speed of current is one - fourth the speed of the boat in still water :
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "explanation : upstream speed = b - s downstream speed = b + s b - s = 15 / 5 = 3 km / h again b = 4 s therefore b - s = 3 = 3 s = > s = 1 and b = 4 km / h therefore b + s = 5 km / h therefore , time during downstream = 15 / 5 = 3 h answer : b ) 3 h"
Answer: b
Python program:
a = 15 / 5
Problem: if 15 % of a is the same as 20 % of b , then a : b is :
Options: a ) 3 : 4 , b ) 4 : 3 , c ) 17 : 16 , d ) 16 : 17 , e ) none of these
Rationale: "expl : 15 % of a i = 20 % of b = 15 a / 100 = 20 b / 100 = 4 / 3 = 4 : 3 answer : b"
Answer: b
Python program:
a = 20 / 100
b = 15 / 100
c = a / b