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
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the integers a and n
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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.
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.
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cramya
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product of the first 8 positive integers is a multiple of a^n, what is the value of a
a^n * some integer K = 1 * 2 * 3 * 4 *5 *6*7*8
Break 1 * 2 * 3 * 4 *5 *6*7*8 in to prime factors
1 * 2 * 3 * 2 * 2 * 5* 2 * 3 * 2 * 2 * 2
Stmt I
a^n=64
4 and 2 both satisfy this condition for a for different values of n and k
INSUFF
Stmt II
n=6
Only 2 fits the bill.
SUFF
Choose B
a^n * some integer K = 1 * 2 * 3 * 4 *5 *6*7*8
Break 1 * 2 * 3 * 4 *5 *6*7*8 in to prime factors
1 * 2 * 3 * 2 * 2 * 5* 2 * 3 * 2 * 2 * 2
Stmt I
a^n=64
4 and 2 both satisfy this condition for a for different values of n and k
INSUFF
Stmt II
n=6
Only 2 fits the bill.
SUFF
Choose B
