Which one of the following is a prime number?
Options:
(A) 55
(B) 2
(C) 74
(D) 25
(E) 21

2 is divisible by 1 and itself So, it is a prime number. So the answer is: (B).

The edge of a cube is 2a cm. Find its surface?
Options:
(A) 24a8
(B) 24a4
(C) 24a1
(D) 24a2
(E) 24a7

6a2 = 6 * 2a * 2a = 24a2 So the answer is: (D).

In a is a positive integer smaller than 200 and (14a)/60 is an integer, then a has how many different positive prime factors?
Options:
(A) 2
(B) 3
(C) 5
(D) 6
(E) 8

7a/30 tells us that a is a factor of 30, which has 2, 3, and 5 as its prime factors. Each of them is distinct. Moreover, all multiples of 30 less than 200 can be derived by multiplying these prime factors alone. Thus, number of different prime factors is 3. So the answer is: (B).

A and B can do a work in 10 days and 15 days respectively. A starts the work and B joins him after 2 days. In how many days can they complete the remaining work?
Options:
(A) 6 days
(B) 2 days
(C) 4 4/5 days
(D) 3 days
(E) 9 days
Work done by A in 2 days = 2/10 = 1/5
Remaining work = 4/5
Work done by both A and B in one day = 1/10 + 1/15 = 5/30 = 1/6
Remaining work = 4/5 * 6/1 = 24/5 = 4 4/5 days. So the answer is: (C).