q: If 100!/30^n is an integer, which of the following is the greatest possible value of n?
Options:
(A) 28
(B) 24
(C) 20
(D) 15
(E) 10
a: Stream of consciousness: 30^n = 2^n * 3^n * 5^n
100! has 97 2's, 48 3's and 24 5's
Since each of 2, 3 and 5 is required to form 30 and there are only 24 5's there can only be 24 30's in 100! The answer is (B).

question: The average amount with a group of seven numbers is Rs. 30. If the newly joined member has Rs. 75 with him, what was the average amount with the group before his joining the group?
Options:
(A) s. 25.6
(B) s. 45/2
(C) s. 16.6
(D) s. 26
(E) s. 25/2
answer: Stream of consciousness: Total members in the group = 7
Average amount = Rs. 30
Total amount with them = 7 * 30 = Rs. 210
One number has Rs. 50. So, the amount with remaining 6 people = 210 - 75 = Rs. 135
The average amount with them = 135/6 = Rs. 45/2 The answer is (B).

q: X can finish a work in 21 days. Y can finish the same work in 15 days. Yworked for 10 days and left the job. how many days does X alone need to finish the remaining work?
Options:
(A) 3
(B) 5
(C) 7
(D) 8
(E) 9
a: Stream of consciousness: Work done by X in 1 day = 1/21
Work done by Y in 1 day = 1/15
Work done by Y in 10 days = 10/15 = 2/3
Remaining work = 1 2/3 = 1/3
Number of days in which X can finish the remaining work = (1/3) / (1/21) = 7 The answer is (C).

question: If the three-digit number 5W2 is evenly divisible by 8, which of the following could be the digit W ?
Options:
(A) 5
(B) 4
(C) 3
(D) 2
(E) 1
answer: Stream of consciousness: Tried to locate a '0' ending multiple of 8 between 500599
Only 560 is present
560 is divisible by 8, so (560 - 8) is also divisible by 8 = 5 The answer is (A).

q: What is the sum of all the prime numbers greater than 10 but less than 40?
Options:
(A) 190
(B) 189
(C) 180
(D) 199
(E) 1981
a: Stream of consciousness: Required sum = (11 +13 + 17 + 19 + 23+ 29 + 31 + 37) = 180
Note: 1 is not a prime number The answer is (C).

q: Which is equal to 11?
Options:
(A) 1.1
(B) -11
(C) 11/11
(D) 11/1
(E) 1/11
a:
Stream of consciousness: 11/1 is equal to 11. The answer is (D).