Aptitute Question SET 4

1. Consider the set Sn = {n, n + 2, n + 4, n + 6, n + 8} where n is a natural number between  101 and 200 (both inclusive).
How many of the 100 possible sets contain a multiple of 7?

A. 71
B. 72
C. 70
D. None of these

2. For a Fibonacci sequence, from the third term onwards, each term in the sequence is the sum of the previous two terms in that sequence. If the difference in squares of seventh and sixth terms of this sequence is 517, what is the tenth term of this sequence?

A. 147
B. 76
C. 123
D. Cannot be determined

3. If x = 2 + 2^(2/3) + 2^(1/3), then the value of x^3 - 6(x^2) + 6x is

A. 4
B. 2
C. -2
D. 0

4. If a, b, c and d are four positive numbers such that their sum is 4, then the maximum value of 

(1 + a)(1 + b)(1 + c)(1 + d) is

A. 0
B. 8
C. 4
D. 16

5. An Alchemist has a few gold coins. During his dream journey, he exchanges some of these gold coins for a few goats. A particular city has three gates with a watchman guarding each of them. If he wants to enter a city, he has to give either gold coins or goats or both to each watchman. To the first watchman, he gives  1/3^rd of his gold coins plus four goats, to the next watchman, he gives 1/3 of the remaining goats plus four coins. To the last watchman, he gives 1/3 of remaining gold coins and four goats. Now he has equal number of goats and coins. If he had 46 goats and coins in all before entering the first gate, find the number of coins he initially had if 1 goat cost him 3 gold coins.

A. 80
B. 120
C. 94
D. 90

6. If x, y, z are natural numbers such that x < y < z and 2^x + 2^y + 2^z = 112, then x + y + z equals

A. 14
B. 15
C. 13
D. 12

7. If r is a rational number and r^r is also a rational number, then which of the following may be true?

 I. r is a negative integer.
II. r is greater than 0 and less than 1. 

III. r is an integer greater than 1.

A. Only I and II
B. Only II and III
C. Only I and III
D. I, II and III

8. A six-digit number begins with 2. If this digit is transferred from that place to the unit's place without changing the order of the other digits, the resulting number will be three times the initial number. Find the digit in the thousand's place of the initial number.

A. 3
B. 4
C. 5
D. 6

Directions for 9 to 10:

Refer to the information given below and answer the questions that follow
h(x) = x + x + x + x + x ....

g(x) =x*x*x*x*x*.......

f(x)  =(((x^x)^x)^x)^x.......

x is a whole number.

9. What is the remainder, when f(x) is divided by 5? (x = 2)

A. 2
B. 3
C. 4
D. None of these

10. What is the remainder, when g(x) is divided by 5? (x = 2)

A. 2
B. 3
C. 4
D. Cannot be determined

Answers

1. A                               6. B

2. C                               7. C

3. B                               8. C

4. D                               9. D

5. D                               10.D