GMAT Changed on April 16th - Read about the latest changes here

It is currently 25 Apr 2018, 07:42

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If k is an even integer, what is the smallest possible value of k

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

Hide Tags

4 KUDOS received
BSchool Forum Moderator
User avatar
D
Joined: 12 Aug 2015
Posts: 2583
GRE 1: 323 Q169 V154
GMAT ToolKit User Premium Member
If k is an even integer, what is the smallest possible value of k [#permalink]

Show Tags

New post 04 Nov 2016, 09:01
4
This post received
KUDOS
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

37% (01:14) correct 63% (00:52) wrong based on 179 sessions

HideShow timer Statistics

If k is a positive even integer, what is the smallest possible value of k such that 3675*k is the square of an integer?

A.3
B.9
C.12
D.15
E.20
[Reveal] Spoiler: OA

_________________


Getting into HOLLYWOOD with an MBA

The MOST AFFORDABLE MBA programs!

STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)

Average GRE Scores At The Top Business Schools!

2 KUDOS received
Manager
Manager
avatar
Joined: 28 Jun 2016
Posts: 207
Location: Canada
Concentration: Operations, Entrepreneurship
Re: If k is an even integer, what is the smallest possible value of k [#permalink]

Show Tags

New post 04 Nov 2016, 11:25
2
This post received
KUDOS
1
This post was
BOOKMARKED
stonecold wrote:
If k is an even integer, what is the smallest possible value of k such that 3675*k is the square of an integer?

A.3
B.9
C.12
D.15
E.20


3675*k= 7^2*5^2*3*k

Since k is even and the integer should be a square.

k=2^2*3=12

C


Sent from my iPhone using GMAT Club Forum mobile app
Expert Post
1 KUDOS received
Target Test Prep Representative
User avatar
G
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2464
Location: United States (CA)
Re: If k is an even integer, what is the smallest possible value of k [#permalink]

Show Tags

New post 07 Nov 2016, 11:50
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
stonecold wrote:
If k is an even integer, what is the smallest possible value of k such that 3675*k is the square of an integer?

A.3
B.9
C.12
D.15
E.20


If 3675*k is a perfect square, then its prime factorization must contain only even exponents. Let’s begin by prime factoring 3,675.

3675 = 25 x 147 = 5 x 5 x 49 x 3 = 5 x 5 x 7 x 7 x 3 = 5^2 x 7^2 x 3^1

We can see that 3,675 is not a perfect square because its prime factorization contains an odd exponent (that is, 3^1). If k only has to be an integer, then the smallest value k can be is 3, since 3675*k would be 5^2 x 7^2 x 3^2, a perfect square. However, since the requirement is that k must be an even integer, we need k to be divisible by an even perfect square (notice that 3675 doesn’t have any even prime factors). Since the smallest even perfect square is 2^2 = 4, the smallest possible value of k is 3 x 4 = 12, so that 3,675*k is a perfect square.
In fact, if k = 12, then 3,675*k = 5^2 x 7^2 x 3^2 x 2^2, which is a perfect square.

[Note: The smallest possible value of k such that 3675*k is the square of an integer is actually 0, since 3675*0 = 0, which is 0^2. To avoid this case, the problem should be stated as “If k is a positive even integer…such that 3675*k is the square of a positive integer?”]

Answer: C
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

BSchool Forum Moderator
User avatar
D
Joined: 12 Aug 2015
Posts: 2583
GRE 1: 323 Q169 V154
GMAT ToolKit User Premium Member
Re: If k is an even integer, what is the smallest possible value of k [#permalink]

Show Tags

New post 07 Nov 2016, 12:42
ScottTargetTestPrep wrote:
stonecold wrote:
If k is an even integer, what is the smallest possible value of k such that 3675*k is the square of an integer?

A.3
B.9
C.12
D.15
E.20


If 3675*k is a perfect square, then its prime factorization must contain only even exponents. Let’s begin by prime factoring 3,675.

3675 = 25 x 147 = 5 x 5 x 49 x 3 = 5 x 5 x 7 x 7 x 3 = 5^2 x 7^2 x 3^1

We can see that 3,675 is not a perfect square because its prime factorization contains an odd exponent (that is, 3^1). If k only has to be an integer, then the smallest value k can be is 3, since 3675*k would be 5^2 x 7^2 x 3^2, a perfect square. However, since the requirement is that k must be an even integer, we need k to be divisible by an even perfect square (notice that 3675 doesn’t have any even prime factors). Since the smallest even perfect square is 2^2 = 4, the smallest possible value of k is 3 x 4 = 12, so that 3,675*k is a perfect square.
In fact, if k = 12, then 3,675*k = 5^2 x 7^2 x 3^2 x 2^2, which is a perfect square.

[Note: The smallest possible value of k such that 3675*k is the square of an integer is actually 0, since 3675*0 = 0, which is 0^2. To avoid this case, the problem should be stated as “If k is a positive even integer…such that 3675*k is the square of a positive integer?”]

Answer: C



Absolutely Spot On.!!
P.S=> Edited the Question.
_________________


Getting into HOLLYWOOD with an MBA

The MOST AFFORDABLE MBA programs!

STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)

Average GRE Scores At The Top Business Schools!

Board of Directors
User avatar
G
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3400
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member
Re: If k is an even integer, what is the smallest possible value of k [#permalink]

Show Tags

New post 07 Nov 2016, 13:07
stonecold wrote:
If k is a positive even integer, what is the smallest possible value of k such that 3675*k is the square of an integer?

A.3
B.9
C.12
D.15
E.20


\(3675 = 3^1 * 5^2 * 7^2\)

Now , is the most important part of this question

K must be even ( negate options A, B and D ) W e are left with C and E

Try one to confirm the answer...

Let's try (E)

\(20 = 2^2 * 5^1\)

\(3675*20 = 2^2 * 3^1 * 5^3 * 7^2\) ( Can not square of an Integer )

So, Answer must be (C)....

Double check to be sure -

\(3675*12 = 2^2 * 3^2 * 5^2 * 7^2\) (Square of an Integer )

Hope this helps !!


_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

BSchool Forum Moderator
User avatar
D
Joined: 12 Aug 2015
Posts: 2583
GRE 1: 323 Q169 V154
GMAT ToolKit User Premium Member
Re: If k is an even integer, what is the smallest possible value of k [#permalink]

Show Tags

New post 07 Nov 2016, 13:10
Abhishek009 wrote:
stonecold wrote:
If k is a positive even integer, what is the smallest possible value of k such that 3675*k is the square of an integer?

A.3
B.9
C.12
D.15
E.20


\(3675 = 3^1 * 5^2 * 7^2\)

Now , is the most important part of this question

K must be even ( negate options A, B and D ) W e are left with C and E

Try one to confirm the answer...

Let's try (E)

\(20 = 2^2 * 5^1\)

\(3675*20 = 2^2 * 3^1 * 5^3 * 7^2\) ( Can not square of an Integer )

So, Answer must be (C)....

Double check to be sure -

\(3675*12 = 2^2 * 3^2 * 5^2 * 7^2\) (Square of an Integer )

Hope this helps !!




You didn't fall for it this time :twisted: :twisted:

Great :)
_________________


Getting into HOLLYWOOD with an MBA

The MOST AFFORDABLE MBA programs!

STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)

Average GRE Scores At The Top Business Schools!

1 KUDOS received
Intern
Intern
User avatar
S
Status: I am not giving up. Not yet.
Joined: 23 Jul 2015
Posts: 46
GMAT ToolKit User Premium Member
Re: If k is an even integer, what is the smallest possible value of k [#permalink]

Show Tags

New post 14 Nov 2016, 15:25
1
This post received
KUDOS
stonecold wrote:
If k is a positive even integer, what is the smallest possible value of k such that 3675*k is the square of an integer?

A.3
B.9
C.12
D.15
E.20



I feel like killing myself for choosing A.
If k is a positive even integer
:x :x EVEN digit...grrr.... :x :x :x
_________________

Cheers
PeeKay

Director
Director
avatar
G
Joined: 07 Dec 2014
Posts: 965
If k is an even integer, what is the smallest possible value of k [#permalink]

Show Tags

New post 10 Jan 2017, 10:29
stonecold wrote:
If k is a positive even integer, what is the smallest possible value of k such that 3675*k is the square of an integer?

A.3
B.9
C.12
D.15
E.20


3675=35*105
if k were odd, then 3 would give us 3*35*105=105^2
so we need an even multiple of 3
12 is only option
4*3*35*105)=(2*105)^2
12
C
BSchool Forum Moderator
User avatar
D
Joined: 12 Aug 2015
Posts: 2583
GRE 1: 323 Q169 V154
GMAT ToolKit User Premium Member
Re: If k is an even integer, what is the smallest possible value of k [#permalink]

Show Tags

New post 29 Apr 2017, 19:18
Here are my 2 cents on this one ->

Given info => K is an even integer.
3675*k=square of an integer.

In a perfect square the power of each prime factor is an even number.
Breaking down 3675*k=> 5^2*7^2*3*k => Perfect square.
Now the general expression for k will be 3*(Any-prime)^even
If the question had not stated that k is even => A would have been sufficient.
But here as k is even => Minimum value of k=> 3*2^2 (why 2^2? => Beacuse 2 is the smallest positive even number )
Hence k=>2^2*3=>12

Hence C.

_________________


Getting into HOLLYWOOD with an MBA

The MOST AFFORDABLE MBA programs!

STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)

Average GRE Scores At The Top Business Schools!

Intern
Intern
avatar
B
Joined: 23 Aug 2016
Posts: 48
Re: If k is an even integer, what is the smallest possible value of k [#permalink]

Show Tags

New post 01 May 2017, 14:10
Ugh, I fell into the trap of forgetting that k is even, and chose A: k=3. I need to remember to always double check the constraints!
BSchool Forum Moderator
User avatar
D
Joined: 12 Aug 2015
Posts: 2583
GRE 1: 323 Q169 V154
GMAT ToolKit User Premium Member
If k is an even integer, what is the smallest possible value of k [#permalink]

Show Tags

New post 03 Jan 2018, 07:17
sealberg wrote:
Ugh, I fell into the trap of forgetting that k is even, and chose A: k=3. I need to remember to always double check the constraints!


We all did my friend. We all did.


P.S -> Here is the Link to the entire Mock series -> https://gmatclub.com/forum/stonecold-s- ... 60-40.html

_________________


Getting into HOLLYWOOD with an MBA

The MOST AFFORDABLE MBA programs!

STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)

Average GRE Scores At The Top Business Schools!

If k is an even integer, what is the smallest possible value of k   [#permalink] 03 Jan 2018, 07:17
Display posts from previous: Sort by

If k is an even integer, what is the smallest possible value of k

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


GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.