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.
Apr 24Get an Extra 30% Off Target Test Prep Plans
08:00 PM EDT
-11:59 PM EDT
Grab 30% off any Target Test Prep GRE plan during our Flash Sale and join Brian and many other students who have used Target Test Prep to score high on the GRE. Just enter the coupon code FLASH30 at checkout to save big.
Apr 26Get a Top GRE Score with Target Test Prep
12:00 PM EDT
-01:00 PM EDT
The Target Test Prep course represents a quantum leap forward in GRE preparation, a radical reinterpretation of the way that students should study. In fact, more and more Target Test Prep students are scoring 329 and above on the GRE.
If a and b are positive integers
[#permalink]
Updated on: 10 Sep 2018, 03:49
Updated on: 10 Sep 2018, 03:49
4
26
Bookmarks
00:00
Question Stats:
36% (01:49) correct
63% (02:01) wrong based on 160 sessions
Hide Show timer Statistics
If a and b are positive integers such that \(a-b\) and \(\frac{a}{b}\) are both even integers. Which of the following must be an odd integer?
A) \(\frac{a}{2}\)
B) \(\frac{b}{2}\)
C) \(\frac{a+b}{2}\)
D) \(\frac{a+2}{2}\)
E) \(\frac{b+2}{2}\)
A) \(\frac{a}{2}\)
B) \(\frac{b}{2}\)
C) \(\frac{a+b}{2}\)
D) \(\frac{a+2}{2}\)
E) \(\frac{b+2}{2}\)
Originally posted by AchyuthReddy on 09 Sep 2018, 21:20.
Last edited by Carcass on 10 Sep 2018, 03:49, edited 1 time in total.
Last edited by Carcass on 10 Sep 2018, 03:49, edited 1 time in total.
Formatted
Re: If a and b are positive integers
[#permalink]
10 Sep 2018, 08:20
10 Sep 2018, 08:20
8
Expert Reply
4
Bookmarks
\(a-b\) even --> either both even or both odd
\(\frac{a}{b}\) even --> either both even or \(a\) is even and \(b\) is odd.
As both statements are true --> \(a\) and \(b\) must be even.
As \(\frac{a}{b}\) is an even integer --> \(a\) must be multiple of 4.
Options A is always even.
Options B can be even or odd.
Options C can be even or odd.
Options D: \(\frac{a+2}{2}=\frac{a}{2}+1\), as \(a\) is multiple of \(4\), \(\frac{a}{2}\) is even integer --> even+1=odd. Hence option D is always odd.
Options E can be even, odd.
Answer: D.
Hope this helps. The answer is one and only.
Regards
\(\frac{a}{b}\) even --> either both even or \(a\) is even and \(b\) is odd.
As both statements are true --> \(a\) and \(b\) must be even.
As \(\frac{a}{b}\) is an even integer --> \(a\) must be multiple of 4.
Options A is always even.
Options B can be even or odd.
Options C can be even or odd.
Options D: \(\frac{a+2}{2}=\frac{a}{2}+1\), as \(a\) is multiple of \(4\), \(\frac{a}{2}\) is even integer --> even+1=odd. Hence option D is always odd.
Options E can be even, odd.
Answer: D.
Hope this helps. The answer is one and only.
Regards
General Discussion
Re: If a and b are positive integers
[#permalink]
10 Sep 2018, 06:23
10 Sep 2018, 06:23
2
The answers are D and E.
Since a-b = even and a/b = even, then both a and b are positive even integers.
We can rewrite D as a/2 + 2/2. a/2 will always be even, 2/2 = 1. Even+1 = Odd.
The same for E
Since a-b = even and a/b = even, then both a and b are positive even integers.
We can rewrite D as a/2 + 2/2. a/2 will always be even, 2/2 = 1. Even+1 = Odd.
The same for E
