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

 It is currently 19 Feb 2019, 17:15

### 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 February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT Prep Hour

February 20, 2019

February 20, 2019

08:00 PM EST

09:00 PM EST

Strategies and techniques for approaching featured GMAT topics. Wednesday, February 20th at 8 PM EST

February 21, 2019

February 21, 2019

10:00 PM PST

11:00 PM PST

Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.

# M26-34

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52971

### Show Tags

16 Sep 2014, 00:26
00:00

Difficulty:

65% (hard)

Question Stats:

57% (00:56) correct 43% (00:57) wrong based on 228 sessions

### HideShow timer Statistics

If $$x$$ is a positive integer, is $$\sqrt{x}$$ an integer?

(1) $$\sqrt{7*x}$$ is an integer

(2) $$\sqrt{9*x}$$ is not an integer

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 52971

### Show Tags

16 Sep 2014, 00:26
Official Solution:

Must know for the GMAT: if $$x$$ is a positive integer then $$\sqrt{x}$$ is either a positive integer or an irrational number. (It cannot be some reduced fraction e.g. $$\frac{7}{3}$$ or $$\frac{1}{2}$$).

Also, note that the question basically asks whether $$x$$ is a perfect square.

(1) $$\sqrt{7*x}$$ is an integer. This statement tells that $$x$$ cannot be a perfect square, because if it is, for example if $$x=n^2$$ for some positive integer $$n$$, then $$\sqrt{7x}=\sqrt{7n^2}=n\sqrt{7} \ne integer$$. Sufficient.

(2) $$\sqrt{9*x}$$ is not an integer. Simplify: $$\sqrt{9*x}=3*\sqrt{x} \ne integer$$, which means that $$\sqrt{x} \ne integer$$. Sufficient.

_________________
Intern
Joined: 23 Apr 2016
Posts: 21
Location: Finland
GPA: 3.65

### Show Tags

07 Nov 2016, 09:32
Statement 1: x is squareroot of an odd power of 7, so not an integer. Sufficient.
Statement 2: x is not a perfect square, hence its square root will not be an integer. Sufficient.
Intern
Joined: 03 Dec 2014
Posts: 5

### Show Tags

03 Sep 2018, 06:20
Statement 1: x needs to have odd number of 7 for \sqrt{7x} to be an integer. Hence \sqrt{x} cannot be an integer. Sufficient
Statement 2: Simplify to 3*\sqrt{x}. For this to be a non-integer, \sqrt{x} cannot be an integer. Sufficient
Manager
Joined: 17 Jun 2018
Posts: 52
Location: India
Schools: IMD '20
GPA: 2.84
WE: Engineering (Consulting)

### Show Tags

08 Sep 2018, 21:47
Bunuel chetan2u
I am new to this community.I an unable to find options for answering these questions.Can you guide me.
Math Expert
Joined: 02 Sep 2009
Posts: 52971

### Show Tags

09 Sep 2018, 00:53
1
arpitkansal wrote:
Bunuel chetan2u
I am new to this community.I an unable to find options for answering these questions.Can you guide me.

This is a data sufficiency question. Options for DS questions are always the same.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

I suggest you to go through the following posts:
ALL YOU NEED FOR QUANT.

Hope this helps.
_________________
Manager
Joined: 17 Jun 2018
Posts: 52
Location: India
Schools: IMD '20
GPA: 2.84
WE: Engineering (Consulting)

### Show Tags

09 Sep 2018, 01:14
Bunuel
thankyou.

Posted from my mobile device
Intern
Joined: 09 Jan 2017
Posts: 3

### Show Tags

04 Nov 2018, 22:54
Hello,

in statement 1 if x=343 then square root of 7*343 is also an integer. but sq root of 343 is not an integer.

In which case statement 1 wont be sufficient.

Please clarify what I am missing?

Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 52971

### Show Tags

04 Nov 2018, 22:58
ss9031 wrote:
Hello,

in statement 1 if x=343 then square root of 7*343 is also an integer. but sq root of 343 is not an integer.

In which case statement 1 wont be sufficient.

Please clarify what I am missing?

Thanks

From (1), as well as from (2), we got that $$\sqrt{x}$$ cannot be an integer, the same answer you got.
_________________
Re: M26-34   [#permalink] 04 Nov 2018, 22:58
Display posts from previous: Sort by

# M26-34

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®.