mathewhe/aqua_rat huggingface dataset:
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 227
(B) 268
(C) 240
(D) 889
(E) 232
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 36 = 15
x + 300 = 540
x = 240 m.
Answer:C
Answer: (C) 240
Question: Out of 17 applicants 8 boys and 9 girls. Two persons are to be selected for the job. Find the probability that at least one of the selected persons will be a girl.
(A) 25/39
(B) 25/32
(C) 25/22
(D) 25/34
(E) 25/333
Rationale: Explanation:
The events of selection of two person is redefined as first is a girl and second is a boy or first is boy and second is a girl or first is a girl and second is a girl.
So the required probability:
Answer: D) 25/34
Answer: (D) 25/34
Question: Harper's Apple Farm began expansion of it's apple harvest in 1900. From 1900 to 1950, the number of apples harvested by Harper's Apple Farm increased by 25%. From 1900 to 2000, the number of apples harvested increased by 350%. What was the percentage increase in the number of apples harvested from the year 1950 to the year 2000?
(A)  100%
(B)  167%
(C)  260%
(D)  250%
(E)  500%
Rationale: Let x be the number of apples harvested in 1900; then, x + 0.25x = 1.25x is the number of apples harvested for 1900-1950, and x + 3.5x = 4.5x is the number of apples harvested for 1900-2000.
Now, percentage increase in the number of apples harvested from the year 1950 to the year 2000 is (4.5x - 1.25x)/1.25x = 2.6 = 260%
Answer is C
Answer: (C)  260%
Question: If k is a non-negative integer and 30^k is a divisor of 929,260 then 3^k - k^3 =
(A) 0
(B) 1
(C) 45
(D) 130
(E) 520
Rationale: 9+2+9+2+6+0 = 28, so this number is not divisible by 3 and thus not divisible by 30.
Therefore, k=0
3^k - k^3 =1-0=1
The answer is B.
Answer: (B) 1
Question: If integer k is equal to the sum of all even multiples of 5 between 300 and 610, what is the greatest prime factor of k?
(A) 32
(B) 7
(C) 11
(D) 13
(E) 17
Rationale: if we break down what the stem is asking what is the sum of all mult of 10 between 300 and 610.
using arithmetic progression to find n : 610 = 300 + (n - 1) 10
310+ 10 = 10n
320 =10n => n = 32
the sum would be: 32* mean
mean = [610 + 300] / 2 = 455
32*455
A
Answer: (A) 32
Question: In a certain pond, 30 fish were caught, tagged, and returned to the pond. A few days later, 30 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what`s the approximate number of fish in the pond?
(A) 400
(B) 750
(C) 1250
(D) 2500
(E) 10 000
Rationale: If x is total number of fish in the pond :
4 = 30/x * 100
=> x = 750
So answer is B
Answer: (B) 750
Question: If grapes are 92% water and raisins are 20% water, then how much did a quantity of raisins, which currently weighs 15 pounds, weigh when all the raisins were grapes? (Assume that the only difference between their raisin-weight and their grape-weight is water that evaporated during their transformation.)
(A) 25 pounds
(B) 46 pounds
(C) 150 pounds
(D) 100 pounds
(E) 146 pounds
Rationale: Since only water evaporates, then the weight of pulp (non-water) in grapes and raisins is the same. Thus 0.08*{weight of grapes}=0.8*{weight of raisins} --> 0.08x = 0.8*15 --> x = 150.
Answer: C.
Answer: (C) 150 pounds
Question: If x = 1 - q and y = 2q + 1, then for what value of q, x is equal to y ?
(A) 0
(B) 1
(C) -1
(D) -2
(E) 3
Rationale: Explanation:
x = y <=> 1 - q = 2q + 1 <=> 3q = 0 <=> q = 0.
Answer: A
Answer: (A) 0
Question: In a certain deck of cards, each card has a positive integer written on it. In a multiplication game, a child draws a card and multiples the integer on the card by the next larger integer. If each possible product is between 29 and 200, then the least and greatest integers on the card could be
(A) 3 and 15
(B) 3 and 20
(C) 5 and 13
(D) 4 and 14
(E) 5 and 14
Rationale: There child draws one number then multiplies that number by the number above it. The number must be more than 29 and less than 200.
x * (x+1)
Answer gives us choices of 3,4 and 5 (JUST ABOVE 29)
3*(3+1) =12 <- WRONG
4*(4+1) =20 <- WRONG
5*(5+1) =30 <- CORRECT AS IT IS ABOVE 29
Answer gives us choices 13,14,15 and 20 (BELOW 200)
Immediately by knowing squares you should be able to rule out 15 (225) and 20 (400). And common sense dictates that as 14^2 is 196 that 14*(14+1) is above 200.
13*(13+1)=182 <- CORRECT
Answer is C) 5 and 13
Answer: (C) 5 and 13
Question: The price of a consumer good increased by pp% during 20122012 and decreased by 1212% during 20132013. If no other change took place in the price of the good and the price of the good at the end of 20132013 was 1010% higher than the price at the beginning of 20122012, what was the value of pp?
(A) −2%
(B) 2%
(C) 22%
(D) 25%
(E) Cannot be determined
Rationale: As per question=> Price was simple 10 percent greater
Hence x[1+10/100] must be the final price.
Equating the two we get
=> x[110/100]=x[1+p/100][88/100]
=> 44p+4400=5500
=> 44p=1100
=> p=1100/44=> 100/4=> 25.
So p must be 25
ANSWER:D
Answer: (D) 25%
Question: The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?
(A) 4
(B) 8
(C) 16
(D) 17
(E) None of these
Rationale: Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit.
Let ten's and unit's digits be 2x and x respectively.
Then, (10 x 2x + x) - (10x + 2x) = 36
9x = 36
x = 4.
Required difference = (2x + x) - (2x - x) = 2x = 8.
Answer:B
Answer: (B) 8
Question: On the independence day, bananas were be equally distributed among the children in a school so that each child would get two bananas. On the particular day 380 children were absent and as a result each child got two extra bananas. Find the actual number of children in the school?
(A) 237
(B) 287
(C) 760
(D) 287
(E) 720
Rationale: Explanation:
Let the number of children in the school be x. Since each child gets 2 bananas, total number of bananas = 2x.
2x/(x - 380) = 2 + 2(extra)
=> 2x - 760 = x => x = 760.
Answer: C
Answer: (C) 760
Question: The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number ?
(A) 69
(B) 78
(C) 96
(D) Cannot be determined
(E) None of these
Rationale: Solution
Let the ten's digit be x and unit's digit be y.
Then, x + y = 15 and x = y =3 or y = x = 3.
Solving x + y = 15 and x - y = 3, we get : x = 9, y = 6.
Solving x + y = 15 and y - x = 3, we get : x = 6, y = 9.
So, the number is either 96 or 69. Hence, the number cannot be determined
Answer D
Answer: (D) Cannot be determined
Question: Mr. Kramer, the losing candidate in a two-candidate election, received 942,568 votes, which was exactly 35 percent of all votes cast. Approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast?
(A) 10%
(B) 12%
(C) 15%
(D) 17%
(E) 23%
Rationale: Lets assume that candidate got 35% votes and total votes is 100.
Candidate won = 35
Remaining = 65
To get 50%, candidate requires 15 votes from 100 which is 15% and 15 votes from 65.
15/65 = 23.07
Which is approx 23%. Hence the answer is E
Answer: (E) 23%
Question: How much is 25% of 40 is greater than 4/5 of 25?
(A) 10
(B) 776
(C) 66
(D) 12
(E) 99
Rationale: (25/100) * 40 – (4/5) * 25
10 - 20 = 10
Answer: A
Answer: (A) 10
Question: The average age of 15 students of a class is 15 years. Out of these, the average age of 4 students is 14 years and that of the other 9 students is 16 years. Tee age of the 15th student is?
(A) 20years
(B) 22years
(C) 24years
(D) 25years
(E) 27years
Rationale: Age of the 15th student
=[15 * 15 - (14 * 4 + 16 * 9)]
= (225 - 200) = 25 years.
Answer:D
Answer: (D) 25years
Question: If a,b are positive integers and a/b=87.5 which of the following could be the value of b?
(A) 1. 25
(B) 2. 26
(C) 3. 27
(D) 4. 28
(E) 5. 30
Rationale: Given a/b = 87.75.
this is 87 and 1/2 = 175/2
Since a and b are integers we know that whatever is the value of b, it must be divisible by 2 completely(to make a an integer)
Ans:B
Answer: (B) 2. 26
Question: Three archers each have an equal chance of hitting a target, and if only two of the three shoot the likelihood of the two hitting the target is 4/9 . What is the likelihood of all three men missing the target?
(A) 1/27
(B) 16/81
(C) 8/27
(D) 19/27
(E) 26/27
Rationale: Let the probability of an archer hitting a target be xx. Then the probability of two hitting the target will be P=x∗x=49P=x∗x=49 --> x=23x=23, so the probability of an archer missing the target will be P=1−23=13P=1−23=13.
The probability of all three men missing the target will be P=(13)3=127P=(13)3=127.
Answer: A.
Answer: (A) 1/27
Question: An analysis of the monthly incentives received by 5 salesmen : The mean and median of the incentives is $7000. The only mode among the observations is $12,000. Incentives paid to each salesman were in full thousands. What is the difference between Q the highest and the lowest incentive received by the 5 salesmen in the month?
(A) $4000
(B) $5000
(C) $9000
(D) $11,000
(E) $13,000
Rationale: Break down the question in to steps:
Step #1: incentives received by 5 salesmen -->abcde
Step #2: mean and median of the incentives is $7000: via number properties --> total incentives = 7,000 * 5 = 35, 000ab7,000de
Step #3: only mode among the observations is $12,000: mode is the value that appears most often in a set of data. Therefore 12,000 must occur more then once and since 12,000 is larger than the mean (7,000) the most it can occur is twice in our list. If we place the numbers in ascending order we haveab7,00012,00012,000
Step #4: What is the difference between the highest and the lowest incentive:
- The total paid has to equal mean * # of numbers = 7,000 * 5 = 35 000.
- The three values we have so far (12,000 12,000 and 7, 000) equal 31,000.
- Therefore the first two numbers( ab) must equal 4, 000
- There is only one mode which is 12,000, therefore 4,000 must be equal to a set of two numbers that are not the and a < b
if a = 1,000 b = 3,000 --> difference Q between the highest and the lowest incentive = 12,000 - 1,000 =11, 000
no other options for a or b to fit the criteria
Final List:1,0003,0007,00012,00012,000
Answer D
Answer: (D) $11,000
Question: Two dogsled teams raced across a 300-mile course in Wyoming. Team A finished the course in 3 fewer hours than did team B. If team A’s average speed was 5 miles per hour greater than that of team B, what was team B’s average speed, in miles per hour?
(A) 12
(B) 15
(C) 18
(D) 20
(E) 25
Rationale: Speed of B= S
Speed of A= S+5
Time taken by B=300/S Time Taken by A= 300/(S+5)
Difference in their time is 3 hrs.
300/S - 3 = 300/(S+5)
Plug in the values from the option
No need of choosing 12 & 18 it won't satisfy
a) if we take 15 then
T(B) = 300/15 =20
T(A)= 300/20 =15. Hence from this option difference comes out to be 5 which is not correct
b) if we take 20 then
T(B) = 300/20 = 15
T(A)= 300/25 = 12
Difference in timing is 3 hence Option D is correct
Answer: (D) 20
Question: If n is the product of the integers from 1 to 8, inclusive, how many different prime factors greater than 1 does n have?
(A) Four
(B) Five
(C) Six
(D) Seven
(E) Eight
Rationale: n=8!, so it has 4 prime factors: 2, 3, 5, and 7.
Answer: A.
Answer: (A) Four
Question: A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest?
(A) 3%
(B) 4%
(C) 5%
(D) 6%
(E) None of these
Rationale: S.I. = Rs. (15500 - 12500) = Rs. 3000.
Rate =((100 x 3000)/(12500 x 4))%	= 6%
Answer :D
Answer: (D) 6%
Question: Ten cards numbered 1 to 10 are placed in a box and then one card is drawn randomly. If it is known that the number on the drawn card is more than 4, what is the probability that it is an odd number?
(A) 1/2
(B) 3/10
(C) 7/10
(D) 5/6
(E) 3/7
Rationale: There are 6 numbers higher than 4 and 3 of them are odd.
The probability is 3/6=1/2.
The answer is A.
Answer: (A) 1/2
Question: Three coins are tossed. What is the probability of getting at most two tails?
(A) 5/8
(B) 6/8
(C) 7/8
(D) 3/8
(E) 1/2
Rationale: Total number of outcomes possible when a coin is tossed = 2 (∵ Head or Tail)
Hence, total number of outcomes possible when 3 coins are tossed, n(S) = 2 × 2 × 2 = 8
(∵ i.e., S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH})
E = event of getting at most two Tails = {TTH, THT, HTT, THH, HTH, HHT, HHH}
Hence, n(E) = 7
P(E) = n(E)/n(S)=7/8
Answer is C.
Answer: (C) 7/8
Question: A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
(A) Rs.3988
(B) Rs.3900
(C) Rs.3228
(D) Rs.3922
(E) Rs.3928
Rationale: Area = (l + b – d) d
(80 + 60 – 10)10 => 1300 m2
1300 * 3
= Rs.3900
Answer:B
Answer: (B) Rs.3900
Question: if the ratio of two number is 3:4 and LCM of the number is 180 then what is the number.
(A) 15
(B) 20
(C) 25
(D) 30
(E) 35
Rationale: product of two no = lcm *hcf
3x*4x=180*x
x=15
ANSWER:A
Answer: (A) 15
Question: The edges of three metal cubes are 4 cm, 5 cm, and 6 cm respectively. A new cube is made by melting these three cubes together. What is the edge of the new cube (in centimeters)?
(A) 6.6
(B) 6.8
(C) 7.0
(D) 7.2
(E) 7.4
Rationale: The total volume is 4^3+5^3+6^3=405
The edge of the new cube is the cube root of 405 which is about 7.4 cm.
The answer is E.
Answer: (E) 7.4
Question: 1. Internet: $80, with no sales tax, plus $10 shipping fee
2. Store X: $70, a 10% discount, plus 30% tax on discounted price
3. Store Y: $90, no tax
4. Store Z: $70, a 30% sales tax, and $10 rebate after tax
Isaac can purchase a certain item in four different ways, as shown in the table. What is the lowest price for which he can purchase this item?
(A) 88.1
(B) 81.0
(C) 81.9
(D) 81.5
(E) 90.0
Rationale: Option 2 = (70 - 7) + 0.3 * 63= 81.90
Option 4 = 70 + 0.3 * 91 - 10
= 81
So the OA is correct - B
Answer: (B) 81.0
Question: A bus covers a certain distance at aspeed of 240 kmph in 5hours. To cover the same distance in 1hr, it must travel at a speed of?
(A) 550 km/hr
(B) 590 km/hr
(C) 600 km/hr
(D) 610 km/hr
(E) 720 km/hr
Rationale: Distance = (240 x 5) = 1200 km.
Speed = Distance/Time
Speed = 1200/(5/3) km/hr. [We can write 1 hours as 5/3 hours]
Required speed = 1200 x 3 km/hr = 720 km/hr.
5
E
Answer: (E) 720 km/hr
Question: In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase or decrease, and by how much?Look at this series: 88, 3, 80, 12, __, 21 ... What number is missing?
(A) 72
(B) 78
(C) 68
(D) 30
(E) 70
Rationale: A72This is an alternating addition and subtraction series. In the first pattern, 8 is subtracted from each number to arrive at the next. In the second, 9 is added to each number to arrive at the next.
Answer: (A) 72
Question: What is the probability of getting a sum 9 from two throws of a dice?
(A) 1/5
(B) 1/9
(C) 1/7
(D) 1/12
(E) 1/6
Rationale: In two throws of a dice, n(S) = (6 x 6) = 36.
Let E = event of getting a sum ={(3, 6), (4, 5), (5, 4), (6, 3)}.
P(E) =	n(E)/n(S)	=	4/36	=	1/9	.
Answer : B.
Answer: (B) 1/9
Question: Machine–A produces 40% of the total output and Machine-B produces 60% of the total output. An average of nine units out of a thousand goods manufactured by Machine-A and one unit of 150 units produced by Machine-B prove to be defective. What is the probability that a unit chosen at random from the total daily output of the factory is defective?
(A) 0.76
(B) 0.076
(C) 0.0076
(D) 0.00076
(E) 7.6e-05
Rationale: Let total Production be 10000 units....
A produces 4000 units and 36 units are defective
B produces 6000 units and 40 units are defective
So, Out of total 10,000 units 76 units are defective...
So the required probability = 76/10000 => 0.0076
Answer will be (C)
Answer: (C) 0.0076
Question: The sum of three integers is 23. The largest integer is 3 times the middle integer, and the smallest integer is 12 less than the largest integer. What is the product of the three integers?
(A) 125
(B) 150
(C) 175
(D) 225
(E) 275
Rationale: Let x be the middle integer. Then the largest is 3x and the smallest is 3x - 12.
3x - 12 + x + 3x = 23
x = 5
The three integers are 3, 5, and 15.
The product is 3*5*15 = 225
The answer is D.
Answer: (D) 225
Question: What is the unit digit in 7^105?
(A) 2
(B) 3
(C) 1
(D) 5
(E) 7
Rationale: Unit digit in 7^105 = unit digit in [(7^4)^26 ]* 7
But unit digit in 7^4=1
unit digit 7^105 = 1*7 = 7
Answer is E
Answer: (E) 7
Question: Andy has 20 pairs of matched gloves. If he loses 13 individual gloves, which of the following is NOT a possible number of matched pairs he has left?
(A) 9
(B) 11
(C) 13
(D) 14
(E) 15
Rationale: We can solve this is second. The question isSelect an answer choice where there is no possibility of having a number as a matched pair
Case1: If 13 gloves are gone the maximum probability of losing maximum gloves is 13 pairs of gloves out of 20. This means i m having 7 pairs of gloves. [Minimum number of gloves i can have is 7 pairs]
Case2: If 13 gloves are gone the maximum probability of losing minimum gloves is 13/2 = 6.5 means i can lose 7 glove. in this scenario i will be having 13 gloves.
Hence10 < Available Glove Pair < 14
any given time I cant possess 14 glove pair for the above mentioned scenario. And thats the answer. D.
Answer: (D) 14
Question: There are a lot of houses such that the numbers of their doorplates are odd numbers and the first number of the doorplates is 445, the last number of the doorplates is 705. How many houses are there?
(A) 141
(B) 111
(C) 121
(D) 131
(E) 101
Rationale: So it starts from 445 and goes like 447, 449,...... 705. and both first and last number are inclusive. Since every other number is odd, it's just 1/2 of the numbers and since it starts with an odd and ends with an odd inclusive add one to the result.
i.e., ([705-445][/2]+1 = 131
Ans D
Answer: (D) 131
Question: The sum q of prime numbers that are greater than 60 but less than 70 is
(A)  67
(B)  128
(C)  191
(D)  197
(E)  260
Rationale: A prime number is a number that has only two factors: 1 and itself. Therefore, a prime number is divisible by two numbers only.
Let's list the numbers from 61 to 69.
61, 62, 63, 64, 65, 66, 67, 68, 69
Immediately we can eliminate the EVEN NUMBERS because they are divisible by 2 and thus are not prime.
We are now left with: 61, 63, 65, 67, 69
We can next eliminate 65 because 65 is a multiple of 5.
We are now left with 61, 63, 67, 69.
To eliminate any remaining values, we would look at those that are multiples of 3. If you don’t know an easy way to do this, just start with a number that is an obvious multiple of 3, such as 60, and then keep adding 3.
We see that 60, 63, 66, 69 are all multiples of 3 and therefore are not prime.
Thus, we can eliminate 63 and 69 from the list because they are not prime.
Finally, we are left with 61 and 67, and we must determine whether they are divisible by 7. They are not, and therefore they must be both prime. Thus, the sum q of 61 and 67 is 128.
Answer B.
Answer: (B)  128
Question: What is the ratio E of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled?
(A) 1/4
(B) 3/8
(C) 1/2
(D) 3/5
(E) 2
Rationale: One side surface area of a cube = x*x = x^2
Total 6 sides = 6x^2
As for the rectangular, Height (H) and Width (W) are same as Cube, x. Only Length = 2x.
L x H = 2x * x = 2x^2 ----> 4 sides = 2x^2 * 4 = 8x^2
W * H = x * x = x^2 ------> 2 sides = x^2 * 2 = 2x^2
Total 6 sides = 8x^2 + 2x^2 = 10x^2
Ratio of cube area to rectangular area E= 6x^2 / 10x^2 ----> 6/10 ----> 3/5 (D)
Answer: (D) 3/5
Question: Given a + b = 1, find the value of 2a + 2b. Two solutions are presented below. Only
one is correct, even though both yield the correct answer.
(A) 3
(B) 5
(C) 4
(D) 2
(E) 1
Rationale: Because a + b = 1,
2a + 2b = 2(a + b) = 2 × 1 = 2.
correct answer D
Answer: (D) 2
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
(A) 271
(B) 180
(C) 188
(D) 127
(E) 211
Rationale: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer:B
Answer: (B) 180
Question: The speed of a boat in upstream is 50 kmph and the speed of the boat downstream is 90 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 70,20 kmph
(B) 78,10 kmph
(C) 70,70 kmph
(D) 78,10 kmph
(E) 70,12 kmph
Rationale: Speed of the boat in still water
= (50+90)/2
= 70 kmph. Speed of the stream
= (90-50)/2
= 20 kmph.
Answer:A
Answer: (A) 70,20 kmph
Question: In the sequence 1, 2, 4, 8, 16, 32, …, each term after the first is twice the previous term. What is the sum of the 17th, and 18th terms in the sequence?
(A) 2^18
(B) 3(2^16)
(C) 7(2^16)
(D) 3(2^16)
(E) 7(2^15)
Rationale: the sequence comes out to be 2^0,2^1,2^2,2^3 and so on...
17th term 2^16
18th term 2^17
adding all three
we get
(2^16)+(2^16)*2
so answer is 2^16(1+2)=>3(2^16)
answer B
Answer: (B) 3(2^16)
Question: If x is an odd integer and y and z are even integers, which of the following CANNOT be an integer?
(A) y/z
(B) x/y
(C) z/x
(D) yx/z
(E) zx/y
Rationale: x = Odd
y = Even
z = Even
Checking Options:
A. y/z Even/Even may be an Integer e.g. 4/2=2 Hence Incorrect Option
B. x/y Odd/Even CAN NEVER be an Integer Hence Correct Option
Answer : B
Answer: (B) x/y
Question: Train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds. The length of train P is three-fourths the length of train Q. What is the ratio of the speed of train P to that of train Q?
(A) 15:8
(B) 15:5
(C) 15:9
(D) 15:2
(E) 15:3
Rationale: Given that train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds.
Let the length of train P be LP and that of train Q be LQ
given that LP = 3/4 LQ
As the train P and Q crosses the pole in 30 seconds and 75 seconds respectively,
=> Speed of train P = VP = LP/30
Speed of train Q = VQ = LQ/75
LP = 3/4 LQ
=> VP = 3/4 LQ/(30) = LQ/40
Ratio of their speeds = VP : VQ
= LQ/40 : LQ/75 => 1/40 : 1/75 = 15:8
Answer:A
Answer: (A) 15:8
Question: Find the greatest number which leaves the same remainder when it divides 20, 40 and 90.
(A) 18
(B) 8
(C) 12
(D) 10
(E) None of these
Rationale: 90 - 40 = 50
40 - 20 = 20
90 - 20 = 70
The H.C.F of 20, 50 and 70 is 10.
ANSWER:D
Answer: (D) 10
Question: It takes one machine 5 hours to complete a production order and another machine 3 hours to complete the same order. How many hours would it take both amhcines working simultaneously at their respective rates to complete the order?
(A) a) 7/12
(B) b) 1 1/2
(C) c) 2 2/9
(D) d) 3 1/2
(E) e) 7
Rationale: RT = W
Given:
R = 1/5 + 1/4 = 9/20
T = ?
W = 1
T = 1 / (9/20) = 20/9 = 2 2/9
Answer: C
Answer: (C) c) 2 2/9
Question: What is the least number to be subtracted from 990 to make it a perfect square?
(A) 100
(B) 90
(C) 30
(D) 71
(E) 80
Rationale: The numbers less than 990 and are squares of certain number is 900.
The least number that should be subtracted from 990 to make it perfect square = 990 - 900 = 90.
ANSWER:B
Answer: (B) 90
Question: The area of a triangle is with base 4m and height 5m?
(A) 20 m2
(B) 10 m2
(C) 82 m2
(D) 54 m2
(E) 28 m2
Rationale: 1/2 * 4 * 5
= 10 m2
Answer:B
Answer: (B) 10 m2
Question: When a random experiment is conducted, the probability that event A occurs is 1/3. If the random experiment is conducted 4 independent times, what is the probability that event A occurs exactly twice?
(A) 8/27
(B) 10/31
(C) 12/37
(D) 14/41
(E) 16/49
Rationale: One case is: 1/3*1/3*2/3*2/3=4/81
The total number of possible cases is 4C2 = 6
P(event A occurs exactly twice) = 6*(4/81) = 8/27
The answer is A.
Answer: (A) 8/27