mathewhe/aqua_rat huggingface dataset:
Question: A train of 45 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long?
(A) 6
(B) 3
(C) 4.2
(D) 9
(E) 4
Rationale: D = 45 * 60 + 1500 = 4200 m
T = 4200/60 * 18/5 = 252 sec = 4.2 mins
Answer:C
Answer: (C) 4.2
Question: Toby is four years younger than Debby. Thrice the sum of the ages of Toby and Debby equals their mother’s age. If the age of the mother is 42, find the ages of Toby and Debby?
(A) 6 and 14
(B) 5 and 9
(C) 8 and 10
(D) 5 and 10
(E) 8 and 16
Rationale: Let the age of Debby be x and Toby be x-4
3 ( x + x-4 ) = 42
x = 9
The ages of Toby and Debby are 5 and 9.
Answer : B
Answer: (B) 5 and 9
Question: what is the cost price of an article sold at rs.199 after two successive discount of 10% and 15%?
(A) 220
(B) 230
(C) 240
(D) 250
(E) 260
Rationale: cost price=199*100/90*100/85
=260
ANSWER:E
Answer: (E) 260
Question: In what ratio should a variety of Rice costing Rs. 10 per kg be mixed with another variety of Rice costing Rs. 13.25 per kg to obtain a mixture costing Rs. 10.75 per kg?
(A) 2 :1
(B) 1 :2
(C) 5 :1
(D) 4 :1
(E) 3:1
Rationale: Let us say the ratio of the quantities of cheaper and dearer varieties = x : y
By the rule of allegation, x/y = (13.25 - 10.75) / (10.75 - 10) = 6/3=2/1
ANSWER:A
Answer: (A) 2 :1
Question: How many different ways can you select a pilot and a co pilot if you have 30 people to choose from?
(A)  870
(B)  920
(C)  1398
(D)  4950
(E)  9900
Rationale: You are not just choosing two from 30. Each of the two people chosen fills a particular slot. The first filling the pilot slot and the second filling the copilot slot is different from the first filling the copilot slot and the second filling the pilot slot.
So the answer is in a sense (30C2) x 2 = 870.
Ans A
Answer: (A)  870
Question: If the perimeter of a rectangular garden is 600 m, its length when its breadth is 100 m is?
(A) 100 m
(B) 200 m
(C) 300 m
(D) 400 m
(E) 500 m
Rationale: perimeter of rectangle=2(l+b)
2(l + 100) = 600
=> l = 200 m
ANSWER:B
Answer: (B) 200 m
Question: The distance from Steve's house to work is 40 Km. On the way back Steve drives twice as fast as he did on the way to work. Altogether, Steve is spending 6 hours a day on the roads. What is Steve's speed on the way back from work?
(A) 5.
(B) 10.
(C) 14.
(D) 15.
(E) 20.
Rationale: Time is in the ratio 2:1 :: to: fro office
Therefore, 2x+1x=6 hrs
Time take to come back - 2 hrs, distance travelled - 40km => Speed = 20kmph
E
Answer: (E) 20.
Question: Find the simple interest on $2000 for 3 years at 10% per annum?
(A) $250
(B) $300
(C) $500
(D) $600
(E) $1000
Rationale: SI = PTR/100
= 2000*3*10/100 = $600
Answer is D
Answer: (D) $600
Question: If n is the product of the integers from 1 to 11, inclusive, how many different prime factors greater than 1 does n have?
(A) Four
(B) Five
(C) Six
(D) Seven
(E) Eight
Rationale: n = 1*2*3*4*5*6*7*8*9*10*11
The prime factors of n are 2, 3, 5, 7, and 11.
There are 5 prime factors.
The answer is B.
Answer: (B) Five
Question: A canoe has two oars, left and right. Each oar either works or breaks. The failure or non-failure of each oar is independent of the failure or non-failure of the other. You can still row the canoe with one oar. The probability that the left oar works is 3/5. The probability that the right oar works is also 3/5. What is the probability W that you can still row the canoe?
(A) 9/25
(B) 10/25
(C) 6/10
(D) 2/3
(E) 21/25
Rationale: Simply look at the question from the other side. What is the probability that you can’t row the canoe? This would be 2/5 x 2/5 = 4/25.
Using the idea that the probability of something happening is 1 – the probability that it doesn’t happen, you can use the following equation to reach the right answer W: 1 – 4/25 = 21/25.Answer choice E.
Answer: (E) 21/25
Question: A train covers a certain distance at a speed of 250kmph in 4 hours. To cover the same distance in 2 hours, it must travel at a speed of
(A) 400km/hr
(B) 500km/hr
(C) 600km/hr
(D) 700km/hr
(E) 800km/hr
Rationale: Explanation:
Distance = 250×4 = 1000km
Required speed = (1000/2) = 500km/hr
Answer: Option B
Answer: (B) 500km/hr
Question: Which of the following is a prime number
(A) 9
(B) 2
(C) 4
(D) 8
(E) 9
Rationale: Explanation:
A prime number is a natural number greater than 1 which has no positive divisors other than 1 or itself.
So from above options 2 is that number
Answer: Option B
Answer: (B) 2
Question: A farmer with 1,350 acres of land had planted his fields with corn, sugar cane, and tobacco in the ratio of 5:2:2, 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?
(A) 90
(B) 150
(C) 270
(D) 300
(E) 450
Rationale: Originally (2/9)*1350 = 300 acres were planted with tobacco.
In the new system (5/9)*1350 = 750 acres were planted with tobacco.
Thus 750-300 = 450 more acres were planted with tobacco.
The answer is E.
Answer: (E) 450
Question: At Company K, 15 percent of the employees are secretaries and 60 percent are salespeople. If there are 40 other employees of Company K, how many employees does Company K have?
(A)  160
(B)  180
(C)  190
(D)  200
(E)  400
Rationale: Let the total number of employees in the company be x
% of secretaries = 15%
% of salespeople = 60%
% of of employees other than secretaries and salespeople = 100 - 75 = 25%
But this number is given as 40
so 25% of x = 40
x = 160
Therefore there a total of 160 employees in the company K
Correct answer - A
Answer: (A)  160
Question: Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is?
(A) 27
(B) 28
(C) 200
(D) 277
(E) 267
Rationale: d2/2 = (20 * 20)/2
= 200
Answer:C
Answer: (C) 200
Question: Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
(A) 17 1/6
(B) 17 1/3
(C) 17 1/7
(D) 17 1/2
(E) 17 1/1
Rationale: 1/20 + 1/30 - 1/40
= 7/120
120/7
= 17 1/7
Answer: C
Answer: (C) 17 1/7
Question: 10 books are placed at random in a shelf. The probability that a pair of books will always be together is ?
(A) 1/7
(B) 2/5
(C) 1/5
(D) 1/3
(E) 3/5
Rationale: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!
Required probability
= 1/5
Answer:C
Answer: (C) 1/5
Question: The average salary of all the workers in a workshop is Rs. 10000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 8000. The total number of workers in the workshop is :
(A) 14
(B) 21
(C) 88
(D) 37
(E) 29
Rationale: Explanation:
Lot the total number of workers be v Then,
10000v = (12000 * 7) + 8000 (v - 7) <=> 2000v = 28000 <=> v = 14
Answer: A) 14
Answer: (A) 14
Question: Pipe A and pipe B fill water into a tank of capacity 1000 litres, at a rate of 200 l/min and 50 l/min. Pipe C drains at a rate of 25 l/min. Pipe A is open for 1 min and closed, then pipe B is open for 2 min and closed. Further the pipe c is opened and drained for another 2 min. This process is repeated until the tank is filled. How long will it take to fill the tank?
(A) 15
(B) 17
(C) 18
(D) 56
(E) 20
Rationale: tank capacity: 1000 L,
1st- 200 l/min for 1 min, volume filled: 200 L
2nd- 100 l/min for 2 min, volume filled: 100 L
3rd (water draining) : 25 l/min*2 : 50 L
total : (200+100)-50 =250 L filled for 1 cycle
number of 250 in 1000 L tank :1000/250 = 4
time taken to fill: 4* total time= 4*5 = 20 (option E)
Answer: (E) 20
Question: The sum of money at compound interest amounts to thrice itself in 5 years. In how many years will it be 21 times itself?
(A) 18 years
(B) 9 years
(C) 12 years
(D) 16 years
(E) 30 years
Rationale: 100 ---- 300 --- 5
900 --- 5
1200---5
1500----5
1800---5
2100---5
6 years
Answer: E
Answer: (E) 30 years
Question: A merchant can place 8 large boxes or 10 small boxes into a carton for shipping. In one shipment, he sent a total of 96 boxes. If there are more large boxes than small boxes, how many cartons did he ship?
(A) 13
(B) 25
(C) 17
(D) 12
(E) 11
Rationale: 11 cartons total
7 large boxes (7 * 8 = 56 boxes)
4 small boxes (4 *10 = 40 boxes
11 total cartons and 96 boxes
Answer: (E) 11
Question: What is the least possible product of 4 different integers, each of which has a value between –2 and 10, inclusive?
(A) –5040
(B) –3600
(C) –720
(D) –1440
(E) –120
Rationale: Maximize the total product with a -ve sign
so -2 * 10 * 9 * 8 = 720 * -2 = -1440
Answer is D.
Answer: (D) –1440
Question: How many odd prime numbers are there less than 75?
(A) 20
(B) 1
(C) 2
(D) 16
(E) 17
Rationale: Odd prime number less than 75:3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73
There is 20 the odd prime number
Answer is A
Answer: (A) 20
Question: Suresh invested a sum of Rs. 15000 at 9 percent per annum Simple interest and Rs. 12000 at 8 percent per annum compound interest for a period of 2 years. What amount of interest did Suresh earn in 2 years?
(A) 4496.8
(B) 4596.8
(C) 4696.8
(D) 4796.8
(E) 4896.8
Rationale: S.I = PTR/100
S.I =15000*9*2/100
S.I= 2700
C.I =P(1+r/100)^n -P
C.I= 12000(1+8/100)^2-12000
C.I=1996.8
total amount in 2 years
as interest = S.I +C.I
= 2700+1996.8
=4696.8
ANSWER:C
Answer: (C) 4696.8
Question: Anish borrowed 15000 at the rate of 12% and an other amount at the rate of 15% for two years. The total interest paid by him was 9000. How much did he borrow?
(A) 32,000
(B) 33,000
(C) 30,000
(D) 35,000
(E) None of these
Rationale: Let x be the other amount
\ 3x⁄10 + 3600 = 900 ⇒ x = 18000
\ total borrowed sum = 33000
Answer B
Answer: (B) 33,000
Question: Let A represent a set of four distinct prime numbers. If the sum of the numbers in A is even and x is a member of A, then what is the least possible value that x can be?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 7
Rationale: We are told that A is a set of four distinct prime numbers, and the sum of the numbers in A is even. Since the question involves odds, evens and the smallest possible prime, you should immediately think of 2, the smallest prime number and the only even prime number.
If 2 were a member of the set, then we would have one even number and three odd numbers. Since such sum would always be odd, 2 cannot be a member of the set. Thus, all the members of A must be odd to yield an even sum.
Since all the members of the set must be odd prime numbers, the answer is the smallest odd prime number, which is 3.
The correct answer is choice (C).
Note:1 is not a prime number.
Answer: (C) 3
Question: An eight-digit telephone number consists of exactly two zeroes. One of the digits is repeated thrice. Remaining three digits are all distinct. If the first three digits (from left to right) are 987, then find the probability of having only one 9, one 8 and one 7 in the telephone number.
(A) 1/18
(B) 1/20
(C) 1/10
(D) 5/47
(E) 5/45
Rationale: Explanation :
Case A: There is only one 9, one 8 and one 7 in the number.
Hence there has to be one digit from {1,2,3,4,5,6} repeated thrice.
Total number of ways in which such a number can exist is :
=>6C1×5!/(3!×2!).
=60.
Case B: One of the three digit {9,8,7} is repeated thrice.
Hence, there will be one digit from {1,2,3,4,5,6}.
Total number of ways in which such a number can exist:
=>3C1×6C1×5!/(3!×2!).
=>540
Total possible telephone numbers:
=60+540=600.
Hence the required Probability is 60/600 = 1/10.
Answer : C
Answer: (C) 1/10
Question: A room is 7 meters 20 centimeters in length and 4 meters 32 centimeters in Width. Find the least number of square tiles of equal size required to cover the entire floor of the room.
(A) 10
(B) 15
(C) 17
(D) 19
(E) 21
Rationale: Let us calculate both the length and width of the room in centimeters.
Length = 7 meters and 20 centimeters = 720 cm
width = 4 meters and 32 centimeters = 432 cm
As we want the least number of square tiles required, it means the length of each square tile should be as large as possible.Further,the length of each square tile should be a factor of both the length and width of the room.
Hence, the length of each square tile will be equal to the HCF of the length and width of the room = HCF of 720 and 432 = 144
Thus, the number of square tiles required = (720 x 432 ) / (144 x 144) = 5 x 3 = 15
Answer: B
Answer: (B) 15
Question: The ratio of Rita's age to her mother's age is 3:8. The difference of their ages is 35 years. The ratio of their ages after 4 years will be:
(A) 7:12
(B) 5:12
(C) 38:43
(D) 42:47
(E) 52:47
Rationale: Rita age=3x
mother's age=8x
their difference = 8x-3x=35
x=7
therefore Rita's current age=21
mother's current age=56
4 years hence their ratio of ages will be 25:60
ans is 5:12
ANSWER:B
Answer: (B) 5:12
Question: City A to city B, Andrew drove for 1 hour at 50 mph and for 3 hours at 60 mph. What was the average speed for the whole trip?
(A) 57
(B) 57.5
(C) 58.2
(D) 59
(E) 62
Rationale: The total distance is 1×50+3×60=2301×50+3×60=230. And the total time is 4 hours. Hence,
Average Speed=(Total DistanceTotal Time)=2304=57.5
B
Answer: (B) 57.5
Question: In how many W ways can the wordGMATbe arranged so that no such arrangement has A as the first letter?
(A) 6
(B) 12
(C) 18
(D) 24
(E) 30
Rationale: Number of ways of arranging the word GMAT = 4! = 24
Number of ways of arranging the word GMAT so that A is always in the first = 3! = 6
Number of ways of arranging GMAT so that A is not in the beginning W= 24 - 6 = 18
Answer: C
Answer: (C) 18
Question: What is the least integer greater than –1+0.5?
(A) –2
(B) –1
(C) 0
(D) 1
(E) 2
Rationale: This question is just about doing careful Arithmetic and remembering what makes a numberbiggerorsmallercompared to another number.
First, let's take care of the Arithmetic:
(-1) + (0.5) = -0.5
On a number line, since we're ADDING +.5 to a number, the total moves to the RIGHT (so we're moving from -1 to -0.5).
Next, the question asks for the LEAST integer that is GREATER than -0.5
Again, we can use a number line. Numbers become greater as you move to the RIGHT. The first INTEGER to the right of -0.5 is 0.
Final Answer:
C
Answer: (C) 0
Question: A watch was sold at a loss of 8%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
(A) 1000
(B) 2876
(C) 1977
(D) 1167
(E) 2711
Rationale: 92%
104%
--------
12% ---- 140
100% ---- ? => Rs.1167
Answer: D
Answer: (D) 1167
Question: 25 x 10 + 25 x 11 = ?
(A) 725
(B) 720
(C) 600
(D) 525
(E) None of them
Rationale: =25 x (10+11) (by distributive law)
=25 x 21
=525
Answer is D
Answer: (D) 525
Question: A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.340 less than the sum lent. What was the sum lent?
(A) 288
(B) 277
(C) 299
(D) 500
(E) 278
Rationale: P - 340 = (P*4*8)/100
P = 500
Answer:D
Answer: (D) 500
Question: If x-y=8, which of the following must be true?
I. If x is positive, y must be positive
II. If x is negative, y must be negative
III.Both x and y are positive
(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III
Rationale: If x-y=8, which of the following must be true?
I. Both x and y are positive
II. If x is positive, y must be positive
III. If x is negative, y must be negative
1. x and y can be negative, for instance, -2 - (-10) = 8 =>Eliminate A and D
2. x can be positive and y can be negative, for instance, 2 - (-6) = 8 => Eliminate B and E
A) I only
B) II only
C) III only
D) I and II
E) II and III
Answer B
Answer: (B) II only
Question: The winning relay team in a high school sports competition clocked 48 minutes for a distance of 13.2 km. Its runners A, B, C and D maintained speeds of 15 kmph, 18 kmph, 17 kmph, and 16 kmph respectively. What is the ratio of the time taken by B to than taken by D?
(A) 5:16
(B) 5:17
(C) 9:8
(D) 8:9
(E) None of these
Rationale: Explanation :
Since it is a relay race, all the runners ran the same distance.
Hence for a same distance, (ratio of times) = 1/(ratio of speeds).
Hence ratio of times taken by B t& D = 16 : 18 = 8 : 9.
Answer : D
Answer: (D) 8:9
Question: If 5x = 6y and xy ≠ 0, what is the ratio of 1/5*x to 1/8*y ?
(A)  48/25
(B)  36/25
(C)  6/5
(D)  5/6
(E)  25/36
Rationale: 5x = 6y => x/y = 6/5
1/5*x to 1/8*y = x/y * 8/5 = (6/5)*(8/5)=48/25
Ans: A
Answer: (A)  48/25
Question: What is the next number of the following sequence
3,7,13,21,?
(A) 22
(B) 31
(C) 41
(D) 35
(E) 42
Rationale: 2^2-1=3
3^2-2=7
4^2-3=13
5^2-4=21
6^2-5=31
ANSWER:B
Answer: (B) 31
Question: A discount electronics store normally sells all merchandise at a discount of 10 percent to 40 percent off the suggested retail price. If, during a special sale, an additional 5 percent were to be deducted from the discount price, what would be the lowest possible price of an item costing $500 before any discount?
(A) $130.00
(B) $285.00
(C) $200.00
(D) $258.00
(E) $210.00
Rationale: Original price : 500 $
Max first discount = -40%
Thus : 500âˆ—(1âˆ’40/100)=300
Second discount on the discounted price = -20%
Thus : 300âˆ—(1âˆ’5/100)=285
Answer B.
Answer: (B) $285.00
Question: Find the total average marks of all the students in 2 separate classes, if the average marks of students in the first class of 39 students is 45 and that of another class of 35 students is 70.
(A) 55.8
(B) 51.8
(C) 53.8
(D) 56.8
(E) 52.8
Rationale: Sum of the marks for the class of 39 students = 39 * 45 = 1755
Sum of the marks for the class of 35 students = 35 * 70 = 2450
Sum of the marks for the class of 74 students =1755+2450=4205
Average marks of all the students = 4205/74
= 56.8
Answer:D
Answer: (D) 56.8
Question: The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 42 kmph, find the speed of the stream?
(A) 87 kmph
(B) 68 kmph
(C) 14 kmph
(D) 76 kmph
(E) 57 kmph
Rationale: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream
= (2+1)/(2-1)
= 3/1 = 3:1
Speed of the stream
= 42/3 = 14 kmph.
Answer:C
Answer: (C) 14 kmph
Question: Each term of a certain sequence is 3 less than the previous term. The first term of this sequence is 29. If the sum of the first n terms of the sequence is n, what is the value of positive integer n?
(A) 1
(B) 13
(C) 15
(D) 21
(E) 47
Rationale: We know that it is a decreasing sequence i.e. the terms keep decreasing till 0 and then negative terms start.
What does this imply?If the sum of the first n terms of the sequence is n
Since number of terms will definitely be positive, we are looking for a positive sum.
19 + 16 + 13 + 10 + 7 + 4 + 1 -2 -5 -7 -10 .... and so on
Note that the first 7 terms are positive and all others negative. Every negative term has greater absolute value than the corresponding positive terms i.e. -2 absolute value is greater than 1 absolute value, -5 absolute value is greater than 4 absolute value, and so on...
Since we have 7 positive terms, we must have less than 7 negative terms to get the sum as positive. If we have 6 negative terms, we will have a total of 13 terms. Of the given options, only 13 is possible and hence it must be the answer.
Answer (D)
Answer: (D) 21
Question: What percent of 60 is 25?
(A) 60%
(B) 50%
(C) 42%
(D) 25%
(E) 10%
Rationale: The phrasing of the question is difficult for some students. "What percent of 60 is 25?" is the same question as "25 is what percent of 60?" Many students find this later way of phrasing the question easier to work with.
If X is Y percent of Z, then X/Z=Y/100; For example, 10 is 50% of 20; X = 10, Y = 50, and Z = 20
Similarly, if you wanted to know what percent of 100 is 50, you would intuitively know that it is 50% since it is 50/100 or 50 per cent (literally, per 100).
Applying this logic to the problem at hand: 25/60= .42 = 42%
Thus, 25 is 42% of 60
If this way of solving the problem is difficult to conceptualize, consider another approach. It should be clear that 30 is 50% (or 1/2) or 60. Since 25 is less than 30, 25 must be less than 50% of 60. This means that any answer that is not less than 50% is wrong.
Since 25% is 1/4 and 1/4 of 60 is 15 (since 15*4=60), 25% is too small. By process of elimination, the answer is 42%
Answer C
Answer: (C) 42%
Question: In a certain growth fund, 3/5 of the investment capital is invested in stocks, and of that portion, 1/3 is invested in preferred stocks. If the mutual fund has $847,000 invested in preferred stocks, what is the total amount of money invested in the fund?
(A) $1,974,000
(B) $2,538,000
(C) $3,264,000
(D) $3,826,000
(E) $4,235,000
Rationale: Portion invested in preferred stock = 3/5 * 1/3 = 1/5
1/5 of fund = 847---
Fund = 5 * 847---
Here, we can avoid the math and simply look at 5 * 7 -> 35. Only option E has 35 in it.
Answer (E).
Answer: (E) $4,235,000
Question: If f(x) = 2x+2 what is f(f(3))?
a. 18
b. 8
c. 64
d. 16
(A) 8
(B) 18
(C) 64
(D) 16
(E) 26
Rationale: f(3)=2*3+2=8
now put this value again in the function
f(8)=2*8+2=18
ANSWER:B
Answer: (B) 18
Question: When a number is multiplied by 13,it will become greater to 105 by an amount with which it is lesser to105 by now. What is the number
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: no is 105-x, then
(105-x)*13 = 105+x
1365 -13 x =105+x
14x = 1260
x= 1260/14 =90
so number is 105-90 = 15
ANSWER:D
Answer: (D) 15
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
(A) 1 : 3
(B) 3 : 2
(C) 3 : 4
(D) 3 : 5
(E) None of these
Rationale: let length of trains are x and y
so speed of the trains will be x/27 and y/17 respectively.
now to cross each other time taken=23 second,
so (x+y)/((x/27)+(y/17))=23
(27*17)(x+y)/17x+27Y=23
so, ((x/y)+1)/17(x/y)+27=23/27*17
(x/y)+1=(23x/27y)+23/17
4*(x/27)=6*(y/17)
so,(x/27):(y/17)=3:2
so ratio of speed of the train will be 3:2
ANSWER:B
Answer: (B) 3 : 2
Question: 75% of the guestrooms at the Stagecoach Inn have a queen-sized bed, and each of the remaining rooms has a king-sized bed. Of the non-smoking rooms, 60% have a queen-sized bed. If 30% of the rooms at the Stagecoach Inn are non-smoking rooms with king-sized beds, what percentage of the rooms permit smoking?
(A) 25%
(B) 30%
(C) 50%
(D) 55%
(E) 75%
Rationale: Let x be the number of non-smoking rooms.
Let N be the total number of rooms at the inn.
40% of non-smoking rooms have a king-sized bed.
0.4x = 0.3N
x = 0.75N
The percentage of rooms which permit smoking is 1 - 0.75 = 25%
The answer is A.
Answer: (A) 25%
Question: If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is
(A) 1/2
(B) 3/4
(C) 3/7
(D) 3/11
(E) 4/7
Rationale: The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2
P(E) = 1 - 1/2 = 1/2.
A)
Answer: (A) 1/2
Question: If y is an integer, then the least possible value of |23 - 8y| is
(A) 5
(B) 2
(C) 3
(D) 4
(E) 1
Rationale: We know that 8y is a multiple of 8, so let’s first look at the multiples of 8 closest to 23. We have “16” and “24”. Let’s subtract both of these from 23 and see which one produces the smallest result. When 2y = 16, y is 2 and when 3y = 24, y is 5. Let’s start with letting y = 4.
|23-8(2)|
|23-16|
|7| = 7
Next, let’s let y equal 3.
|23-8(3)|
|23-24|
|-1| = 1
We see that the smallest possible value of |23-8y| is 1.
Answer E.
Answer: (E) 1
Question: A sum of money lent out at S.I. amounts to a total of $590 after 2 years and to $815 after a further period of 5 years. What was the initial sum of money that was invested?
(A) $490
(B) $500
(C) $510
(D) $520
(E) $530
Rationale: S.I for 5 years = $815 - $590 = $225
The S.I. is $45/year
S.I. for 2 years = $90
Principal = $590 - $90 = $500
The answer is B.
Answer: (B) $500
Question: Excluding stoppages,the speed of the bus is 54kmph and
including stoppages,it is 18kmph. For how many minutes does the bus stop per hr
(A) 12 min
(B) 11 min
(C) 13 min
(D) 20 min
(E) 40 min
Rationale: Due to stoppages,it covers 36km less.
time taken to cover 36 km is [36/54 *60] min = 40min
Answer is E.
Answer: (E) 40 min