Can n /192 be an integer?
(1) n is a multiple of 24 but not 16.
(2) n is a multiple of 8 but not 48.
OA D
(1) n is a multiple of 24 but not 16.
(2) n is a multiple of 8 but not 48.
OA D
192 ƒ = 2^6 x 3jack0997 wrote:Can n /192 be an integer?
(1) n is a multiple of 24 but not 16.
(2) n is a multiple of 8 but not 48.
OA D
Thus, n/192 can be an integer only if n is divisible by 2^6 and by 3.
The exponent of '2' must be 6 or greater and exponent of '3' must be 1 or greater.
Statement 1:
n is a multiple of 24, i.e. 2^3 x 3 =ƒ> n is divisible by 2^3 and by 3.
n is not a multiple of 16, i.e. 2^4 ƒ=> n is not divisible by 2^4 (Maximum exponent of '2' is NOT 6.)
ƒ=> n is not divisible by 192.
Thus, n/192 cannot be an integer. - Sufficient
Statement 2:
n is a multiple of 8, i.e. 2^3 =ƒ> n is divisible by 2^3.
n is not a multiple of 48, i.e. 2^4 x 3.
Thus, there might be two possibilities:
1. Since n is not a multiple of 48, it is not a multiple 3; hence, it is definitely not a
multiple of 192.
2. The highest exponent of 2 by which n is divisible is 3, i.e. n is divisible by 2^3, but
not by 2^6, hence, it is definitely not a multiple of 192.
Thus, n/192 cannot be an integer. - Sufficient
The correct answer: D
Hope this helps!
Relevant book: Manhattan Review GMAT Data Sufficiency Guide
-Jay
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