GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 18 Jul 2018, 03:52

Close

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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If y is an integer, is y^2 divisible by 4?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

1 KUDOS received
Intern
Intern
avatar
Joined: 18 Jan 2012
Posts: 22
If y is an integer, is y^2 divisible by 4? [#permalink]

Show Tags

New post Updated on: 08 Feb 2012, 02:16
1
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

75% (00:30) correct 25% (00:40) wrong based on 91 sessions

HideShow timer Statistics

If y is an integer, is y^2 divisible by 4?

(1) y is divisible by 4
(2) y is divisible by 6

Originally posted by nimc2012 on 07 Feb 2012, 20:41.
Last edited by Bunuel on 08 Feb 2012, 02:16, edited 1 time in total.
Edited the question
Expert Post
1 KUDOS received
Magoosh GMAT Instructor
User avatar
G
Joined: 28 Dec 2011
Posts: 4667
Re: Number Properties - Question 2 [#permalink]

Show Tags

New post 07 Feb 2012, 23:09
1
Hi, there. I'm happy to help with this.

Prompt: if y is an integer , is y^2 divisible by 4?

Fact #1: In order for an integer N to be divisible by 4, N must have at least two factors of 2 in its prime factorization.

Fact #2: When you square a number, say T^2, whatever prime factors are in the prime factorization of T are doubled in the prime factorization of T^2. Say a particular prime factor appears three times in T --- then it will appear six times in T^2.

Fact #3: An even number, by definition, has at least one factor of 2 in its prime factorization.

Therefore, the square of any even number will have at least two factors of 2, and therefore will be divisible by 4.

The question "is y^2 divisible by 4?" is entirely equivalent to the question "is y an even integer?"

All of that was the mathematical heavy-lifting for the question. Now, the statements will be a piece of cake.

Statement #1: y is divisible by 4. Therefore y is even. Sufficient.

Statement #2: y is divisible by 6. Therefore y is even. Sufficient.

Both statements sufficient. Answer = D

Does all that make sense?

Here's another odd/even DS question for practice.

http://gmat.magoosh.com/questions/868

Please let me know if you have any questions.

Mike :)
_________________

Mike McGarry
Magoosh Test Prep

Image

Image

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47071
Re: Number Properties - Question 2 [#permalink]

Show Tags

New post 08 Feb 2012, 02:16
If y is an integer, is y^2 divisible by 4?

(1) y is divisible by 4 --> as y itself is divisible by 4 then y^2 will also be divisible by 4. Sufficient.
(2) y is divisible by 6 --> y=6k, for some integer k --> y^2=36k^2=4*(9k^2) --> we can see that y^2 has 4 as a factor hence it is divisible by 4. Sufficient.

Answer: D.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Expert Post
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 5839
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
If y is an integer, is y^2 divisible by 4? [#permalink]

Show Tags

New post 26 Nov 2017, 11:28
nimc2012 wrote:
If y is an integer, is y^2 divisible by 4?

(1) y is divisible by 4
(2) y is divisible by 6


Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variables and 0 equation, we need to consider each condition one by one.

Condition 1)
\(y = 4n\) for some integer \(n\).
\(y^2 = 16n^2\)
Since \(16\) is divisible by \(4\), this is sufficient.

Condition 2)
\(y = 4m\) for some integer \(m\).
\(y^2 = 36m^2\)
Since \(36\) is divisible by \(4\), this is sufficient.

Therefore, the answer is D.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

If y is an integer, is y^2 divisible by 4?   [#permalink] 26 Nov 2017, 11:28
Display posts from previous: Sort by

If y is an integer, is y^2 divisible by 4?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.