question:The H.C.F of two numbers is 23 and the other two factors of their L.C.M are 13 and 14. The larger of the two numbers is:
Options:
(A) 276
(B) 299
(C) 322
(D) 345
(E) 355
answer:(C)
Stream of consciousness:Clearly, the numbers are (23 * 13) and (23 * 14). Larger number = (23 * 14) = 322.

question:The average of 13 numbers is 59. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number?
Options:
(A) 59
(B) 83
(C) 45
(D) 53
(E) 64
answer:(A)
Stream of consciousness:Sum of all the 13 numbers = 13 * 59 = 767
Sum of the first 7 of them = 7 * 57 = 399
Sum of the last 7 of them = 7 * 61 = 427
So, the 8th number = 427 + 399 - 767 = 59.

question:What number comes next in the following series? 4, 14, 44, 134, 404, ____
Options:
(A) 1204
(B) 1208
(C) 1214
(D) 1216
(E) 1220
answer:
(C)
Stream of consciousness:4
4 3 + 2 = 14
14 3 + 2 = 44
44 3 + 2 = 134
134 3 + 2 = 404
404 3 + 2 = 1214