(Ans). (E)
(Question). For some integer x, x^2 - 5 is divisible by all of the following EXCEPT
Options:
(A) 41
(B) 38
(C) 29
(D) 31
(E) 30
(CoT). Hint: x^2-5 (x is an integer) is never multiple of 3 (try to prove this), hence 30 is out.

(Ans). (A)
(Question). A pharmaceutical company received $4 million in royalties on the first $50 million in sales of and then $12 million in royalties on the next $170 million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $50 million in sales to the next $170 million in sales?
Options:
(A) 12%
(B) 15%
(C) 45%
(D) 52%
(E) 56%
(CoT). (12/170)/(4/50) = 15/17 = 88% it means that 12/170 represents only 88%. Therefore a decrease of 12%.

(Ans). (B)
(Question). If a man walks to his office at 3/4 of his usual rate, he reaches office 1/3 of an hour later than usual. What is his usual time to reach office.
Options:
(A) 12 hr
(B) 1 hr
(C) 34 hr
(D) 2 hrs
(E) None of these
(CoT). If new speed is ab of original speed, then usual time (ba - 1) = change in time
usual time (43 - 1) = 13
usual time = 13 3 = 1 hr

(Ans). (C)
(Question).
The year next to 1991 having the same calendar as that of 1990 is
Options:
(A) 1998
(B) 2001
(C) 2002
(D) 2003
(E) None of these
(CoT). We go on counting the odd days from 1991 onward still the sum is divisible by 7. The number of such days are 14 upto the year 2001. So, the calender for 1991 will be repeated in the year 2002.