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.
Apr 2301:30 AM EDT
-02:30 AM EDT
Struggling with GMAT Verbal as a non-native speaker? Harsh improved his score from 595 to 695 in just 45 days—and scored a 99 %ile in Verbal (V88)! Learn how smart strategy, clarity, and guided prep helped him gain 100 points.
Apr 2212:30 AM EDT
-01:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
Apr 2308:00 PM PDT
-09:00 PM PDT
Video explanations + diagnosis of 10 weakest areas + 150+ short videos + study plan!
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
22 Mar 2010, 11:56
Kudos
Bookmarks
N
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
36% (01:56) correct
64%
(01:40)
wrong
based on 253
sessions
History
Date
Time
Result
Not Attempted Yet
If x is positive is x divisible by 2 ?
(1) x^3+x is divisible by 4
(2) 5x+4 is divisible by 6
(1) x^3+x is divisible by 4
(2) 5x+4 is divisible by 6
22 Mar 2010, 18:39
Kudos
Bookmarks
anaik100
I don't think that this is a GMAT question. In it's current form it's way beyond the GMAT scope.
First of all note that we are not told that \(x\) is an integer.
Given: \(x>0\). Question: is \(x\) even (integer)?
(1) \(x^3+x=x(x^2+1)=4n\)
If x is an integer then either:
A. \(x\) is a multiple of 4 and \(x^2+1\) is odd;
OR
B. \(x\) is odd and \(x^2+1\) is a multiple of 4. But this scenario is not possible. Why? Because in case \(x=2k+1\) (\(x\) is odd), \(x^2+1=4k^2+4k+2\), which is not a multiple of 4, (it's even never multiple of 4.)
So if \(x\) is an integer it must be multiple of 4.
But \(x\) also can be a non-integer, for example equation \(x^3+x=4\) has one real root (\(x\approx{1.38}\)), which is not an integer OR equation \(x^3+x=8\) also has one real root (\(x\approx{1.83}\)), which is not an integer.
Not sufficient.
(2) \(5x+4=6k\)
If \(x\) is an integer, then \(x\) must be even as \(5x+4=even\) --> \(5x=even-4=even\) --> \(x=even\).
But \(x\) can also be a fraction, for example \(\frac{2}{5}\), or \(\frac{8}{5}\) - basically \(x\) can be a fraction of a form \(x=\frac{a}{5}\), where \(a\) is an integer.
Not sufficient.
(1)+(2) Now if \(x\) is an integer then it's even as we concluded.
But can x be reduced fraction of a form \(x=\frac{a}{5}\)? We'll have \(\frac{a^3}{125}+\frac{a}{5}=4n\) --> \(a^3+25a=a(a^2+25)=500n\) --> as \(a\) and \(n\) are integers, \(a\) must be multiple of 5 (at least) --> hence \(x=\frac{a}{5}=integer\), so \(x\) can not be reduced fraction --> and if \(x\) is an integer, then we know it must be even.
Answer: C.
If we were told that \(x\) is an integer, then the answer would be D.
General Discussion
22 Mar 2010, 13:01
Kudos
Bookmarks
IMO B
A) x could be 2 or 3
B) x is 4, 10, 16 so it jumps every 6 numbers and even plus even equals even so x will always be even therefore divisible by 2. What's the OA?
A) x could be 2 or 3
B) x is 4, 10, 16 so it jumps every 6 numbers and even plus even equals even so x will always be even therefore divisible by 2. What's the OA?
