soni_pallavi wrote:Q1)If 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
Thanks
Explanation: a>1 and n > 1
1 * 2 * 3 * 4* 5* 6* 7* 8 = X( a ^ n)
=> 1 * (2 ^ 7 )* (3 ^ 2) * 5 * 7 = X ( a ^ n)
Statement 2: n = 6
1 * (2 ^ 7 )* (3 ^ 2) * 5 * 7 = X ( a ^ n) can be written as
1 * (2 ^ 7 )* (3 ^ 2) * 5 * 7 = X ( a ^ 6)
clearly, a should be 2 since no other number can have power 6 or more in the above expression.
we see power of 2 as 7 since this is a multiple of x (2 ^6).
Statement 2 is sufficient
statement 1: a^n = 64
This can be 2 ^6 or 4 ^3 or 8 ^2
so we can't conclude which among above is a^n.
Statement 1 is not sufficient.
Answer is (B).
PS: This is a classic example of "C TRAP" questions. If you take both statements together, you don't even need the question stem to answer. Whenever you see these type of questions, you can pretty much conclude answer is NOT 'c'.
