GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
N is a positive odd integer.
[#permalink]
04 Aug 2024, 22:52
04 Aug 2024, 22:52
Expert Reply
00:00
Question Stats:
73% (00:50) correct
26% (00:53) wrong based on 15 sessions
Hide Show timer Statistics
N is a positive odd integer.
Quantity A |
Quantity B |
Number of positive odd integers less than N |
\(\frac{N-1}{2 }\) |
Part of the project: GRE Quant & Verbal ADVANCED Daily Challenge 2024 Edition - Gain 20 Kudos & Get FREE Access to GRE Prep Club TESTS
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Free Materials for the GRE General Exam - Where to get it!!
Shorter GRE - Preparing for the Quantitative Reasoning Measure
Shorter GRE - Preparing for the Verbal Reasoning Measure
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Free Materials for the GRE General Exam - Where to get it!!
Shorter GRE - Preparing for the Quantitative Reasoning Measure
Shorter GRE - Preparing for the Verbal Reasoning Measure
Re: N is a positive odd integer.
[#permalink]
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.
[#permalink]
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).
