mathewhe/aqua_rat huggingface dataset:
Question: If x = 5 and y = −2, what is the value of (x − 2y)^y?
(A) −100
(B) 0.2
(C) 0.01
(D) 4
(E) 8
Rationale: Quickly we can spot that answer is neither integer nor negative. Eliminate A, DE
6+4= 10 by inversing and squaring 0.01
Answer:C
Answer: (C) 0.01
Question: Under the Below list which is the smallest prime number:
(A) 48
(B) 41
(C) 38
(D) 32
(E) 30
Rationale: B
41
Answer: (B) 41
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 360 m and they cross each other in 12 sec, then the speed of each train is?
(A) 22
(B) 77
(C) 36
(D) 108
(E) 21
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (360 + 360)/12 => x = 30
Speed of each train = 30 m/sec.
= 30 * 18/5 =- 108 km/hr.
Answer: D
Answer: (D) 108
Question: If Rs.1000 be invested at interest rate of 5% & the interest be added to the principal every 10 yrs, then the no. of yrs in which it will amount to Rs.2000 is:
(A) 16 years
(B) 16 1/2 years
(C) 16 2/3 years
(D) 17 years
(E) 17 2/3 years
Rationale: Total time= (10+6 2/3) = 16 2/3 years
C
Answer: (C) 16 2/3 years
Question: An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?
(A) 270º
(B) 360º
(C) 280º
(D) 90º
(E) 180º
Rationale: Angle traced by the hour hand in 6 hours =	(360/12 x 6)º = 180º.
Answer E
Answer: (E) 180º
Question: A work which could be finished in 12 days was finished 3 days earlier after 10 more men joined. The number of men employed was?
(A) 22
(B) 20
(C) 88
(D) 71
(E) 10
Rationale: x ------- 12
(x + 10) ---- 6
x * 12 = (x + 10)6
x = 10
\Answer: E
Answer: (E) 10
Question: 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:
(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) 14
Question: If a class of 10 students has five men, how many ways can the men and women be arranged in a circle so that no two men sit next to each other?
(A) 5!4!
(B) 5!5!
(C) 4!4!
(D) 10!
(E) 10!/5!
Rationale: Let's say that we make a man sits in spot 1. Then, a man must also sit in spots 3, 5, 7, 9. There are 5! ways of arranging the man this way. However, since this is a table (ie: circle), there are 5 ways where the initial man can sit, so we must divide 5! by 5, which equals to 4!.
It follows that a woman must sit in spots 2, 4, 6, 8, 10. There are 5! ways to arrange this.
Therefore, we get 4!5!. So the answer is A) 5!4!
Answer: (A) 5!4!
Question: Which one of the following is the least number of four digits divisible by 71?
(A) 1288
(B) 1065
(C) 1229
(D) 1727
(E) 1781
Rationale: Explanation:
1000/71 = 14 6/71
1000 + 71 â€“ 6 = 1065
Answer:B
Answer: (B) 1065
Question: A train of 24 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 1.4 km long?
(A) 2 mins 14 sec
(B) 2 mins 34 sec
(C) 2 mins 54 sec
(D) 4 mins 54 sec
(E) 2 mins 44 sec
Rationale: D = 25 * 60 + 1400 = 2900 m
T = 2900/60 * 18/5 = 174 sec = 2 mins 54 sec
ANSWER:C
Answer: (C) 2 mins 54 sec
Question: It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the car is?
(A) 3:8
(B) 3:1
(C) 3:4
(D) 3:9
(E) 3:2
Rationale: Let the speed of the train be x km/hr and that of the car be y km/hr.
Then, 120/x + 480/y = 8 or 1/x + 4/y = 1/15 --- (i)
And, 200/x + 400/y = 25/3 or 1/x + 2/y = 1/24 --- (ii)
Solving (i) and (ii), we get x = 60 and y = 80
Ratio of speeds = 60:80 = 3:4
Answer:C
Answer: (C) 3:4
Question: Excluding stoppages,the speed of the bus is 72kmph and
including stoppages,it is 54kmph. For how many minutes does the bus stop per hr
(A) 12 min
(B) 11 min
(C) 13 min
(D) 15 min
(E) 17 min
Rationale: Due to stoppages,it covers 18km less.
time taken to cover 18 km is [18/72 *60] min = 15min
Answer is D.
Answer: (D) 15 min
Question: .009/?= .01
(A) .9
(B) .09
(C) .009
(D) .0009
(E) None of them
Rationale: Let .009/x = .01;
Then x = .009/.01
= .9/1
= .9
Answer is A
Answer: (A) .9
Question: There are 200 cats in Cat-City. Out of the 200, 70 are street cats and the rest are domestic cats. 110 cats are gray, 25 out of the gray cats are NOT domestic ones. How many domestic cats are there which are not gray in Cat-City?
(A) 90.
(B) 45.
(C) 50.
(D) 40.
(E) 25.
Rationale: STREET-CAT DOMESTIC-Cat
70 130
(25gray+45other) 85gray+45other
Answer:B
Answer: (B) 45.
Question: A credit card number has 6 digits (between 1 to 9). The first two digits are 12 in that order, the third digit is bigger than 4, the forth is divisible by 3 and the fifth digit is 3 times the sixth. How many different credit card numbers exist?
(A) 27
(B) 36
(C) 72
(D) 112
(E) 45
Rationale: {1}{2}{greater than 6}{divisible by 3}{3x}{x}:
The third digit can take 5 values: 5,6,7, 8, or 9.
The fourth digit can take 3 values: 3, 6, or 9.
The fifth and sixth digits can take 3 values: 31, 62, or 93.
Total = 5*3*3 = 45.
Answer: E.
Answer: (E) 45
Question: If the price of petrol increases by 25, by how much must a user cut down his consumption so that his expenditure on petrol remains constant?
(A) 25%
(B) 20%
(C) 16.67%
(D) 33.33%
(E) None of these
Rationale: Explanation :
let us assume before increase the petrol will be Rs. 100.
After increase it will be Rs (100+25) i.e 125.
Now, his consumption should be reduced to :-
=125−100125∗100.
Hence, the consumption should be reduced to 20%.
Answer : B
Answer: (B) 20%
Question: A clock shows the time as 9 a.m. If the minute hand gains 5 minutes every hour, how many minutes will the clock gain by 4 p.m.?
(A) 30 min
(B) 35 min
(C) 45 min
(D) 50 min
(E) 55 min
Rationale: there are 7 hours in between 9 a.m. to 4 p.m.
7*5=35 minutes.
ANSWER:B
Answer: (B) 35 min
Question: X and Y are positive two-digit integers such that the tens digit in X is the same as the units digit in Y, and the units digit in X is the same as the tens digit in Y. Which of the following CANNOT be the difference of X and Y ?
(A) 72
(B) 45
(C) 27
(D) 33
(E) 9
Rationale: X and Y are positive two-digit integers such that the tens digit in X is the same as the units digit in Y, and the units digit in X is the same as the tens digit in Y:
X = 10a + b
Y = 10a + b
X - Y = (10a + b) - (10a + b) = 9(a - b). As you can see the difference must be a multiple of 9. Only option D is not a multiple of 9.
Answer: D.
Answer: (D) 33
Question: Shobha’s mathematics test had 75 problems i.e.10 arithmetic, 30 algebra and 35 geometry problems. Although she answered 70% of the arithmetic ,40% of the algebra, and 60% of the geometry problems correctly. she did not pass the test because she got less than 60% of the problems right. How many more questions she would have to answer correctly to earn 60% of the passing grade?
(A) 3
(B) 2
(C) 6
(D) 5
(E) 4
Rationale: Number of questions attempted correctly
=(70% of 10 + 40% of 30 + 60% 0f 35)
=7 + 12+21= 45
questions to be answered correctly for 60% grade=60% of 75 = 45
therefore required number of questions= (45-40) = 5
Answer is D.
Answer: (D) 5
Question: Solve the following quadratic equation by factoring.
X2+15X=50
(A) 10,4
(B) 4,-10
(C) 5,10
(D) -5,10
(E) 6,3
Rationale: Now all we need to do is use the zero factor property to get,
X+5 = 0 X=-5 OR
X+10=0, X = -10
ANSWER D
Answer: (D) -5,10
Question: A caterer ordered 125 ice-cream bars and 125 sundaes. If the total price was $275.00 and the price of each ice-cream bar was $0.60, what was the price of each sundae?
(A) $0.60
(B) $0.80
(C) $1.00
(D) $1.20
(E) $1.60
Rationale: Let price of a sundae = S
Price of ice cream bar = .6 $
125 * .6 + 125*S = 275
=> 125*S =200
=> S = 1.6
Answer E
Answer: (E) $1.60
Question: If x and y are prime numbers such that x > y > 1, then x^2 − y^2 must be divisible by which one of the following numbers?
(A)  3
(B)  4
(C)  5
(D)  9
(E)  12
Rationale: If x=3 and y=2, then x^2-y^2=5 and 5 is divisible only by 5 from the options, thus it must be correct.
Answer: C.
Answer: (C)  5
Question: Set S consists of all prime integers less than 10. If two numbers are chosen form set S at random, what is the probability that the product of these numbers will be greater than the product of the numbers which were not chosen?
(A) 1/3
(B) 2/3
(C) 1/2
(D) 7/10
(E) 4/5
Rationale: S={2, 3, 5, 7}
The simplest way would be to realize that we choose half of the numbers (basically we divide the group of 4 into two smaller groups of 2) and since a tie is not possible then the probability that the product of the numbers in either of subgroup is more than that of in another is 1/2 (the probability doesn't favor any of two subgroups).
Answer: C
Answer: (C) 1/2
Question: Salaries of Ravi and Sumit are in the ratio 2:3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40:57. What is Sumit's present salary?
(A) Rs.38,0387
(B) Rs.38,038
(C) Rs.38,036
(D) Rs.38,000
(E) Rs.38,098
Rationale: Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.
Then, (2x + 4000)/(3x + 4000) = 40/57
6x = 68000 => 3x = 34000
Sumit's present salary = (3x + 4000) = 34000 + 4000 = Rs.38,000.
Answer: D
Answer: (D) Rs.38,000
Question: How much time will it take for an amount of Rs. 600 to yield Rs. 30 as interest at 2% per annum of simple interest?
(A) 8.1 years
(B) 4.2 years
(C) 7 years
(D) 6 years
(E) 2.5 years
Rationale: Explanation:
Time = (100 x 81)/(450 x 4.5) years
= 2.5 years.
Answer: E
Answer: (E) 2.5 years
Question: If there are 4 peanuts in a box and Mary puts 6 more peanuts inside, how many peanuts are in the box?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: 6+4=10
correct answer is C)10
Answer: (C) 10
Question: Cars C1 and C2 travel to a place at a speed of 30 and 45 km/h respectively. If car C2 takes 21⁄2 hours less time than C1 for the journey, the distance of the place is
(A) 300 km
(B) 400 km
(C) 350 km
(D) 225 km
(E) None of these
Rationale: Let C1 takes t hrs. Then,
∴ Distance is same.
∴ 30t = 45(t - 5⁄2)
⇒ t = 15⁄2 hrs.
∴ Distance = 30 × 15⁄2 = 225 km
Answer D
Answer: (D) 225 km
Question: Solution X is 10 percent alcohol by volume, and solution Y is 30 percent alcohol by volume. How many milliliters of solution Y must be added to 300 milliliters of solution X to create a solution that is 22 percent alcohol by volume?
(A) 300
(B) 350
(C) 400
(D) 450
(E) 500
Rationale: 22% is 12%-points higher than 10% but 8%-points lower than 30%.
Thus there should be 2 parts of solution X for 3 parts of solution Y.
We should add 450 ml of solution Y.
The answer is D.
Answer: (D) 450
Question: If each term in the sum a1+a2+a3+.....+an is either 7 or 77 and the sum equals 357, which of the following could be equal to n?
(A) 38
(B) 39
(C) 40
(D) 41
(E) 42
Rationale: Since, there is no 51 in the answer choices (357/7 = 51), we know there is at least one 77.
357 - 77 = 280
280/7 = 40
40+1 = 41.
If 41 wasn't there, I would have subtracted 77 from 280 and continued in a similar way.
Ans. D
Answer: (D) 41
Question: If a(a - 4) = 21 and b(b - 4) = 21, where a ≠ b, then a + b =
(A)  −48
(B)  −2
(C)  4
(D)  46
(E)  48
Rationale: a(a - 4) = 21 and b(b - 4) = 21
=> a, b must be integers and if a is -3 or 7, b will be 7 and -3 respectively
=> a+b = 4
Ans: C
Answer: (C)  4
Question: The areas, in kilometers squared, of some countries are given below. USA: 9,629,091, Russia: 22,098,242, China: 9,598,094, Canada: 9,984,670, the UK: 242,400 and India: 3,287,263.
What is the difference between the areas of Russia and China?
(A) 5,476,811 kilometers squared
(B) 12,500,148 kilometers squared
(C) 9,843,123 kilometers squared
(D) 1,878,965 kilometers squared
(E) 4,787,900 kilometers squared
Rationale: he difference between the areas of Russia and China is given by
22,098,242 - 9,598,094 = 12,500,148 kilometers squared
correct answer B
Answer: (B) 12,500,148 kilometers squared
Question: A circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per second does the larger rim makes in terms of x ?
(A) 4x/5
(B) 75x
(C) 48x
(D) 24x
(E) x/75
Rationale: Let's try the explanation. We have two wheels. One with 28pi and the other one with 35pi. They have the same speed. In the smaller wheel it's 28pi*x, which must be equal to the speed of the bigger one (35pi*a number of revolutions).They are asking that number of revolutions (but in minutes, which makes the question even harder).
Anyway, we have 28pi*x=35pi*a.
(28pi*x)/(35pi). = 4x/5.
Ans :A
Answer: (A) 4x/5
Question: A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 8 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?
(A) 7.5
(B) 7.4
(C) 7.9
(D) 7.2
(E) 8.0
Rationale: Net part filled in 1 hour = (1/4 - 1/9) = 1/8
The cistern will be filled in 8/1 hrs i.e., 8 hrs.Answer: E
Answer: (E) 8.0
Question: A train 75 metres long overtook a man who was walking at the rate of 6 km/h and passed him in 18 seconds. Again, the train overtook a second person in 15 seconds. At what rate was the second person travelling ?
(A) 3 km/h
(B) 2.5 km/h
(C) 4 km/h
(D) 1.5 km/h
(E) None of these
Rationale: Let actual speed of train ST km/h.
Then, ST - 6 = 75⁄18 × 18⁄5 = 15
⇒ ST = 21 km/h
Now, let speed of second man = Sm
21 - Sm = 75⁄15 × 18⁄5 = 18
⇒ Sm = 3 km/h
Answer A
Answer: (A) 3 km/h
Question: For a three-digit number xyz, where x, y, and z are the digits of the number, f(xyz)=5^x 2^y 3^z . If f(abc)=3*f(def), what is the value of abc-def ?
(A) 1
(B) 2
(C) 3
(D) 9
(E) 27
Rationale: Since f(abc) = 3*f(def), I would assume that f = c - 1 from the function above.
The answer should be (A)
Answer: (A) 1
Question: If 0 < n < 1, what is the median of the values n, n^-1, n^2, n^1/2 and n^3?
(A) n
(B) n^-1
(C) n^2
(D) n^1/2
(E) n^3
Rationale: A. To make the problem less confusing, I picked a number between 0 and 1 such as n = 1/4 and calculate:
n = 1/4
n^-1 = 4
n^2 = 1/16
n^(1/2) = 1/2
n^3 = 1/8.
From this, rearrange the number and the median is 1/4, which is n. Answer A
Answer: (A) n
Question: Total expenses of a boarding house are partly fixed and partly varying linearly with the number of boarders.The average expense per boarder is Rs. 700 when there are 25 boarders and Rs 600 when there are 50 boarders.What is the average expense per boarders when there are boarder ?
(A) 550
(B) 580
(C) 540
(D) 570
(E) None of these
Rationale: Explanation :
Let x be the fixed cost and y the variable cost
17500 = x + 25y … (i)
30000 = x + 50y … (ii)
Solving the equation (i) and (ii), we get
x = 5000, y = 500
Now if the average expense of 100 boarders be ‘A’.
Then,
=> 100 × A = 5000 + 500 × 100 .
∴ A = 550.
Answer : A
Answer: (A) 550
Question: A bookstore made 11000 dollars selling 3000 math books and 1000 physics books. A customer bought 1 math book and 1 physics book and paid 7 dollars. What is the price of each book?
(A) 4 and 3
(B) 1 and 6
(C) 2 and 5
(D) None
(E) Cannot be determined
Rationale: Solution:
Let x be the price of the math book and y be the price of the physics book
x + y = 7
3000 × x + 1000 × y = 11000
Use x + y = 7 to solve for y
x - x + y = 7 - x
y = 7 - x
Substitute 7 - x for y in 3000 × x + 1000 × y = 11000
3000 × x + 1000 × (7 - x) = 11000
3000x + 7000 - 1000x = 11000
2000x = 11000 - 7000
2000x = 4000
x = 2 since 2000 × 2 = 4000
Since 2 + 5 = 7, y = 5
The price of a math book is 2 dollars and the price of a physics book is 5 dollars.
Answer C
Answer: (C) 2 and 5
Question: Find the value of x: 2x² − 4.
(A) 0,2
(B) -2,2
(C) -2,1
(D) 0,4
(E) -1,4
Rationale: That quadratic is factored as follows:2x² − 4 = (2x − 2)(x + 2).Now, it is easy to see that the second factor will be 0 when x = −2.As for the value of x that will make2x − 4	=	0,we must solve that equation We have:2x	=	4x = 2The solutions are:x	=	-2 and 2 B
Answer: (B) -2,2
Question: A group of hikers is planning a trip that will take them up a mountain using one route and back down using another route. They plan to travel down the mountain at a rate of one and a half times the rate they will use on the way up, but the time each route will take is the same. If they will go up the mountain at a rate of 7 miles per day and it will take them two days, how many miles long is the route down the mountain?
(A) 18
(B) 19
(C) 20
(D) 21
(E) 22
Rationale: On the way down, the rate is 1.5*7 = 10.5 miles per day.
The distance of the route down the mountain is 2*10.5 = 21 miles.
The answer is D.
Answer: (D) 21
Question: A can do a work in 3 days. B can do the same work in 6 days. If both A & B are working together in how many days they will finish the work?
(A) 3
(B) 5
(C) 4
(D) 2
(E) 6
Rationale: A rate = 1/3
B rate = 1/6
(A+B) rate = (1/3)+(1/6) = 1/2
A & B finish the work in 2days
correct option is D
Answer: (D) 2
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is?
(A) 30 years
(B) 35 years
(C) 40 years
(D) 50 years
(E) 55 years
Rationale: Sum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years.
Sum of the present ages of wife and child = (20 x 2 + 5 x 2) years = 50 years.
Husband's present age = (90 - 50) years = 40 years.
C)
Answer: (C) 40 years
Question: A rectangular table seats 3 people on each of two sides, with every person directly facing another person across the table. If six people choose their seats at random, what is probability that any two of them directly face other?
(A) 1/5
(B) 1/8
(C) 1/7
(D) 15/56
(E) 4/7
Rationale: A B C
------------
| TABLE |
------------
D E F
A to F are 6 people.
Prob to select any 1 person = 1
Prob to select the person opposite to the chosen person = 1/5
For ex. If we select A as the person than prob of choosing D is 1/5.
Hence, answer will be A.
Answer: (A) 1/5
Question: If a store adds 20 chairs to its current inventory, the total number of chairs will be the same as three-halves the current inventory of chairs. If the manager wants to increase the current inventory by 50%, what will the new inventory of chairs be?
(A) 40
(B) 60
(C) 100
(D) 140
(E) 160
Rationale: Explanation:
Letâ€™s say t = total current inventory of chairs. The first sentence states that 20 + t = (3/2)t. First solve for the current inventory:
20 + t = (3/2)t
20 = (3/2)t âˆ’ t
20 = (1/2)t
40 = t
The manager wants to increase this by 50%.
50% of 40 is 20, so the new inventory will be 60.
Answer: B
Answer: (B) 60
Question: Tough and Tricky questions: Statistics.
Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer Q represents the product of all elements in set X and if 11Q is an even number, what is the range of set X?
(A)  14
(B)  16
(C)  17
(D)  20
(E)  26
Rationale: Since 11Q = Even therefore Q has to beEVENsince 11 is a odd integer (Even * Odd = Even)
Similarly, Q is the product of all integers in set X But all integers in Set X are odd except the unknown K and since X contains only prime numbers, K has to equal to 2... ( 2 is the only even prime number and the product of all prime numbers in set X has to be Even, Even * Odd = Even)
Since you know value of K you can calculate the range = Largest integer in the set minus Smallest integer in the set = 19-2 =17
Answer is C
Answer: (C)  17
Question: What will be the compound interest on a sum of Rs. 22,000 after 3 years at the rate of 12% p.a.?
(A) Rs. 8908.42
(B) Rs. 9720
(C) Rs. 10123.20
(D) Rs. 10483.20
(E) None
Rationale: Amount = [22000 * (1 + 12/100)3]
= 22000 * 28/25 * 28/25 * 28/25 = Rs. 30908.42
C.I. = (30908.42 - 22000) = Rs. 8908.42
ANSWER:A
Answer: (A) Rs. 8908.42
Question: If the least common multiple of 9, 10, 12,
and v is 540, which of the following
could be v?
(A) 18
(B) 24
(C) 27
(D) 36
(E) 45
Rationale: To begin, notice that 540 isn’t a multiple of 24, so you can rule out Choice (B). Now find
the least common multiple (LCM) of 9, 10, and 12. The LCM of 9 and 10 is 90, so the LCM of
9, 10, and 12 must be a multiple of 90. Here are the first six multiples of 90:
90, 180, 270, 360, 450, 540
The number 180 is a multiple of 12 as well, so the LCM of 9, 10, and 12 is 180. However, 180
also is a multiple of 18, 36, and 45. So if any of these numbers were v, the LCM of 9, 10, 12,
and v would be 180. As a result, you can rule out Choices (A), (D), and (E), leaving Choice(C) as your only answer.
Answer: (C) 27
Question: A and B started a partnership business investing Rs. 20,000 and Rs. 15,000 respectively. C joined them with Rs. 20,000 after six months. Calculate B's share in total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
(A) 6500
(B) 2500
(C) 5000
(D) 10000
(E) 7500
Rationale: A : B : C
=20000×24:15000×24:20000×18
=20×4:15×4:20×3
=4×4:3×4:4×3
=4:3:3
B's share = 25000×(3/10)=7500
Answer is E.
Answer: (E) 7500
Question: The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.20 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
(A) 399
(B) 272
(C) 799.2
(D) 277
(E) 311
Rationale: Answer: Option C
Explanation:
a2 = 3136 => a = 56
56 * 4 * 3 = 672 â€“ 6 = 666 * 1.2 = 799.2 Answer: C
Answer: (C) 799.2
Question: Bill’s compact disc player randomly plays a song, so that no song is repeated before the entire album is played. If Bill plays a disc with 17 songs, what are the chances that the third song he hears will be his favorite?
(A) 1/17
(B) 1/12
(C) 1/11
(D) 3/14
(E) 1/3
Rationale: The player plays the songs on the album at random, so there are 17 songs that can be the third one played. Only 1 of these ways will result in Bill's favorite song being the third one played.
Total outcomes ==> 17
Total positive outcomes ==> 1
Correct answer is A) 1/17
Answer: (A) 1/17
Question: If x, y, and z are positive integers such that x^2 + y^2 + z^2 = 64,470, which of the following could be the values of x, y, and z?
I)x=541 y=401 z=100
II)x=530 y=400 z=100
III)X=501 y=300 z=200
(A) I only
(B) II only
(C) III only
(D) I​ and II
(E) I and III
Rationale: 10 sec answer if you know how to find the units digit of a number
The number given is of the form of square, so calculate the units digit - Here your objective is to find the sum where last digit is 0
x = 530, so x^2 will have units digit 0
y = 400, so y^2 will have units digit 0
z = 100, so z^2 will have units digit 0
Calculate the units digit , the units digit will be 0
Only option II will satisfy the condition , hence this will be our answer is option B.
Answer: (B) II only
Question: The division of a whole number N by 13 gives a quotient of 22 and a remainder of 2. Find N.
(A) 797
(B) 197
(C) 288
(D) 997
(E) 297
Rationale: According to the division process of whole numbers, N can be written, using multiplication, as follows
N = quotient *divisor + remainder = 22* 13 + 2 = 288 correc answer C
Answer: (C) 288
Question: The income of P and Q are in the ratio of 2 : 3 and their expenses are in the ratio of 3 : 5. If each of them saves Rs. 500, then the income of P is:
(A) Rs. 3000
(B) Rs. 2000
(C) Rs. 1500
(D) None of these
(E) Cannot be determined
Rationale: Let incomes for P and Q be = 2x, 3x
And their expenses be 2x-500, 3x-500
2x − 500/3x − =3/5
�solving X= Rs. 1000. So Income of P is Rs. 2000.
Answer:	B
Answer: (B) Rs. 2000
Question: To furnish a room in a model home an interior decorator is to select 2 chairs and 2 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 150 different combinations are possible, how many tables e are there in the warehouse?
(A) 6
(B) 8
(C) 10
(D) 15
(E) 30
Rationale: Total number of ways to choose 2 chairs from 5 e= 5C2=10
Total number of combination=150
That means we need get 15 combinations from the selection of tables....
Screening through the answers.... 6C2=15..... 15*10=150
Answer is 6... A
Answer: (A) 6