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

 It is currently 22 Oct 2019, 11:59

### 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

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

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

Author Message
TAGS:

### Hide Tags

Current Student
Joined: 12 Aug 2015
Posts: 2562
Schools: Boston U '20 (M)
GRE 1: Q169 V154
If k is an even integer, what is the smallest possible value of k  [#permalink]

### Show Tags

04 Nov 2016, 09:01
4
7
00:00

Difficulty:

85% (hard)

Question Stats:

42% (01:39) correct 58% (01:20) wrong based on 156 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

_________________
Manager
Joined: 28 Jun 2016
Posts: 214
Concentration: Operations, Entrepreneurship
Re: If k is an even integer, what is the smallest possible value of k  [#permalink]

### Show Tags

04 Nov 2016, 11:25
2
2
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
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8129
Location: United States (CA)
Re: If k is an even integer, what is the smallest possible value of k  [#permalink]

### Show Tags

07 Nov 2016, 11:50
1
1
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?”]

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Current Student
Joined: 12 Aug 2015
Posts: 2562
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: If k is an even integer, what is the smallest possible value of k  [#permalink]

### Show Tags

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?”]

Absolutely Spot On.!!
P.S=> Edited the Question.
_________________
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4774
Location: India
GPA: 3.5
Re: If k is an even integer, what is the smallest possible value of k  [#permalink]

### Show Tags

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 )

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 )
Current Student
Joined: 12 Aug 2015
Posts: 2562
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: If k is an even integer, what is the smallest possible value of k  [#permalink]

### Show Tags

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 )

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

Great
_________________
Intern
Status: I am not giving up. Not yet.
Joined: 23 Jul 2015
Posts: 40
Re: If k is an even integer, what is the smallest possible value of k  [#permalink]

### Show Tags

14 Nov 2016, 15:25
1
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
EVEN digit...grrr....
_________________
Cheers
PeeKay
VP
Joined: 07 Dec 2014
Posts: 1224
If k is an even integer, what is the smallest possible value of k  [#permalink]

### Show Tags

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
Current Student
Joined: 12 Aug 2015
Posts: 2562
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: If k is an even integer, what is the smallest possible value of k  [#permalink]

### Show Tags

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.

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

### Show Tags

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!
Current Student
Joined: 12 Aug 2015
Posts: 2562
Schools: Boston U '20 (M)
GRE 1: Q169 V154
If k is an even integer, what is the smallest possible value of k  [#permalink]

### Show Tags

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

_________________
Intern
Joined: 09 Oct 2018
Posts: 1
If k is an even integer, what is the smallest possible value of k  [#permalink]

### Show Tags

04 Oct 2019, 10:22
It is mentioned that K is even integer so eliminate options A, B, D,

so consider option c-12*3675=44100 which is a perfect square of 210.

Ans is- C-12
If k is an even integer, what is the smallest possible value of k   [#permalink] 04 Oct 2019, 10:22
Display posts from previous: Sort by