BTGmoderatorLU wrote:Source: GMAT Prep
If \(n\) is a positive integer and \(r\) is the remainder when \((n-1)(n+1)\) is divided by \(24\), what is the value of \(r\)?
1) \(n\) is not divisible by \(2\).
2) \(n\) is not divisible by \(3\).
The OA is C
Let's take each statement one by one.
1) \(n\) is not divisible by \(2\).
Case 1: Say n = 1
\((n-1)(n+1)\) = 0. We see that 0 divided by 24 leaves a remainder 0. Thus, r = 0.
Case 1: Say n = 3
\((n-1)(n+1)\) = 2*4 = 8. We see that 8 divided by 24 leaves a remainder 8. Thus, r = 8.
No unique answer. Insufficient.
2) \(n\) is not divisible by \(3\).
Case 1: Say n = 1
\((n-1)(n+1)\) = 0. We see that 0 divided by 24 leaves a remainder 0. Thus, r = 0.
Case 1: Say n = 2
\((n-1)(n+1)\) = 1*3 = 3. We see that 3 divided by 24 leaves a remainder 3. Thus, r = 3.
No unique answer. Insufficient.
(1) and (2) together
From (1) and (2), we have n = 1, 5, 7, 11, and other prime numbers
Case 1: Say n = 1
\((n-1)(n+1)\) = 0. We see that 0 divided by 24 leaves a remainder 0. Thus, r = 0.
Case 2: Say n = 5
\((n-1)(n+1)\) = 4*6. We see that 24 divided by 24 leaves a remainder 0. Thus, r = 0.
Case 3: Say n = 7
\((n-1)(n+1)\) = 6*8. We see that 48 divided by 24 leaves a remainder 0. Thus, r = 0.
Case 4: Say n = 11
\((n-1)(n+1)\) = 10*12. We see that 120 divided by 24 leaves a remainder 0. Thus, r = 0.
So, in each case, we get the remainder 0. Sufficient.
The correct answer:
C
Hope this helps!
-Jay
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