the integers a and n are greater than 1 and the product of the first 8 positive integers is a multiple of a^n, what is the value of a?
1) a^n=64
2) n=6
OA B
1) a^n=64
2) n=6
OA B
IMO B.
Product of first 8 integers can be expresses as 2^7 * 3 ^ 2 * 5 * 7
from Stmt 1, a ^ n = 64 ==> a and n can be pairs of (2,6) or (8,2). Hence insufficient.
From stmt 2, n = 6. Then a ^ n where n is 6 is possible is only when a = 2. Hence sufficient.
