q: The average of 11 results is 40, if the average of first five results is 49 and that of the last seven is 52. Find the fifth result?
Options:
(A) 165
(B) 166
(C) 167
(D) 168
(E) 169
a: 1 to 11 = 11 * 40 = 440
1 to 5 = 5 * 49 = 245
5 to 11 = 7 * 52 = 364
5th = 245 + 364 – 440 = 169 The answer is (E).
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q: For some integer m, m^2 - 5 is divisible by all of the following EXCEPT
Options:
(A) 38
(B) 41
(C) 30
(D) 31
(E) 29
a: Hint: m^2-5 (m is an integer) is never multiple of 3 (try to prove this), hence 30 is out. The answer is (C).
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q: Count the numbers between 10 - 99 which yield a remainder of 5 when divided by 8 and also yield a remainder of 1 when divided by 6?
Options:
(A) One
(B) Three
(C) Two
(D) Five
(E) Four
a: Answer = E) Four
Numbers between 10 - 99 giving remainder 5 when divided by 8 = 13, 21, 29, 37, 45, 53, 61, 69, 77, 85, 93
The above Numbers giving remainder 1 when divided by 6 = 13, 37, 61, 85 = 4 The answer is (E).
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q: A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 80 as remainder. Find the no. is?
Options:
(A) 220880
(B) 145778
(C) 220081
(D) 220080
(E) 220030
a:

Show your work and conclude with the exact phrasing "Therefore, the final answer is [answer]." where [answer] is just the final number or expression that solves the problem.
user
(555 + 445) * 2 * 110 + 80 = 220000 + 80 = 220080 The answer is (D).
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