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 2512:30 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 2601:30 AM EDT
-02:30 AM EDT
Learn how Keshav, a Chartered Accountant, scored an impressive 705 on GMAT in just 30 days with GMATWhiz's expert guidance. In this video, he shares preparation tips and strategies that worked for him, including the mock, time management, and more.
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.
May 0111:00 AM PDT
-12:00 PM PDT
Free- full-length test + 15 concept videos + 150+ short videos + study plan!
18 Feb 2012, 06:08
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
43% (02:30) correct
57%
(02:03)
wrong
based on 129
sessions
History
Date
Time
Result
Not Attempted Yet
If y is a positive integer, is y^2 - y divisible by 4 ?
(1) y^2 + y is not divisible by 4
(2) y^3 - y is divisible by 4
(1) y^2 + y is not divisible by 4
(2) y^3 - y is divisible by 4
18 Feb 2012, 07:27
Kudos
Bookmarks
Interesting question. Kudos to you. Very simple explanation though 
Question: If \(y\) is a positive integer , is \(y^2 - y\) divisible by \(4\)?
Lets factor \(y^2 - y\):
\(y^2-y=y*(y-1)\)
So we know that these are two consecutive integers, so one of them has to be odd and one of them is even. Which means only one of them can be a multiple of \(4\). So we need to establish that either \(y\) is a multiple of \(4\) or \((y-1)\) is a multiple of \(4\).
Statement A: \(y^2 + y\) is not divisible by \(4\)
Lets factor this one out : \(y^2+y=y*(y+1)\)
These again are consecutive integers and the statement says that niether of them is a factor of \(4\). Remember our original conditions. either \(y\) is a multiple of \(4\) or \((y-1)\) is a multiple of \(4\). This statement tells us that \(y\) is not a multiple of \(4\) but it does not tell us whether \((y-1)\) is a multiple of \(4\) or not. Also note that this again does not tell us whether \(y\) is even or \((y-1)\) is even.So Insufficient.
Statement B: \(y^3-y\) is divisible by \(4\)
Lets factor this one out : \(y^3-y=y*(y-1)*(y+1)\) and again these are \(3\) consecutive integers. The only thing we have found out (from the statement) is that one of them is definitely a multiple of \(4\) but we do not know which one it is. Also note that we are not sure that one of them is even or two of them are even. And if it is one even, it could be \(2\) so it is still not sufficient. We need at-least \(2\) multiples of \(2\) in there. If there were \(2\) even numbers, we would be sure that it is divisible by \(4\). So Insufficient
Combined:
We know that \(y\) and \((y+1)\) are not multiples of \(4\) from the first statement so from our second statement combined we have found out that \((y-1)\) is then, logically speaking, a multiple of \(4\) and since \((y-1)\) is one of our original factors from the question stem, the answer is YES. \(y^2-1\) whose factors are \(y*(y-1)\) is divisible by \(4\) because of the presence of \((y-1)\) as a factor. A Kudos won't hurt here!
Answer C
Question: If \(y\) is a positive integer , is \(y^2 - y\) divisible by \(4\)?
Lets factor \(y^2 - y\):
\(y^2-y=y*(y-1)\)
So we know that these are two consecutive integers, so one of them has to be odd and one of them is even. Which means only one of them can be a multiple of \(4\). So we need to establish that either \(y\) is a multiple of \(4\) or \((y-1)\) is a multiple of \(4\).
Statement A: \(y^2 + y\) is not divisible by \(4\)
Lets factor this one out : \(y^2+y=y*(y+1)\)
These again are consecutive integers and the statement says that niether of them is a factor of \(4\). Remember our original conditions. either \(y\) is a multiple of \(4\) or \((y-1)\) is a multiple of \(4\). This statement tells us that \(y\) is not a multiple of \(4\) but it does not tell us whether \((y-1)\) is a multiple of \(4\) or not. Also note that this again does not tell us whether \(y\) is even or \((y-1)\) is even.So Insufficient.
Statement B: \(y^3-y\) is divisible by \(4\)
Lets factor this one out : \(y^3-y=y*(y-1)*(y+1)\) and again these are \(3\) consecutive integers. The only thing we have found out (from the statement) is that one of them is definitely a multiple of \(4\) but we do not know which one it is. Also note that we are not sure that one of them is even or two of them are even. And if it is one even, it could be \(2\) so it is still not sufficient. We need at-least \(2\) multiples of \(2\) in there. If there were \(2\) even numbers, we would be sure that it is divisible by \(4\). So Insufficient
Combined:
We know that \(y\) and \((y+1)\) are not multiples of \(4\) from the first statement so from our second statement combined we have found out that \((y-1)\) is then, logically speaking, a multiple of \(4\) and since \((y-1)\) is one of our original factors from the question stem, the answer is YES. \(y^2-1\) whose factors are \(y*(y-1)\) is divisible by \(4\) because of the presence of \((y-1)\) as a factor. A Kudos won't hurt here!
Answer C
General Discussion
18 Feb 2012, 14:04
Kudos
Bookmarks
If y is a positive integer , is y^2 - y divisible by 4
y > 0
is y (y - 1) divisible by 4 ?
1. y^2 + y is not divisible by 4
y (y+1) is not divisible by 4
Not sufficient.
2. y^3 - y is divisible by 4
y (y-1) (y+1) is divisible by 4
Not sufficient.
1 + 2
(y - 1) is divisible by 4.
Hence, y (y - 1) is divisible by 4. Sufficient.
y > 0
is y (y - 1) divisible by 4 ?
1. y^2 + y is not divisible by 4
y (y+1) is not divisible by 4
Not sufficient.
2. y^3 - y is divisible by 4
y (y-1) (y+1) is divisible by 4
Not sufficient.
1 + 2
(y - 1) is divisible by 4.
Hence, y (y - 1) is divisible by 4. Sufficient.
