euclaise/mathqa_programs huggingface dataset:
Problem: a japanese rock band made ¥ 3 million on their first album with sales of ¥ 12 million , and made ¥ 5 million on their second album with sales of ¥ 30 million . by approximately what percent did the ratio of profit to sales decrease from the first album to second album ?
Options: a ) 24 % , b ) 27 % , c ) 30 % , d ) 33 % , e ) 36 %
Rationale: solution : this is a percent decrease problem . we will use the formula : percent change = ( new – old ) / old x 100 to calculate the final answer . we first set up the ratios of profits to sales . the first ratio will be for the first album , and the second ratio will be for the next album . because all of the sales are in millions , we do not have to express all the trailing zeros in our ratios . first album profit / sales = 3 / 12 = 1 / 4 second album profit / sales = 5 / 30 = 1 / 6 we can simplify each ratio by multiplying each by the lcm of the two denominators , which is 12 . keep in mind that we are able to do this only because our answer choices are expressed in percents . first album profit / sales = ( 1 / 4 ) x 12 = 3 next 2 million profit / sales = ( 1 / 6 ) x 12 = 2 we can plug 3 and 2 into our percent change formula : ( 2 – 3 ) / 3 x 100 = - 1 / 3 x 100 so approximately a 33 % decrease . answer d .
Answer: d
Python program:
a = 5 / 30
b = 3 / 12
c = a / b
d = 1 - c
e = d * 100
Problem: an inspector rejects 0.05 % of the meters as defective . how many will he examine to reject 2 ?
Options: a ) a ) 1500 , b ) b ) 2000 , c ) c ) 2500 , d ) d ) 3000 , e ) e ) 4000
Rationale: "let the number of meters to be examined be x then , 0.05 % of x = 2 ( 5 / 100 ) * ( ( 1 / 100 ) * x = 2 x = 4000 answer is e"
Answer: e
Python program:
a = 2 * 100
b = a / 0
Problem: a number is doubled and 9 is added . if resultant is trebled , it becomes 69 . what is that number
Options: a ) 7 , b ) 10 , c ) 12 , d ) 14 , e ) 15
Rationale: "explanation : = > 3 ( 2 x + 9 ) = 69 = > 2 x + 9 = 23 = > x = 7 answer : option a"
Answer: a
Python program:
a = 3 * 9
b = 69 - a
c = 3 * 2
d = b / c
Problem: a motor boat takes 12 hours to go downstream and it takes 24 hours to return the same distance . what is the time taken by boat in still water ?
Options: a ) 26 h , b ) 16 h , c ) 86 h , d ) 96 h , e ) 66 h
Rationale: explanation : if t 1 and t 2 are the upstream and down stream times . then time taken in still water is given by \ inline \ frac { 2 \ times t 1 \ times t 2 } { t 1 + t 2 } = \ frac { 2 \ times 12 \ times 24 } { 36 } = 16 h answer : b
Answer: b
Python program:
a = 12 * 24
b = 2 * a
c = 12 + 24 
d = b / c
Problem: if x is a positive integer , then the least value of x for which x ! is divisible by 100000 is ? can someone please explain intuitively what the question is asking ?
Options: a ) 5 , b ) 9 , c ) 12 , d ) 20 , e ) 30
Rationale: in order x ! to be divisible by 1,000 , it should have at least 3 trailing zeros . a trailing 0 in factorial of a number is produced by 2 and 5 in it : 2 * 5 = 10 . so , we need 10 to be in x ! at least in power of 3 . 5 ! = 120 has 1 trailing zeros . 10 ! will have 2 trailing zeros . 15 ! will have 3 trailing zeros . 20 ! will have 5 trailing zeros . answer : d .
Answer: d
Python program:
a = 1 + 4 
b = a * 1000
c = 100000 / b
Problem: a certain sum of money is divided among a , b and c such that a gets one - third of what b and c together get and b gets two - seventh of what a and c together get . if the amount received by a is $ 30 more than that received by b , find the total amount shared by a , b and c .
Options: a ) $ 1080 , b ) $ 1180 , c ) $ 1280 , d ) $ 1380 , e ) $ 1480
Rationale: a = 1 / 3 ( b + c ) = > c = 3 a - b - - - ( 1 ) b = 2 / 7 ( a + c ) = > c = 3.5 b - a - - ( b ) a - b = $ 30 a = 30 + b ( 1 ) = = = > c = 90 + 3 b - b = 2 b + 90 = = > 2 b - c = - 90 - - - ( 3 ) ( 2 ) = = = > c = 3.5 b - b - 30 = 2.5 b - 30 = = > 2.5 b - c = 30 - - - ( 4 ) from ( 4 ) and ( 3 ) 0.5 b = 120 b = $ 240 a = $ 270 c = 810 - 240 = $ 570 total amount = 270 + 240 + 570 = $ 1080 answer : a
Answer: a
Python program:
a = 3 * 30
b = a * 2
c = 2 * 30
d = b + c 
e = 3 * 30
f = e * 2
g = 2 * 30
h = f + g 
i = h + 30 
j = d + i 
k = 3 * 30
l = k * 2
m = 2 * 30
n = l + m 
o = n + 30 
p = o * 3
q = 3 * 30
r = q * 2
s = 2 * 30
t = r + s 
u = p - t
v = j + u
Problem: if 0.25 of a number is equal to 0.05 of another number , the ratio of the numbers is :
Options: a ) 2 : 5 , b ) 3 : 4 , c ) 1 : 5 , d ) 20 : 5 , e ) 30 : 7
Rationale: "0.25 a = 0.05 b - > a / b = 0.05 / 0.25 = 5 / 25 = 1 / 5 : . a : b = 1 : 5 answer : c"
Answer: c
Python program:
a = 0 * 5
b = 0 * 25
c = a / b
Problem: what is the compound interest on rs : 50,000 for 4 months at the rate of 5 % per annum
Options: a ) 1058.24 , b ) 2006.24 , c ) 838.55 , d ) 848.55 , e ) 858.55
Rationale: "it is monthly compound rate = 5 / 12 % per month 50000 * ( 1 + 5 / 1200 ) ^ 4 - 50000 = 838.55 answer : c"
Answer: c
Python program:
a = 3 * 100
b = a * 100
c = 4 * 3
d = 4 / c
e = 5 * d
f = b * e
g = f / 100
Problem: if k and w are the dimensions of a rectangle that has area 20 and if k and w are integers such that k > w , what is the total number of possible values of k ?
Options: a ) two
b ) three
c ) four
d ) five
e ) six
Rationale: kw = 20 = 20 * 1 = 10 * 2 = 5 * 4 - - > k can take 3 values , answer : b
Answer: b
Python program:
a = 3 * 1
Problem: danny is sitting on a rectangular box . the area of the front face of the box is half the area of the top face , and the area of the top face is 1.5 times the area of the side face . if the volume of the box is 648 , what is the area of the side face of the box ?
Options: a ) 32
b ) 78
c ) 84
d ) 90
e ) 72
Rationale: lets suppose length = l , breadth = b , depth = d front face area = l * w = 1 / 2 w * d ( l = 1 / 2 d or d = 2 l ) top face area = w * d side face area = w * d = 1.5 d * l ( w = 1.5 l ) volume = l * w * d = 648 l * 1.5 l * 2 l = 648 l = 6 side face area = l * d = l * 2 l = 6 * 2 * 6 = 72 e is the answer
Answer: e
Python program:
a = 648 ** 2
b = 3 * a
c = 1 / 3
d = b ** c
e = d / 1
Problem: the speed of a car increases by 2 kms after every one hour . if the distance travelling in the first one hour was 30 kms . what was the total distance traveled in 12 hours ?
Options: a ) 252 kms , b ) 152 kms , c ) 492 kms , d ) 752 kms , e ) 152 kms
Rationale: "explanation : total distance travelled in 12 hours = ( 30 + 32 + 34 + . . . . . upto 12 terms ) this is an a . p with first term , a = 30 , number of terms , n = 12 , d = 2 . required distance = 12 / 2 [ 2 x 30 + { 12 - 1 ) x 2 ] = 6 ( 82 ) = 492 kms . answer : c"
Answer: c
Python program:
a = 2 * 30
b = 12 - 1
c = b * 2
d = a + c 
e = 12 / 2
f = d * e
Problem: how many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 54 kmph ?
Options: a ) 22 sec , b ) 77 sec , c ) 16.7 sec , d ) 18 sec , e ) 17 sec
Rationale: "d = 100 + 150 = 250 s = 54 * 5 / 18 = 15 mps t = 250 / 15 = 16.7 sec answer : c"
Answer: c
Python program:
a = 150 + 100 
b = 54 * const_0_2778
c = a / b
Problem: if x and g are integers and 2 x – g = 11 , then 4 x + g can not be
Options: a ) – 5 , b ) 1 , c ) 13 , d ) 17 , e ) 551
Rationale: 2 x - g = 11 . . . . g = 2 x - 11 4 x + g = 4 x + 2 x - 11 = 6 x - 11 6 x - 11 = - 5 . . . x = 1 6 x - 11 = 1 . . . x = 2 6 x - 11 = 13 . . . x = 4 6 x - 11 = 17 . . x is not integer 6 x - 11 = 551 . . x is not integer i think the choice e is 55 not 551 . otherwise both de can not be solution = d
Answer: d
Python program:
a = 4 + 2 
b = a * 3
c = b - 1
Problem: a fair 8 - sided dice labeled 1 to 8 is tossed 3 times . what is the probability the value of the dice shown is 3 at least once ?
Options: a ) 57 / 512 , b ) 7 / 512 , c ) 55 / 512 , d ) 9 / 512 , e ) 11 / 512
Rationale: this is a fair dice with 8 fair sides , so the probability of the dice landing on any sides is equal . the question ask if the value of the dice is shown 3 at least once so the calculation of the first possible outcomes is 1 / 8 * 1 / 8 * 1 / 8 ( all of the dice thrown shown the value of 3 ) this is follow by the second possible outcomes if the dice thrown show the value of 3 2 times ( 1 / 8 * 1 / 8 * 7 / 8 ) * 7 here referring to any number besides 3 the third possible outcomes is that the dice show the value 3 one time ( 1 / 8 * 7 / 8 * 7 / 8 ) so the answer is 1 / 512 + 7 / 512 + 49 / 512 = 57 / 512 answer : a
Answer: a
Python program:
a = 8 * 3
b = a * 3
c = b - 8
d = c - 3
e = d - 3
f = e - 1
g = 8 * 8
h = 8 * g
i = f / h
Problem: in what time will a train 100 m long cross an electric pole , it its speed be 216 km / hr ?
Options: a ) 2.5 sec , b ) 2.9 sec , c ) 1.7 sec , d ) 7.5 sec , e ) 2.4 sec
Rationale: "speed = 215 * 5 / 18 = 60 m / sec time taken = 100 / 60 = 1.7 sec . answer : c"
Answer: c
Python program:
a = 216 * const_0_2778
b = 100 / a
Problem: consider below info to be a table : amount of bacteria time - amount 1 pm - 10 gms 4 pm - x gms 7 pm - 12.1 gms data for a certain biology experiment are given in the table above . if the amount of bacteria present increased by the same factor during each of the two 3 - hour periods shown , how many grams of bacteria were present at 4 pm ?
Options: a ) 12.0 , b ) 12.1 , c ) 12.2 , d ) 12.3 , e ) 11.0
Rationale: let say the factor is x , the at 7 pm quantity = 10 ( i . e . quantity @ 1 pm ) * x ^ 2 = 12.1 = > x ^ 2 = 1.21 or x = 1.1 = > @ 4 pm quantity = 10 x = 10 * 1.1 = 11 . answer e
Answer: e
Python program:
a = 10 + 12 
b = a / 2
Problem: every day daniel drives 120 miles back from work . on sunday , daniel drove all the way back from work at a constant speed of x miles per hour . on monday , daniel drove the first 32 miles back from work at ( 2 x ) miles per hour , and the rest of the way at ( x / 2 ) miles per hour . the time it took daniel to drive back from work on monday is longer than the time it took him to drive back from work on sunday by what percent ?
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 60 %
Rationale: let ' s test x = 4 . . . . on sunday , daniel drove 120 miles at 4 miles / hour . d = ( r ) ( t ) 120 = ( 4 ) ( t ) 120 / 4 = 30 = t it takes 30 hours to drive home on monday , daniel drove the first 32 miles at ( 2 ) ( 4 ) = 8 miles / hour and the rest of the way ( 88 miles ) at 4 / 2 = 2 miles / hour d = ( r ) ( t ) 32 = ( 8 ) ( t ) 32 / 8 = 4 = t it takes 4 hours for the first part d = ( r ) ( t ) 88 = ( 2 ) ( t ) 88 / 2 = 44 = t it takes 44 hours for the second part total time to drive home on monday = 4 + 44 = 48 hours we ' re asked by what percent 48 hours is greater than 30 hours . 48 / 30 = 1.6 , so it is 60 % greater . answer : e
Answer: e
Python program:
a = 32 / 2
b = 120 - 32
c = b * 2
d = a + c 
e = d - 120
f = e / 120
g = f * 100
Problem: how many multiples of 4 are there between 1 and 100 , inclusive ?
Options: a ) 25 , b ) 22 , c ) 23 , d ) 30 , e ) 36
Rationale: "25 multiples of 4 between 1 and 100 inclusive . from 4 * 1 upto 4 * 25 , ( 1,2 , 3,4 , . . . , 25 ) . hence , 25 multiples ! correct option is a"
Answer: a
Python program:
a = 100 - 1
b = a / 4
c = b + 1
Problem: caleb spends $ 66.50 on 50 hamburgers for the marching band . if single burgers cost $ 1.00 each and double burgers cost $ 1.50 each , how many double burgers did he buy ?
Options: a ) 5 , b ) 33 , c ) 20 , d ) 40 , e ) 45
Rationale: "solution - lets say , single hamburgersxand double hamburgersy given that , x + y = 50 and 1 x + 1.5 y = 66.50 . by solving the equations y = 33 . ans b ."
Answer: b
Python program:
a = 66 - 50
b = 1 - 50
c = a / b
Problem: a pump can fill a tank with water in 2 hours . because of a leak , it took hours to fill the tank . the leak can drain all the water of the tank in :
Options: a ) 33 , b ) 37 , c ) 76 , d ) 14 , e ) 29
Rationale: explanation : work done by the leak in 1 hour = { \ color { black } \ left ( \ frac { 1 } { 2 } - \ frac { 3 } { 7 } \ right ) = \ frac { 1 } { 14 } } { \ color { black } \ therefore } leak will empty the tank in 14 hrs answer : d ) 14 hours
Answer: d
Python program:
a = 1 / 2
b = 1 / 3
c = 2 + b 
d = 1/(c)
e = a - d
f = 1/(e)
Problem: rectangular tile each of size 70 cm by 30 cm must be laid horizontally on a rectangular floor of size 900 cm by 600 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is :
Options: a ) 50 , b ) 70 , c ) 80 , d ) 90 , e ) 100
Rationale: "area of tile = 90 * 30 = 2700 area of floor = 900 * 300 = 270000 no of tiles = 270000 / 2700 = 100 so , the no of tile = 100 answer : e"
Answer: e
Python program:
a = 900 * 600
b = 70 * 30
c = a / b
Problem: a merchant has selected two items to be placed on sale , one of which currently sells for 45 percent less than the other . if he wishes to raise the price of the cheaper item so that the two items are equally priced , by what percentage must he raise the price of the less expensive item ?
Options: a ) 100 % , b ) 90 % , c ) 80 % , d ) 70 % , e ) 60 %
Rationale: "expensive item = $ 100 ; cheap item = $ 55 ; we must increase $ 55 to $ 100 , so by $ 45 , which is approximately 80 % increase : ( 100 - 55 ) / 55 = 3 / 7 = ~ 0.81 . answer : c ."
Answer: c
Python program:
a = 45 / 100
b = 45 / 100
c = 1 - b
d = a / c
e = d * 100
Problem: running at the same rate , 8 identical machines can produce 560 paperclips a minute . at this rate , how many paperclips could 15 machines produce in 6 minutes ?
Options: a ) 1344 , b ) 6300 , c ) 8400 , d ) 50400 , e ) 67200
Rationale: "8 machines produce 560 in 1 min 8 machines produce 560 * 6 in 6 min 15 machine produce 560 * 6 * ( 15 / 8 ) in 6 minutes 560 * 6 * 15 / 8 = 6300 answer is b ."
Answer: b
Python program:
a = 15 / 8
b = 560 * a
c = b * 6
Problem: in how many ways 3 boys and 3 girls can be seated in a row so that boys and girls are alternate ?
Options: a ) 69 , b ) 70 , c ) 71 , d ) 72 , e ) 73
Rationale: "number of ways = 2 * 3 ! * 3 ! = 72 answer is d"
Answer: d
Python program:
a = math.factorial(3)
b = math.factorial(3)
c = a * b
Problem: if 7 gallons of gasoline are added to a tank that is already filled to 3 / 4 of its capacity , the tank is then filled to 9 / 10 of its capacity . how many gallons does the tank hold ?
Options: a ) 20 , b ) 24 , c ) 36 , d ) 42 , e ) 60
Rationale: "let the capacity of the tank = c ( 3 / 4 ) c + 7 = ( 9 / 10 ) c = > ( 9 / 10 ) c - ( 3 / 4 ) c = 7 = > ( 3 / 20 ) c = 7 = > c = ( 7 * 20 ) / 3 = 46.66 number of gallons of gasoline that the tank currently holds = 3 / 4 * c + 7 = 34.99 + 7 = 41.99 = 42 answer d"
Answer: d
Python program:
a = 9 / 10
b = 3 / 4
c = a - b
d = 7 / c
e = 3 / 4
f = d * e
g = f + 7
Problem: working at constant rate , pump x pumped out half of the water in a flooded basement in 6 hours . the pump y was started and the two pumps , working independently at their respective constant rates , pumped out rest of the water in 3 hours . how many hours would it have taken pump y , operating alone at its own constant rate , to pump out all of the water that was pumped out of the basement ?
Options: a ) a . 10 , b ) b . 12 , c ) c . 14 , d ) d . 28 , e ) e . 24
Rationale: "rate of x = 1 / 8 rate of x + y = 1 / 6 rate of y = 1 / 6 - 1 / 8 = 1 / 24 28 hours d"
Answer: d
Python program:
a = 3 + 6 
b = 1 + a 
c = b + 1 
d = c + 1 
e = d + 1 
f = e + 1 
g = f + 6 
h = g + 1 
i = h + 1 
j = i + 1 
k = j + 1 
l = k + 1 
m = l + 1
Problem: speed of a boat in standing water is 9 kmph and the speed of the stream is 6 kmph . a man rows to place at a distance of 170 km and comes back to the starting point . the total time taken by him is :
Options: a ) 12 hours , b ) 68 hours , c ) 36 hours , d ) 58 hours , e ) none
Rationale: "sol . speed upstream = 3 kmph ; speed downstream = 15 kmph . ∴ total time taken = [ 105 / 7.5 + 105 / 10.5 ] hours = 68 hours . answer b"
Answer: b
Python program:
a = 9 + 6 
b = 170 / a
c = 9 - 6
d = 170 / c
e = b + d
Problem: if the cost price of 17 articles is equal to the selling price of 16 articles , what is the percentage of profit or loss that the merchant makes ?
Options: a ) 20 % loss , b ) 6.25 % profit , c ) 33.33 % loss , d ) 30.33 % loss , e ) none of these
Rationale: "explanation : let cost price of 1 article be re . 1 . therefore , cost price of 17 articles = rs . 17 . selling price of 16 articles = rs . 17 therefore , selling price of 17 articles is : - = > 17 / 16 ã — 17 = > 18.06 therefore , profit = selling price - cost price . = > 18.06 â ˆ ’ 17 = 1.06 hence , the percentage of profit = profit x 100 / c . p . = > 1.06 / 17 ã — 100 . = > 6.25 % profit . answer : b"
Answer: b
Python program:
a = 100 * 16
b = a / 17
c = 100 - b
d = 100 * 16
e = d / 17
f = c / e
g = 100 * f
Problem: according to a recent student poll , 4 / 5 out of 20 members of the finance club are interested in a career in investment banking . if two students are chosen at random , what is the probability that at least one of them is interested in investment banking ?
Options: a ) 62 / 95 , b ) 52 / 95 , c ) 92 / 95 , d ) 42 / 95 , e ) 32 / 95
Rationale: "16 students are interested , 4 are not interested prob = 1 - 4 c 2 / 20 c 2 = 1 - ( 4 * 3 / ( 20 * 19 ) ) = 1 - 3 / 95 = 92 / 95 answer : c"
Answer: c
Python program:
a = math.comb(20, 2)
b = 4 / 5
c = 20 * b
d = 20 - c
e = math.comb(d, 2)
f = a - e
g = math.comb(20, 2)
h = f / g
Problem: let p be a prime number . if n = 8 p , how many distinct even divisors does n have ?
Options: a ) 1 , b ) 4 , c ) 5 , d ) 2 , e ) 3
Rationale: "the correct answer is d . there are two : 2 and 2 p . 8 p = 2 * 2 * 2 p = ( 2 * 2 ) * 2 p . since we care only about distinct divisors , we ignore the fact that 2 appears three times ."
Answer: d
Python program:
a = 1 / 2
b = 8 / 2
c = b - 2
d = a + c
Problem: a candidate who gets 30 % of the marks fails by 30 marks . but another candidate who gets 45 % marks gets 15 marks more than necessary for passing . find the number of marks for passing ?
Options: a ) 100 marks , b ) 200 marks , c ) 280 marks , d ) 371 marks , e ) 120 marks
Rationale: "30 % - - - - - - - - - - - - 30 45 % - - - - - - - - - - - - 15 - - - - - - - - - - - - - - - - - - - - - - 15 % - - - - - - - - - - - - - 45 30 % - - - - - - - - - - - - - - ? 90 + 30 = 120 marks answer : e"
Answer: e
Python program:
a = 30 + 15 
b = 45 / 100
c = 30 / 100
d = b - c
e = a / d
f = 30 / 100
g = e * f
h = g + 30
Problem: in a forest 190 deer were caught , tagged with electronic markers , then released . a week later , 50 deer were captured in the same forest . of these 50 deer , it was found that 5 had been tagged with the electronic markers . if the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest , and if no deer had either left or entered the forest over the preceding week , what is the approximate number of deer in the forest ?
Options: a ) 150 , b ) 750 , c ) 1,250 , d ) 1,900 , e ) 2,500
Rationale: "the percentage of tagged deer in the second sample = 5 / 50 * 100 = 10 % . so , 190 tagged deers comprise 10 % of total # of deers - - > total # of deers = 190 * 10 = 1,900 . answer : d ."
Answer: d
Python program:
a = 50 * 5
Problem: a person ' s present age is two - fifth of the age of his mother . after 6 years , he will be one - half of the age of his mother . how old is the mother at present ?
Options: a ) a ) 25 , b ) b ) 40 , c ) c ) 32 , d ) d ) 45 , e ) e ) 30
Rationale: "let the mother ' s present age be x years then the person ' s present age = 2 x / 5 ( 2 x / 5 ) + 6 = 1 / 2 ( x + 6 ) 2 ( 2 x + 30 ) = 5 ( x + 6 ) x = 30 answer is e"
Answer: e
Python program:
a = 2 + 3 
b = 6 - a
c = 1 / 2
d = 2 + 3 
e = 2 / d
f = c - e
g = b / f
Problem: two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 20 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 22 , b ) 88 , c ) 48 , d ) 99 , e ) 72
Rationale: "relative speed = 20 + 30 = 50 km / hr . 50 * 5 / 18 = 125 / 9 m / sec . distance covered = 500 + 500 = 1000 m . required time = 1000 * 9 / 125 = 72 sec answer : e"
Answer: e
Python program:
a = 20 + 30
Problem: the average of marks obtained by 120 boys was 37 . if the average of marks of passed boys was 39 and that of failed boys was 15 , the number of boys who passed the examination is ?
Options: a ) 100 , b ) 110 , c ) 120 , d ) 130 , e ) 140
Rationale: let the number of boys who passed = x . then , 39 x x + 15 x ( 120 - x ) = 120 x 37 24 x = 4440 - 1800 = > x = 2640 / 24 x = 110 . hence , the number of boys passed = 110 . answer : b
Answer: b
Python program:
a = 37 * 120
b = 120 * 15
c = a - b
d = 39 - 15
e = c / d
Problem: a fruit drink is made of orange , watermelon , and grape juice , where 25 percent of the drink is orange juice and 40 percent is watermelon juice . if the drink is made with 105 ounces of grape juice , how many ounces is the drink total ?
Options: a ) 220 , b ) 250 , c ) 280 , d ) 300 , e ) 340
Rationale: "let the total number of ounces in the drink be x . % of orange = 25 % % of watermelon = 40 % % of grape = 100 % - 65 % = 35 % 0.35 x = 105 x = 300 therefore there are a total of 300 ounces in the drink . the answer is d ."
Answer: d
Python program:
a = 105 * 25
b = 40 + 25 
c = 100 - b
d = a / c
e = 105 + d 
f = 105 * 40
g = 40 + 25 
h = 100 - g
i = f / h
j = e + i
Problem: find the least number which when divided by 5 , 6,7 , and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder
Options: a ) 1683 , b ) 1684 , c ) 1685 , d ) 1582 , e ) 1584
Rationale: "explanation : l . c . m . of 5,6 , 7,8 = 840 . required number is of the form 840 k + 3 least value of k for which ( 840 k + 3 ) is divisible by 9 is k = 2 . required number = ( 840 x 2 + 3 ) = 1683 answer is a"
Answer: a
Python program:
a = math.lcm(5, 6)
b = 8 + a
Problem: it is the new year and mandy has made a resolution to lose weight this year . she plans to exercise and do yoga . for exercise she plans to workout at the gym and ride her bicycle in the ratio of 2 : 3 everyday . she will also do yoga in the ratio , yoga : exercise = 2 : 3 . if she does yoga for 25 minutes , how much time will she spend in the gym ?
Options: a ) 35 min , b ) 5 min , c ) 15 min , d ) 25 min , e ) 20 min
Rationale: "the ratio is 2 : 3 = yoga : exer , so ( 25 ) ( 3 / 2 ) = 37.5 minutes for exercise , and 2 : 3 = gym : ride , and ( 2 / 3 ) ( 37.5 ) = 25 minutes in the gym . answer : d"
Answer: d
Python program:
a = 2 + 3 
b = 3 / a
c = 25 * b
d = 2 + 3 
e = 3 / d
f = 2 + 3 
g = 3 / f
h = e * g
i = c / h
Problem: find the compound interest accrued on an amount of rs . 14,800 at 13.5 % p . a at the end of two years . ( round off your answer to nearest integer ?
Options: a ) 2828 , b ) 2338 , c ) 377 , d ) 4266 , e ) 288
Rationale: "ci = 14800 { [ 1 + 13.5 / 100 ] 2 - 1 } = 14800 { [ 1 + 27 / 200 ] 2 - 1 = 14800 { 2 + 27 / 200 } { 27 / 200 } = ( 74 ) [ 2 + 27 / 200 ] ( 27 ) = 1998 [ 2 + 27 / 200 ] = 3996 + 269.73 = rs . 4266 . answer : d"
Answer: d
Python program:
a = 3 + 4 
b = a * 2
c = 2 + 3 
d = c * 2
e = 100 * d
f = b * e
g = 2 + 3 
h = g * 2
i = h - 2
j = i * 100
k = f + j 
l = 13 / 5
m = 1 + l 
n = m ** 2
o = n - 1
p = k * o
Problem: the ratio between the perimeter and the width of a rectangle is 5 : 1 . if the area of the rectangle is 150 square centimeters , what is the length of the rectangle in centimeters ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "perimeter = 2 ( w + l ) = 5 w 3 w = 2 l w = 2 l / 3 wl = 150 2 l ^ 2 / 3 = 150 l ^ 2 = 225 l = 15 cm the answer is a ."
Answer: a
Python program:
a = 150 / 10
Problem: how many odd numbers between 10 and 1500 are the squares of integers ?
Options: a ) 11 , b ) 14 , c ) 17 , d ) 20 , e ) 23
Rationale: "the numbers are the squares of 5 , 7 , 9 , . . . , 37 which includes 17 numbers . the answer is c ."
Answer: c
Python program:
a = 10 + 4