If n is a positive integer and r is the remainder when n^2 - 1 is divided by 8, what is the value of r?
(1) n is odd
(2) n is not divisible by 8
OA A
Source: Manhattan Prep
If n is a positive integer and r is the remainder when
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What is the remainder when (n+1)(n-1) is divided by 8?BTGmoderatorDC wrote:If n is a positive integer and r is the remainder when n^2 - 1 is divided by 8, what is the value of r?
(1) n is odd
(2) n is not divisible by 8
Statement 1:
Since n is odd, both n-1 and n+1 are EVEN, implying that (n-1)(n+1) = the product of two consecutive even integers.
Given any two consecutive even integers, one will be a multiple of 4, while the other will be an even non-multiple of 4.
Since (multiple of 4)(even) = (multiple of 8), the product of any two consecutive integers will always be a multiple of 8.
Thus, when (n-1)(n+1) is divided by 8, the remainder will be 0.
SUFFICIENT.
Statement 2:
If n=1, then (n²-1)/8 = 0/8 = 0 R0.
If n=2, then (n²-1)/8 = 3/8 = 0 R3.
Since the remainder can be different values, INSUFFICIENT.
The correct answer is A.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
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