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N is a positive odd integer.
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04 Aug 2024, 22:52
04 Aug 2024, 22:52
Expert Reply
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Question Stats:
81% (00:50) correct
18% (00:53) wrong based on 22 sessions
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N is a positive odd integer.
Quantity A |
Quantity B |
Number of positive odd integers less than N |
\(\frac{N-1}{2 }\) |
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Shorter GRE - Preparing for the Quantitative Reasoning Measure
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Re: N is a positive odd integer.
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09 Dec 2024, 11:01
09 Dec 2024, 11:01
Expert Reply
We know $\(N\)$ is a positive integer; we need to compare the remainder when $\(\left(N^2-N\right)\)$ is divided by 2 with 0 .
The given expression $\(\left(\mathrm{N}^2-\mathrm{N}\right)=\mathrm{N}(\mathrm{N}-1)\)$ is a product of two consecutive positive integers, which must be divisible by 2 . So, the remainder when $\(\left(N^2-N\right)\)$ is divided by 2 must be 0 .
(Note: - Product of n consecutive positive integers is divisible by $\(n!\)$ )
Hence column A quantity equals column B quantity, so the answer is (C).
The given expression $\(\left(\mathrm{N}^2-\mathrm{N}\right)=\mathrm{N}(\mathrm{N}-1)\)$ is a product of two consecutive positive integers, which must be divisible by 2 . So, the remainder when $\(\left(N^2-N\right)\)$ is divided by 2 must be 0 .
(Note: - Product of n consecutive positive integers is divisible by $\(n!\)$ )
Hence column A quantity equals column B quantity, so the answer is (C).
Re: N is a positive odd integer.
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17 Dec 2024, 06:40
17 Dec 2024, 06:40
1
N could potentially be 3,5,7,9...
for N=3, QA is 0 and QB is (3-1)/2=1.
for N=5, QA is 1 (so n.3 from above) and QB is (5-1)/2=2. This is true for all values of N. Then why is it not B (QB is larger every time).
for N=3, QA is 0 and QB is (3-1)/2=1.
for N=5, QA is 1 (so n.3 from above) and QB is (5-1)/2=2. This is true for all values of N. Then why is it not B (QB is larger every time).
