Events & Promotions
|
|
GMAT 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.
May 0510:00 AM PDT
-11:00 AM PDT
GMAT Inequalities is a high-frequency topic in GMAT Quant, but many students struggle because the concepts behave differently from standard algebra. Understanding the right rules, patterns, and edge cases can significantly improve both speed and accuracy.- May 06
08:30 AM PDT
-09:30 AM PDT
In Episode 3 of our GMAT Ninja Critical Reasoning series, we tackle Discrepancy, Paradox, and Explain an Oddity questions. You know the feeling: the passage gives you two facts that seem completely contradictory.... - May 08
08:00 AM PDT
-08:30 AM PDT
Join the special YouTube live-stream for selecting the winners of GMAT Club MBA Scholarships sponsored by Juno live. Watch who gets these coveted MBA scholarships offered by GMAT Club and Juno.
16 Sep 2014, 00:22
Kudos
Bookmarks
If \(p\) and \(q\) are nonzero integers and \(n=\frac{p}{q}\), is \(n\) an integer?
(1) \(n^2\) is an integer.
(2) \(\frac{2n+4}{2}\) is an integer.
(1) \(n^2\) is an integer.
(2) \(\frac{2n+4}{2}\) is an integer.
16 Sep 2014, 00:22
Kudos
Bookmarks
Official Solution:
If \(p\) and \(q\) are nonzero integers and \(n=\frac{p}{q}\), is \(n\) an integer?
(1) \(n^2\) is an integer.
For \(n^2\) to be an integer, \(n\) must either be an integer or an irrational number such as \(\sqrt{3}\) (it's important to note that \(n\) cannot be a reduced fraction like \(\frac{2}{3}\) or \(\frac{11}{3}\) because in these cases \(n^2\) would not yield an integer). However, since \(n\) can be represented as the ratio of two integers (i.e., \(n=\frac{p}{q}\)), it cannot be an irrational number (by definition, an irrational number is any real number that cannot be expressed as a fraction \(\frac{a}{b}\), where \(a\) and \(b\) are integers). Consequently, the only remaining possibility is that \(n\) is an integer. This is sufficient.
(2) \(\frac{2n+4}{2}\) is an integer.
The above gives \(\frac{2n+4}{2}=n+2 =\text{integer}\). From this it follows that \(n\) must be an integer. Sufficient.
Answer: D
If \(p\) and \(q\) are nonzero integers and \(n=\frac{p}{q}\), is \(n\) an integer?
(1) \(n^2\) is an integer.
For \(n^2\) to be an integer, \(n\) must either be an integer or an irrational number such as \(\sqrt{3}\) (it's important to note that \(n\) cannot be a reduced fraction like \(\frac{2}{3}\) or \(\frac{11}{3}\) because in these cases \(n^2\) would not yield an integer). However, since \(n\) can be represented as the ratio of two integers (i.e., \(n=\frac{p}{q}\)), it cannot be an irrational number (by definition, an irrational number is any real number that cannot be expressed as a fraction \(\frac{a}{b}\), where \(a\) and \(b\) are integers). Consequently, the only remaining possibility is that \(n\) is an integer. This is sufficient.
(2) \(\frac{2n+4}{2}\) is an integer.
The above gives \(\frac{2n+4}{2}=n+2 =\text{integer}\). From this it follows that \(n\) must be an integer. Sufficient.
Answer: D
General Discussion
ENGRTOMBA2018
Joined: 20 Mar 2014
Last visit: 01 Dec 2021
Posts: 2,319
Given Kudos: 816
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
Products:
10 Jul 2015, 11:05
Kudos
Bookmarks
Bunuel
Good question. I was wondering why do we have n=P/Q with both p,q = non zero integers, but this information is useful to evaluate statement 1.
Per statement 1, \(n^2\) = integer. Now \(n^2=4\) or \(n^2 =2\) but \(n^2\)=not possible as this will give n = \(\sqrt{2}\) but as n=P/Q (ratio of integers), it can not be equal to \(\sqrt{2}\). For n = \(\sqrt{2}\) = \(\sqrt{2}/1\) ----> this means that P = \(\sqrt{2}\) and this will violate the information in the question that P is an integer. Thus this statement is sufficient.
Per statement 2, 2n+4 / 2 = integer ---> n+2 = integer ---> n = integer - 2 = another integer. Thus this statement is sufficient as well.
Thus D is the correct answer.
