euclaise/mathqa_programs huggingface dataset:
Problem: a boy multiplied 987 by a certain number and obtained 559981 as his answer . if in the answer both 98 are wrong and other digits are correct , then the correct answer would be :
Options: a ) 553681 , b ) 555181 , c ) 555681 , d ) 556581 , e ) 555581
Rationale: "987 = 3 x 7 x 47 . so , the required number must be divisible by each one of 3 , 7 , 47 553681 - - > sum of digits = 28 , not divisible by 3 555181 sum of digits = 25 , not divisible by 3 555681 is divisible by each one of 3 , 7 , 47 . 556581 sum of digits = 30 , not divisible by 7 555581 sum of digits = 29 , not divisible by 3 so the answer is c ."
Answer: c
Python program:
a = 559981 / 987
b = a - 4
c = b - const_0_33
d = c * 987
Problem: given f ( x ) = 2 x – 3 , for what value of x does 2 * [ f ( x ) ] – 11 = f ( x – 2 ) ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "2 ( 2 x - 3 ) - 11 = 2 ( x - 2 ) - 3 2 x = 10 x = 5 the answer is d ."
Answer: d
Python program:
a = 2 * 3
b = a + 11 
c = 2 * 2
d = c + 3 
e = b - d
f = 2 * 2
g = 2 * 1
h = f - g
i = e / h
Problem: pipe a fills a tank of capacity 750 liters at the rate of 40 liters a minute . another pipe b fills the same tank at the rate of 30 liters a minute . a pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute . if pipe a is kept open for a minute and then closed and pipe b is open for a minute and then closed and then pipe c is open for a minute and then closed and the cycle is repeated , when will the tank be full ?
Options: a ) 45 minutes , b ) 14 minutes , c ) 39 minutes , d ) 40 minutes 20 seconds , e ) none of these
Rationale: "in one cycle they fill 40 + 30 - 20 = 50 liters 750 = 50 * n = > n = 15 here n = number of cycles . total time = 15 * 3 = 45 as in one cycle there are 3 minutes . thus 45 minutes answer : a"
Answer: a
Python program:
a = 40 + 30 
b = a - 20
c = 750 / b
d = c * 3
Problem: the first doughnut is priced at $ 1 and then if you purchase additional doughnuts as dozens then the price is $ 6 / dozen . what is the total number of doughnuts purchased if you paid $ 21 ?
Options: a ) 33 , b ) 35 , c ) 37 , d ) 39 , e ) 41
Rationale: "$ 21 = 3 * $ 6 + $ 3 the number of doughnuts is 3 * 12 + 3 = 39 the answer is d ."
Answer: d
Python program:
a = 21 / 6
b = a * 12
Problem: all the milk in container a which was filled to its brim was poured into two containers b and c . the quantity of milk in container b was 62.5 % less than the capacity of container a . if 150 liters was now transferred from c to b , then both the containers would have equal quantities of milk . what was the initial quantity of milk in container a ?
Options: a ) 1200 , b ) 1723 , c ) 1129 , d ) 2613 , e ) 1372
Rationale: "a b has 62.5 % or ( 5 / 8 ) of the milk in a . therefore , let the quantity of milk in container a ( initially ) be 8 k . quantity of milk in b = 8 k - 5 k = 3 k . quantity of milk in container c = 8 k - 3 k = 5 k container : a b c quantity of milk : 8 k 3 k 5 k it is given that if 150 liters was transferred from container c to container b , then both the containers would have equal quantities of milk . 5 k - 150 = 3 k + 150 = > 2 k = 300 = > k = 150 the initial quantity of milk in a = 8 k = 8 * 150 = 1200 liters ."
Answer: a
Python program:
a = 1/(2)
b = 62 / 5
c = 1 - b
d = a - c
e = 150 / d
Problem: a train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 17 seconds . what is the length of the platform in meters ?
Options: a ) 240 meters , b ) 260 meters , c ) 420 meters , d ) 600 meters , e ) can not be determined
Rationale: "speed of the train in metres / sec = 72000 / 3600 = 20 distance travelled by train to cross the platform = 30 * 20 = 600 = length of train + length of platform distance travelled by train to cross the man = 17 * 20 = 340 = length of train length of platform = 600 - 340 = 260 answer : b"
Answer: b
Python program:
a = 72 * 1000
b = a / 3600
c = b * 30
d = 72 * 1000
e = d / 3600
f = e * 17
g = c - f
Problem: two numbers have a h . c . f of 14 and a product of two numbers is 2562 . find the l . c . m of the two numbers ?
Options: a ) 140 , b ) 150 , c ) 160 , d ) 170 , e ) 183
Rationale: "l . c . m of two numbers is given by ( product of the two numbers ) / ( h . c . f of the two numbers ) = 2562 / 14 = 183 . answer : e"
Answer: e
Python program:
a = 2562 / 14
Problem: a can complete a work in 10 days and b can do the same work in 5 days . if a after doing 2 days , leaves the work , find in how many days b will do the remaining work ?
Options: a ) 2 days , b ) 4 days , c ) 6 days , d ) 7 days , e ) 10 days
Rationale: "the required answer = ( 10 - 2 ) * 5 / 10 = 40 / 10 = 4 days answer is b"
Answer: b
Python program:
a = 10 * 2
b = 10 / 2
c = a + b
Problem: let the number which when multiplied by 13 is increased by 180 .
Options: a ) 14 , b ) 20 , c ) 15 , d ) 28 , e ) 30
Rationale: "solution let the number be x . then , 13 x - x = 180 ‹ = › 12 x = 180 x ‹ = › 15 . answer c"
Answer: c
Python program:
a = 13 - 1
b = 180 / a
Problem: 10 ^ ( 655 ) ã · 10 ^ ( 652 ) = ?
Options: a ) 1 , b ) 100 , c ) 10000 , d ) 100000 , e ) 1000
Rationale: "10 ^ ( 655 ) ã · 10 ^ ( 652 ) = 10 ^ ( 655 - 652 ) = 10 ^ 3 = 1000 answer : e"
Answer: e
Python program:
a = 655 - 652
b = 10 ** a
Problem: if 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent , then in how many points do they intersect ?
Options: a ) 110 , b ) 130 , c ) 150 , d ) 170 , e ) 190
Rationale: if two lines are not parallel , then they will intersect in exactly one point . lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel . we are also given that no three lines are concurrent . this means that no three lines intersect at the same point . so every pair of two lines we select will have a unique point of intersection which they will not share with any third line . the number of ways to select 2 lines from 20 lines is 20 c 2 = 190 the answer is e .
Answer: e
Python program:
a = math.factorial(20)
b = 20 - 2
c = math.factorial(b)
d = math.factorial(2)
e = c * d
f = a / e
Problem: the jogging track in a sports complex is 1000 meters in circumference . deepak and his wife start from the same point and walk in opposite directions at 20 km / hr and 12 km / hr respectively . they will meet for the first time in ?
Options: a ) 32 min , b ) 40 min , c ) 35 min , d ) 25 min , e ) 20 min
Rationale: "clearly , the two will meet when they are 1000 m apart to be 20 + 12 = 32 km apart , they take 1 hour to be 1000 m apart , they take 32 * 1000 / 1000 = 32 min . answer is a"
Answer: a
Python program:
a = 20 + 12
Problem: an escalator moves towards the top level at the rate of 15 ft . sec and its length is 180 feet . if a person walks on the moving escalator at the rate of 3 feet per second towards the top level , how much time does he take to cover the entire length .
Options: a ) 12 sec , b ) 20 sec , c ) 15 sec , d ) 18 sec , e ) 10 sec
Rationale: "explanation : time taken to cover the entire length = tot . dist / resultant speed = 180 / ( 15 + 3 ) = 10 sec answer : e"
Answer: e
Python program:
a = 15 + 3 
b = 180 / a
Problem: a new home buyer pays 4 % annual interest on her first mortgage and 9 % annual interest on her second mortgage . if she borrowed a total of $ 335,000 , 80 % of which was in the first mortgage , what is her approximate monthly interest payment ?
Options: a ) $ 1,395 , b ) $ 1,733 , c ) $ 3,466 , d ) $ 13,333 , e ) $ 20,796
Rationale: "0.04 x + 0.09 y = 335000 [ 1 ] 0.04 x = 0.80 * 335000 = 268000 [ 2 ] 268000 + 0.09 y = 320000 - - > 0.09 y = 67000 [ 3 ] 268000 / 12 = 22333.3333 [ 4 ] 67000 / 12 = 5583.333 [ 5 ] adding [ 4,5 ] we get : 27916 [ 6 ] dividing [ 6 ] / 2 to get an average we get 1.395 , ans a"
Answer: a
Python program:
a = 4 * 2
b = 9 - a
Problem: a train 200 meters long completely crosses a 300 meters long bridge in 45 seconds . what is the speed of the train is ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: "s = ( 200 + 300 ) / 45 = 500 / 45 * 18 / 5 = 40 answer : d"
Answer: d
Python program:
a = 200 + 300 
b = a / 1000
c = 45 / 3600
d = b / c
Problem: john and ingrid pay 30 % and 40 % tax annually , respectively . if john makes $ 56000 and ingrid makes $ 72000 , what is their combined tax rate ?
Options: a ) 32 % , b ) 34.4 % , c ) 35 % , d ) 35.6 % , e ) 36.4 %
Rationale: "( 1 ) when 30 and 40 has equal weight or weight = 1 / 2 , the answer would be 35 . ( 2 ) when 40 has larger weight than 30 , the answer would be in between 35 and 40 . unfortunately , we have 2 answer choices d and e that fit that condition so we need to narrow down our range . ( 3 ) get 72000 / 128000 = 72 / 128 = 9 / 16 . 9 / 16 is a little above 8 / 16 = 1 / 2 . thus , our answer is just a little above 35 . answer : d"
Answer: d
Python program:
a = 30 / 100
b = a * 56000
c = 40 / 100
d = c * 72000
e = b + d 
f = 72000 + 56000 
g = e / f
h = g * 100
Problem: john ' s bank ' s saving amount is decreased 30 % due to loan payment and current balance is rs . 7000 . find the actual balance before deduction ?
Options: a ) 8000 , b ) 8500 , c ) 9000 , d ) 9500 , e ) 10000
Rationale: "cp * ( 70 / 100 ) = 7000 cp = 100 * 100 = > cp = 10000 answer : e"
Answer: e
Python program:
a = 7000 * 30
b = a / 100
c = b + 7000
Problem: during a special promotion , a certain filling station is offering a 10 percent discount on gas purchased after the first 6 gallons . if kim purchased 20 gallons of gas , and isabella purchased 25 gallons of gas , then isabella ‟ s total per - gallon discount is what percent of kim ‟ s total per - gallon discount ?
Options: a ) 80 % , b ) 100 % , c ) 109 % , d ) 120 % , e ) 140 %
Rationale: kim purchased 20 gallons of gas . she paid for 6 + 0.9 * 14 = 18.6 gallons , so the overall discount she got was 1.4 / 20 = 7 % . isabella purchased 25 gallons of gas . she paid for 6 + 0.9 * 19 = 23.1 gallons , so the overall discount she got was 1.9 / 25 = 7.6 % . 7.6 is 7.6 / 7 * 100 = 109 % of 7 . answer : c .
Answer: c
Python program:
a = 10 - 1
b = 10 + a 
c = 100 - 10
d = b * c
e = d / 100
f = e + 6 
g = f / 25
h = 1 - g
i = h * 100
j = 10 + 4 
k = 100 - 10
l = j * k
m = l / 100
n = 6 + m 
o = n / 20
p = 1 - o
q = p * 100
r = i / q
s = r * 100
Problem: a farmer with 1,350 acres of land had planted his fields with corn , sugar cane , and tobacco in the ratio of 3 : 2 : 4 , respectively , but he wanted to make more money , so he shifted the ratio to 2 : 2 : 5 , respectively . how many more acres of land were planted with tobacco under the new system ?
Options: a ) 90 , b ) 150 , c ) 270 , d ) 300 , e ) 450
Rationale: "originally ( 4 / 9 ) * 1350 = 600 acres were planted with tobacco . in the new system ( 5 / 9 ) * 1350 = 750 acres were planted with tobacco . thus 750 - 600 = 150 more acres were planted with tobacco . the answer is b ."
Answer: b
Python program:
a = 100 * 10
b = 3 * 100
c = a + b 
d = 3 * 10
e = c + d 
f = 3 + 2 
g = f + 2 
h = 3 / g
i = e * h
j = 100 * 10
k = 3 * 100
l = j + k 
m = 3 * 10
n = l + m 
o = 3 + 2 
p = o + 2 
q = 2 / p
r = n * q
s = i - r
Problem: if two of the 4 expressions x + y , x + 5 y , x - y , and 5 x - y are chosen at random , what is the probability w that their product will be of the form of x ^ 2 - ( by ) ^ 2 , where b is an integer ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) w = 1 / 6
Rationale: only ( x + y ) ( x - y ) pair will give the form x ^ 2 - ( by ) ^ 2 the probability of selecting these two pairs are 1 / 4 * 1 / 3 = 1 / 12 , assuming x + y is picked first , then x - y , but x - y can be picked first followed by x + y . so the probability w = 1 / 12 * 2 = 1 / 6 ans e
Answer: e
Python program:
a = math.factorial(4)
b = math.factorial(2)
c = a / b
d = math.factorial(2)
e = c / d
f = 1 / e
Problem: if 4 men working 10 hours a day earn rs . 1200 per week , then 9 men working 6 hours a day will earn how much per week ?
Options: a ) rs 840 , b ) rs 1320 , c ) rs 1620 , d ) rs 1680 , e ) none of these
Rationale: "explanation : ( men 4 : 9 ) : ( hrs / day 10 : 6 ) : : 1200 : x hence 4 * 10 * x = 9 * 6 * 1200 or x = 9 * 6 * 1200 / 4 * 10 = 1620 answer : c"
Answer: c
Python program:
a = 9 * 6
b = 4 * 10
c = a / b
d = c * 1200
Problem: a test has 180 questions . each question has 5 options , but only 1 option is correct . if test - takers mark the correct option , they are awarded 1 point . however , if an answer is incorrectly marked , the test - taker loses 0.25 points . no points are awarded or deducted if a question is not attempted . a certain group of test - takers attempted different numbers of questions , but each test - taker still received the same net score of 40 . what is the maximum possible number of such test - takers ?
Options: a ) 29 , b ) 33 , c ) 35 , d ) 40 , e ) 42
Rationale: "a correct answers get you 1 point , an incorrect answer gets you minus 1 / 4 point and a skipped question gets you 0 points . since there are 200 total questions , there are a variety of ways to get a total of 40 points . let c be the number of correct answers and let i be the number of incorrect answers . to get 40 points , a test taker must have at least 40 correct answers . then c = > 40 . for every correct question above 40 , the test taker has 4 incorrect answers . then , the i = 4 * ( c - 40 ) . also , i + c < = 180 . thus 5 c < = 340 and so c < = 68 . then 40 < = c < = 68 and c can have 29 possible values . the answer is a ."
Answer: a
Python program:
a = 180 - 40
b = a / 5
c = b + 1 
d = c + 1
Problem: jean drew a gumball at random from a jar of pink and blue gumballs . since the gumball she selected was blue and she wanted a pink one , she replaced it and drew another . the second gumball also happened to be blue and she replaced it as well . if the probability of her drawing the two blue gumballs was 16 / 49 what is the probability that the next one she draws will be pink ?
Options: a ) 1 / 49 , b ) 4 / 7 , c ) 3 / 7 , d ) 16 / 49 , e ) 40 / 49
Rationale: "the probability of drawing a pink gumball both times is the same . the probability that she drew two blue gumballs = 16 / 49 = ( 4 / 7 ) * ( 4 / 7 ) therefore probability that the next one she draws is pink = 3 / 7 option ( c )"
Answer: c
Python program:
a = 16 / 49
b = math.sqrt(a)
c = 1 - b
Problem: if x is 25 percent greater than 88 , then x =
Options: a ) 110 , b ) 70.4 , c ) 86 , d ) 105.6 , e ) 108
Rationale: "x = 88 * 1.25 = 110 so the answer is a ."
Answer: a
Python program:
a = 25 / 100
b = a * 88
c = 88 + b
Problem: a cistern 8 meters long and 4 meters wide contains water up to a depth of 1 meter 25 cm . what is the total area of the wet surface ?
Options: a ) 40 , b ) 48 , c ) 54 , d ) 62 , e ) 76
Rationale: "area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 4 x 1.25 + 8 x 1.25 ) + 8 x 4 ] = 62 the answer is d ."
Answer: d
Python program:
a = 8 * 4
b = 25 / 100
c = 1 + b 
d = 4 * c
e = 2 * d
f = a + e 
g = 25 / 100
h = 1 + g 
i = 8 * h
j = 2 * i
k = f + j
Problem: at a certain food stand , the price of each apple is 40 ¢ and the price of each orange is 60 ¢ . mary selects a total of 10 apples and oranges from the food stand , and the average ( arithmetic mean ) price of the 10 pieces of fruit is 54 ¢ . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 48 ¢ ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "if the average price is 54 , then mary has 7 oranges and 3 apples ( a ratio of 7 : 3 ) . for the average price to be 48 , the ratio should be 2 : 3 . mary must put back 5 oranges . the answer is e ."
Answer: e
Python program:
a = 60 * 10
b = 54 * 10
c = a - b
d = 60 - 40
e = c / d
f = e * 40
g = 60 * 10
h = 54 * 10
i = g - h
j = 60 - 40
k = i / j
l = 10 - k
m = l * 60
n = f + m 
o = 48 * 10
p = n - o
q = 60 - 48
r = p / q
Problem: david has $ 1800 at the beginning of his trip , after spending money , he still has exactly $ 800 less than he spent on the trip . how much money does john still have ?
Options: a ) $ 200 , b ) $ 500 , c ) $ 600 , d ) $ 800 , e ) $ 1,200
Rationale: suppose total money spent = x not spend ( money he still has ) = x - 800 x + x - 800 = 1800 x = 1300 money not spend = 1300 - 800 = 500 answer : b
Answer: b
Python program:
a = 1800 - 800
b = a / 2
Problem: two cylinders of the radius in the ratio 3 : 5 and heights in the ratio 10 : 9 . then find the volumes ratio ?
Options: a ) 4 : 5
b ) 1 : 5
c ) 3 : 5
d ) 1.5 : 5
e ) 2 : 5
Rationale: π r ( power 2 ) h : π r ( power 2 ) h 9 × 10 : 25 × 9 90 : 225 2 : 5 answer is e .
Answer: e
Python program:
a = 3 ** 2
b = a * 10
c = 5 ** 2
d = c * 9
e = b / d
Problem: angelo and isabella are both salespersons . in any given week , angelo makes $ 540 in base salary plus 8 percent of the portion of his sales above $ 1,000 for that week . isabella makes 10 percent of her total sales for any given week . for what amount of weekly sales would angelo and isabella earn the same amount of money ?
Options: a ) 23,000 , b ) 24,500 , c ) 25,500 , d ) 26,500 , e ) 27,500
Rationale: "let the weekly sales of both = x 540 + ( x − 1000 ) 8 / 100 = 10 / 100 x x = 23000 answer : a"
Answer: a
Python program:
a = 8 / 100
b = 1 * 0
c = 540 - b
d = 10 / 100
e = 8 / 100
f = d - e
g = c / f
h = g / 1
i = math.floor(h)
Problem: a computer store offers employees a 30 % discount off the retail price . if the store purchased a computer from the manufacturer for $ 1500 dollars and marked up the price 30 % to the final retail price , how much would an employee save if he purchased the computer at the employee discount ( 30 % off retail price ) as opposed to the final retail price .
Options: a ) 525 , b ) 545 , c ) 565 , d ) 575 , e ) 585
Rationale: "cost price = 1500 profit = 30 % = 30 % of 1500 = 450 selling price = cp + profit sp = 1950 a discount of 30 % to employees means 30 % off on 1950 so 30 % of 1950 = 585 ans e"
Answer: e
Python program:
a = 1500 * 30
b = a / 100
c = b + 1500 
d = 1500 / 100
e = d * 2
f = c / e
Problem: car a runs at the speed of 65 km / hr & reaches its destination in 5 hr . car b runs at the speed of 70 km / h & reaches its destination in 4 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 11 : 6 , b ) 12 : 7 , c ) 13 : 7 , d ) 15 : 6 , e ) 65 : 56
Rationale: sol . distance travelled by car a = 65 ã — 5 = 325 km distance travelled by car b = 70 ã — 4 = 280 km ratio = 325 / 280 = 65 : 56 e
Answer: e
Python program:
a = 65 * 5
b = 70 * 4
c = a / b
Problem: if 9 a - b = 10 b + 70 = - 12 b - 2 a , what is the value of 11 a + 11 b ?
Options: a ) - 4 , b ) - 2 , c ) 0 , d ) 2 , e ) 4
Rationale: "( i ) 9 a - 11 b = 70 ( ii ) 2 a + 22 b = - 70 adding ( i ) and ( ii ) : 11 a + 11 b = 0 the answer is c ."
Answer: c
Python program:
a = 70 / 2
b = a * 2
c = negate * (
Problem: how many distinct integer values of n satisfy the inequality | | n - 3 | + 4 | ≤ 17 ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "so i can write this as in - 3 i + 4 < = 17 or in - 3 i < = 13 so n can have - 10 to 16 = 15 true values . . . . a"
Answer: a
Python program:
a = 3 * 4
b = a + 1
Problem: there are 250 men and 150 women in a committee , if all will work they will complete 12 units per day , if all men work they will complete 15 units per day , how many units will women complete per day ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 7
Rationale: i think there is a mistake in this question . if all men and women together complete 12 units , how only men can do 15 units of work a day ? forgetting about the reality , women can do - 3 units a day . answer : b
Answer: b
Python program:
a = 15 - 12
Problem: the cash difference between the selling prices of an article at a profit of 10 % and 6 % is rs . 3 . the ratio of the two selling prices is ?
Options: a ) 52 : 56 , b ) 55 : 53 , c ) 52 : 50 , d ) 22 : 56 , e ) 52 : 51
Rationale: "let c . p . of the article be rs . x . then , required ratio = 110 % of x / 106 % of x = 110 / 106 = 55 / 53 = 55 : 53 answer : b"
Answer: b
Python program:
a = 100 + 10 
b = 100 + 6 
c = a / b
Problem: in order to obtain an income of rs . 650 from 10 % stock at rs . 96 , one must make an investment of
Options: a ) 5363 , b ) 6240 , c ) 2368 , d ) 1987 , e ) 2732
Rationale: to obtain rs . 10 , investment = rs . 96 . to obtain rs . 650 , investment = = rs . 6240 . answer : b
Answer: b
Python program:
a = 96 / 10
b = a * 650
Problem: there are 380 doctors and nurses in a hospital . if the ratio of the doctors to the nurses is 8 : 11 , then how many nurses are there in the hospital ?
Options: a ) 152 , b ) 209 , c ) 57 , d ) 171 , e ) 220
Rationale: "given , the ratio of the doctors to the nurses is 8 : 11 number of nurses = 11 / 19 x 380 = 220 answer : e"
Answer: e
Python program:
a = 11 - 8
b = 8 * a
c = b * 11
Problem: we invested a total of $ 1,000 . we invested one part of the money at 3 % and the rest of the money at 5 % . the total investment with interest at the end of the year was $ 1,046 . how much money did we invest at 3 % ?
Options: a ) $ 200 , b ) $ 240 , c ) $ 280 , d ) $ 320 , e ) $ 360
Rationale: "let x be the money invested at 3 % . 1.03 x + 1.05 ( 1000 - x ) = 1046 . 0.02 x = 1050 - 1046 . 0.02 x = 4 . 2 x = 400 . x = 200 . the answer is a ."
Answer: a
Python program:
a = 2 + 3 
b = a * 2
c = 100 * b
d = 5 / 100
e = d + 1 
f = c * e
g = 2 + 3 
h = g * 2
i = 100 * h
j = 2 + 3 
k = j * 2
l = k * 3
m = i + l 
n = 2 * 3
o = m + n 
p = f - o
q = 5 / 100
r = q + 1 
s = 3 / 100
t = s + 1 
u = r - t
v = p / u
Problem: a 5 - digit number divisible by 3 is to be formed using numerical 0 , 1 , 2 , 3 , 4 and 5 without repetition . the total number e of ways this can be done is :
Options: a ) 122 , b ) 210 , c ) 216 , d ) 217 , e ) 225
Rationale: we should determine which 5 digits from given 6 , would form the 5 digit number divisible by 3 . we have six digits : 0 , 1 , 2 , 3 , 4 , 5 . their sum = 15 . for a number to be divisible by 3 the sum of the digits must be divisible by 3 . as the sum of the six given numbers is 15 ( divisible by 3 ) only 5 digits good to form our 5 digit number would be 15 - 0 = { 1 , 2 , 3 , 4 , 5 } and 15 - 3 = { 0 , 1 , 2 , 4 , 5 } . meaning that no other 5 from given six will total the number divisible by 3 . second step : we have two set of numbers : 1 , 2 , 3 , 4 , 5 and 0 , 1 , 2 , 4 , 5 . how many 5 digit numbers can be formed using these two sets : 1 , 2 , 3 , 4 , 5 - - > 5 ! as any combination of these digits would give us 5 digit number divisible by 3 . 5 ! = 120 . 0 , 1 , 2 , 4 , 5 - - > here we can not use 0 as the first digit , otherwise number wo n ' t be any more 5 digit and become 4 digit . so , desired # would be total combinations 5 ! , minus combinations with 0 as the first digit ( combination of 4 ) 4 ! - - > 5 ! - 4 ! = 4 ! ( 5 - 1 ) = 4 ! * 4 = 96 120 + 96 = 216 = e answer : c .
Answer: c
Python program:
a = math.factorial(5)
b = math.factorial(4)
c = 4 * b
d = a + c
Problem: the lenght of a room is 5.5 m and width is 4 m . find the cost of paving the floor by slabs at the rate of rs . 700 per sq . metre .
Options: a ) s . 15,550 , b ) s . 15,400 , c ) s . 16,500 , d ) s . 17,600 , e ) s . 17,900
Rationale: "area of the floor = ( 5.5 ã — 4 ) m 2 = 22 m 2 . cost of paving = rs . ( 800 ã — 22 ) = rs . 15400 answer : option b"
Answer: b
Python program:
a = 5 * 5
b = 700 * a
Problem: a car takes 6 hours to cover a distance of 270 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 10 kmph , b ) 20 kmph , c ) 25 kmph , d ) 30 kmph , e ) 27 kmph
Rationale: "time = 6 distence = 270 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 270 / 9 = 30 kmph d )"
Answer: d
Python program:
a = 6 * 3
b = a / 2
c = 270 / b