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

 It is currently 11 Dec 2018, 13:07

### 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 11, 2018

December 11, 2018

09:00 PM EST

10:00 PM EST

Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.
• ### The winning strategy for 700+ on the GMAT

December 13, 2018

December 13, 2018

08:00 AM PST

09:00 AM PST

What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

# The integers x and y are positive. Is the sqrt (x^2 +7xy) an integer?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 13 Aug 2017
Posts: 8
The integers x and y are positive. Is the sqrt (x^2 +7xy) an integer?  [#permalink]

### Show Tags

Updated on: 03 Jul 2018, 07:12
1
00:00

Difficulty:

45% (medium)

Question Stats:

70% (01:57) correct 30% (02:03) wrong based on 81 sessions

### HideShow timer Statistics

The integers x and y are positive. Is the $$\sqrt{x^2 + 7xy}$$ an integer?

(1) y = 5x
(2) y - x = 4

Originally posted by neiln413b on 03 Jul 2018, 06:54.
Last edited by Bunuel on 03 Jul 2018, 07:12, edited 1 time in total.
Renamed the topic and edited the question.
Intern
Joined: 27 Feb 2018
Posts: 36
Location: India
WE: Engineering (Real Estate)
Re: The integers x and y are positive. Is the sqrt (x^2 +7xy) an integer?  [#permalink]

### Show Tags

03 Jul 2018, 07:00
neiln413b wrote:
Hi, any help with this DS question would be greatly appreciated!

The integers x and y are positive. Is the sqrt(x^2 + 7xy) an integer?

1) y=5x
2) y-x=4

IMO A:
option A when substituted gives the answer as 6x, since x is a positive integer 6x will be an integer.

option B when substituted gives an expression which cant be simplified in square root.
DS Forum Moderator
Joined: 21 Aug 2013
Posts: 1412
Location: India
Re: The integers x and y are positive. Is the sqrt (x^2 +7xy) an integer?  [#permalink]

### Show Tags

03 Jul 2018, 10:10
neiln413b wrote:
The integers x and y are positive. Is the $$\sqrt{x^2 + 7xy}$$ an integer?

(1) y = 5x
(2) y - x = 4

Square root of x^2 + 7xy will be an integer if x^2 + 7xy is a perfect square.

(1) Substituting y=5x, we get
x^2 + 7xy = x^2 + 7*x*5x = x^2 + 35x^2 = 36x^2.

Now since x is a positive integer, x^2 is a perfect square, and 36 is already a perfect square. So 36x^2 will also be a perfect square. Thus its square root will be an integer. Sufficient.

(2) Substituting y = 4+x we get
x^2 + 7xy = x^2 + 7x(4+x) = x^2 + 28x + 7x^2 = 8x^2 + 28x = 4x(2x+7).

Now say x=1, then 4x(2x+7) = 4*1(2+7) = 4*9 which is a perfect square.
But if say x=2, then 4x(2x+7) = 4*2(4+7) = 8*11 which is not a perfect square.
Thus this statement is Not Sufficient.

Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3325
Location: India
GPA: 3.12
Re: The integers x and y are positive. Is the sqrt (x^2 +7xy) an integer?  [#permalink]

### Show Tags

03 Jul 2018, 10:13
neiln413b wrote:
The integers x and y are positive. Is the $$\sqrt{x^2 + 7xy}$$ an integer?

(1) y = 5x
(2) y - x = 4

1. y = 5x
The expression becomes $$\sqrt{x^2 + 7x(5x)} = \sqrt{36x^2} = 6x$$
Since, integers x and y are positive integers, the expression will be an integer (Sufficient)

2. Here, y = x + 4
The expression becomes $$\sqrt{x^2 + 7x(x+4)} = \sqrt{8x^2 + 28x} = \sqrt{4x(2x + 7)}$$
If x = 1, the expression is an integer whereas if x = 2, it is not an integer (Insufficient) (Option A)
_________________

You've got what it takes, but it will take everything you've got

Director
Joined: 11 Feb 2015
Posts: 611
Re: The integers x and y are positive. Is the sqrt (x^2 +7xy) an integer?  [#permalink]

### Show Tags

04 Jul 2018, 08:21
Statement 1 is sufficient as it is mentioned that x is an integer and this statement simplifies to 6x which has to be an integer (i.e. integer * integer = integer)

Statement 2 is Not sufficient.

Hence the correct answer is A
_________________

"Please hit +1 Kudos if you like this post"

_________________
Manish

"Only I can change my life. No one can do it for me"

Re: The integers x and y are positive. Is the sqrt (x^2 +7xy) an integer? &nbs [#permalink] 04 Jul 2018, 08:21
Display posts from previous: Sort by