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10 Jul 2007, 18:28
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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
(1) a^n=64
(2) n=6
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10 Jul 2007, 18:48
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1*2*3*4*5*6*7*8 = 1 * 2^7 * 3^2 * 5 * 7
a^n = x(1 * 2^7 * 3^2 * 5 * 7) where x is an integer
St1:
64 = x(1 * 2^7 * 3^2 * 5 * 7)
could be 2^6, 4^3..etc Insufficient.
St2:
a^6 = x(1 * 2^7 * 3^2 * 5 * 7)
Can only be a = 2. Sufficient.
Ans B
a^n = x(1 * 2^7 * 3^2 * 5 * 7) where x is an integer
St1:
64 = x(1 * 2^7 * 3^2 * 5 * 7)
could be 2^6, 4^3..etc Insufficient.
St2:
a^6 = x(1 * 2^7 * 3^2 * 5 * 7)
Can only be a = 2. Sufficient.
Ans B
