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

 It is currently 16 Dec 2018, 12:13

### 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

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Free GMAT Prep Hour

December 16, 2018

December 16, 2018

03:00 PM EST

04:00 PM EST

Strategies and techniques for approaching featured GMAT topics
• ### FREE Quant Workshop by e-GMAT!

December 16, 2018

December 16, 2018

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

# M26-21

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51229

### Show Tags

16 Sep 2014, 00:25
1
3
00:00

Difficulty:

25% (medium)

Question Stats:

70% (01:00) correct 30% (01:09) wrong based on 193 sessions

### HideShow timer Statistics

What is the smallest positive integer $$k$$ such that $$126*\sqrt{k}$$ is the square of a positive integer?

A. 14
B. 36
C. 144
D. 196
E. 441

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 51229

### Show Tags

16 Sep 2014, 00:25
Official Solution:

What is the smallest positive integer $$k$$ such that $$126*\sqrt{k}$$ is the square of a positive integer?

A. 14
B. 36
C. 144
D. 196
E. 441

$$126=2*3^2*7$$, so in order $$126*\sqrt{k}$$ to be a square of an integer, $$\sqrt{k}$$ must complete the powers of 2 and 7 to even number, so the least value of $$\sqrt{k}$$ must equal $$2*7=14$$, which makes the least value of $$k$$ equal to $$14^2=196$$.

_________________
Director
Joined: 02 Sep 2016
Posts: 681

### Show Tags

06 Jan 2017, 03:56
Bunuel wrote:
Official Solution:

What is the smallest positive integer $$k$$ such that $$126*\sqrt{k}$$ is the square of a positive integer?

A. 14
B. 36
C. 144
D. 196
E. 441

$$126=2*3^2*7$$, so in order $$126*\sqrt{k}$$ to be a square of an integer, $$\sqrt{k}$$ must complete the powers of 2 and 7 to even number, so the least value of $$\sqrt{k}$$ must equal $$2*7=14$$, which makes the least value of $$k$$ equal to $$14^2=196$$.

Hi Bunuel

Your help here would be great.

Please guide me where I went wrong.

126*\sqrt{k}= (a)^2

Here a is the number we are talking about in the question stem.

126= 2*3^2*7

So 2*3^2*7*\sqrt{k}= a^2

Squaring both the sides

2^2*3^4*7^2*\sqrt{k}= a

So the lowest we can plug in is 36 (6^2) as we already have all the numbers with even powers.
Math Expert
Joined: 02 Sep 2009
Posts: 51229

### Show Tags

06 Jan 2017, 04:29
1
Shiv2016 wrote:
Bunuel wrote:
Official Solution:

What is the smallest positive integer $$k$$ such that $$126*\sqrt{k}$$ is the square of a positive integer?

A. 14
B. 36
C. 144
D. 196
E. 441

$$126=2*3^2*7$$, so in order $$126*\sqrt{k}$$ to be a square of an integer, $$\sqrt{k}$$ must complete the powers of 2 and 7 to even number, so the least value of $$\sqrt{k}$$ must equal $$2*7=14$$, which makes the least value of $$k$$ equal to $$14^2=196$$.

Hi Bunuel

Your help here would be great.

Please guide me where I went wrong.

126*\sqrt{k}= (a)^2

Here a is the number we are talking about in the question stem.

126= 2*3^2*7

So 2*3^2*7*\sqrt{k}= a^2

Squaring both the sides

2^2*3^4*7^2*\sqrt{k}= a

So the lowest we can plug in is 36 (6^2) as we already have all the numbers with even powers.

If you square $$2*3^2*7*\sqrt{k}= a^2$$ you get $$2^2*3^4*7^2*k= a^4$$.
_________________
Director
Joined: 02 Sep 2016
Posts: 681

### Show Tags

06 Jan 2017, 21:27
1
Bunuel wrote:
Shiv2016 wrote:
Bunuel wrote:
Official Solution:

What is the smallest positive integer $$k$$ such that $$126*\sqrt{k}$$ is the square of a positive integer?

A. 14
B. 36
C. 144
D. 196
E. 441

$$126=2*3^2*7$$, so in order $$126*\sqrt{k}$$ to be a square of an integer, $$\sqrt{k}$$ must complete the powers of 2 and 7 to even number, so the least value of $$\sqrt{k}$$ must equal $$2*7=14$$, which makes the least value of $$k$$ equal to $$14^2=196$$.

Hi Bunuel

Your help here would be great.

Please guide me where I went wrong.

126*\sqrt{k}= (a)^2

Here a is the number we are talking about in the question stem.

126= 2*3^2*7

So 2*3^2*7*\sqrt{k}= a^2

Squaring both the sides

2^2*3^4*7^2*\sqrt{k}= a

So the lowest we can plug in is 36 (6^2) as we already have all the numbers with even powers.

If you square $$2*3^2*7*\sqrt{k}= a^2$$ you get $$2^2*3^4*7^2*k= a^4$$.

Then k= a^4/(2^2*3^4*7^2)

As we do not know the value of a, we will have to take a as 2^2*7^2 because the power of a is 4. 2,3,7, and k are its prime factors and hence will take the power of 4.

These silly mistakes are going out of my hand.
Manager
Joined: 25 Jul 2017
Posts: 94

### Show Tags

15 Aug 2018, 19:56
Bunuel wrote:
What is the smallest positive integer $$k$$ such that $$126*\sqrt{k}$$ is the square of a positive integer?

A. 14
B. 36
C. 144
D. 196
E. 441

This question can be easily solved by factorisation.

126*√k
=> 2*3*3*7*√k
=> 3^2*14*√k

i.e. we need another 14 to make it a square of positive number
i.e. √k=14
K= 14^2 = 196
Re: M26-21 &nbs [#permalink] 15 Aug 2018, 19:56
Display posts from previous: Sort by

# M26-21

Moderators: chetan2u, Bunuel

 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®.