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

 It is currently 21 Nov 2018, 04:07

### 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
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

## Events & Promotions

###### Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### All GMAT Club Tests are Free and open on November 22nd in celebration of Thanksgiving Day!

November 22, 2018

November 22, 2018

10:00 PM PST

11:00 PM PST

Mark your calendars - All GMAT Club Tests are free and open November 22nd to celebrate Thanksgiving Day! Access will be available from 0:01 AM to 11:59 PM, Pacific Time (USA)
• ### Free lesson on number properties

November 23, 2018

November 23, 2018

10:00 PM PST

11:00 PM PST

Practice the one most important Quant section - Integer properties, and rapidly improve your skills.

# Is positive integer x divisible by 24?

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

### Hide Tags

Intern
Joined: 21 Nov 2013
Posts: 39
Is positive integer x divisible by 24?  [#permalink]

### Show Tags

23 Jan 2014, 12:50
3
19
00:00

Difficulty:

55% (hard)

Question Stats:

59% (01:32) correct 41% (01:46) wrong based on 445 sessions

### HideShow timer Statistics

Is positive integer x divisible by 24?

(1) √x is divisible by 4.
(2) x^2 is not divisible by 9.
##### Most Helpful Community Reply
Intern
Joined: 21 Nov 2013
Posts: 39
Re: Is positive integer x divisible by 24?  [#permalink]

### Show Tags

23 Jan 2014, 12:52
10
4
Prime factors of 24: 2^3 * 3^1. In order for a number (x) to be divisible by 24, it needs to have all these prime factors at least.
(It may or may not have additional factors).

Statement 1: Square on both sides (imagine this is a equation). This yields that x is divisible by 16.
This means: x = k*16 for some constant k. Now, 16 = 2^4 which is more than 2^3. But no 3. In case k includes at least a 3,
x is divisible by 24. In case k does not include a 3, x is not divisible by 24. INSUFFICIENT

Statement 2: x^2 is not divisible by 9. Again imagine an equation, but take now the square root on both sides.
This means that x is not divisible by 3. This also means that x does not have a single 3 as one of its prime factors.
But in order to be divisible by 24, we know it needs at least 3^1 (i.e. at least one 3). Thus, we know that x cannot be
divided by 24 as it lacks 3 as its prime factor. SUFFICIENT

Answer is B.
##### General Discussion
Math Expert
Joined: 02 Sep 2009
Posts: 50729
Re: Is positive integer x divisible by 24?  [#permalink]

### Show Tags

27 Jan 2014, 00:47
BabySmurf wrote:
Is positive integer x divisible by 24?

(1) √x is divisible by 4. (this means to read square root of x is divisible by 4)
(2) x^2 is not divisible by 9.

All DS Divisibility/Multiples/Factors questions to practice: search.php?search_id=tag&tag_id=354
All PS Divisibility/Multiples/Factors questions to practice: search.php?search_id=tag&tag_id=185

Hope this helps.
_________________
Manager
Joined: 03 Jul 2013
Posts: 89
Schools: ISB '17 (A), IIMC (A)
GMAT 1: 660 Q48 V32
Re: Is positive integer x divisible by 24?  [#permalink]

### Show Tags

03 Oct 2014, 10:40
Can someone please explain why statement 1 is not suffificent. If x=16, not divisible by 24. x=64, not divisible by 24. x=144, not divisible by 24 and so on...
_________________

Sometimes standing still can be, the best move you ever make......

Math Expert
Joined: 02 Sep 2009
Posts: 50729
Re: Is positive integer x divisible by 24?  [#permalink]

### Show Tags

03 Oct 2014, 10:46
1
aadikamagic wrote:
Is positive integer x divisible by 24?

(1) √x is divisible by 4.
(2) x^2 is not divisible by 9.

Can someone please explain why statement 1 is not suffificent. If x=16, not divisible by 24. x=64, not divisible by 24. x=144, not divisible by 24 and so on...

144 is divisible by 24: 144/24 = 6.
_________________
Retired Moderator
Joined: 19 Mar 2014
Posts: 944
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
Re: Is positive integer x divisible by 24?  [#permalink]

### Show Tags

08 Jul 2017, 12:37
1
1
BabySmurf wrote:
Is positive integer x divisible by 24?

(1) √x is divisible by 4.
(2) x^2 is not divisible by 9.

In order to check the divisibility by x first lets check the factors of $$24$$

$$24 = 3 * 8 = 3 * 2 * 2 * 2 = 3^1 * 2^3$$

Hence, For any number of be divisible by 24 we will need one 3 and three 2's.

Lets check the options.

(1) $$\sqrt{x}$$ is divisible by $$4$$

$$= \frac{\sqrt{x}}4$$

Squaring Numerator and Denominator

$$= \frac{x}{16} = \frac{x}{2*2*2*2} = \frac{x}{2^4}$$

This means x = k * x is divisible by 2^3

If the value of k has 3 then x is divisible by 24

However, if the value of k does not have 3 then x is not divisible by 24

Hence, (1) ===== is NOT SUFFICIENT

(2) $$x^2$$ is not divisible by 9

As $$x^2$$ is not divisible by 9, x will not be divisible by 3.

In order for a number to be divisible by 24, we need at least one prime number - 3, and as x is not divisible by 3 we can say that x is not divisible by 24.

As we are able to answer the question - x divisible by 24? (2) is SUFFICIENT

Hence, Answer is B
_________________

"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475

Manager
Joined: 09 Oct 2016
Posts: 89
Location: United States
GMAT 1: 740 Q49 V42
GPA: 3.49
Re: Is positive integer x divisible by 24?  [#permalink]

### Show Tags

08 Jul 2017, 14:54
Accidentally hit C but the answer is B

Prime Factorization of 24 = 2^3 * 3

A) Tells us that root X is divisible by 4, meaning that X will have at least 4 2s (4*4), making it divisible by 8. There is no mention of 3, so this is not sufficient.

B) Tells us that x^2 is not divisible by 9. If 3 was a factor of X then x^2 would be divisible by 9 (3*3). Thus, X cannot possibly be divisible by 24 since 3 is not a factor of X

Hope this helps
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 485
Re: Is positive integer x divisible by 24?  [#permalink]

### Show Tags

28 Aug 2018, 06:02
BabySmurf wrote:
Is positive integer x divisible by 24?

(1) √x is divisible by 4.
(2) x^2 is not divisible by 9.

$$x \geqslant 1\,\,\operatorname{int}$$

$$\frac{x}{{{2^3} \cdot 3}}\,\,\,\mathop = \limits^? \,\,\,\operatorname{int}$$

$$\left( 1 \right)\,\,\,\,\frac{{\sqrt x }}{{{2^2}}}\,\,\, = \,\,\,\operatorname{int} \,\,\,\,\,\,\left\{ \begin{gathered} \,Take\,\,x = {2^4}\,\,\,\,\left\langle {{\text{NO}}} \right\rangle \hfill \\ \,Take\,\,x = {\left( {{2^3} \cdot 3} \right)^2}\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \hfill \\ \end{gathered} \right.$$

$$\left( 2 \right)\,\,\,{\left( {\frac{x}{3}} \right)^2} = \frac{{{x^2}}}{{{3^2}}}\,\,\, \ne \,\,\,\operatorname{int} \,\,\,\,\, \Rightarrow \,\,\,\,\,\frac{x}{3}\,\,\, \ne \,\,\,\operatorname{int} \,\,\,\,\,\,\,\mathop \Rightarrow \limits^{FOCUS\,!} \,\,\,\,\,\frac{x}{3}\,\,\, \ne \,\,\,{2^3} \cdot \operatorname{int} \,\,\,\,\, \Rightarrow \,\,\,\,\,\frac{x}{{{2^3} \cdot 3}}\,\,\, \ne \,\,\,\operatorname{int} \,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle$$

The above follows the notations and rationale taught in the GMATH method.
_________________

Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or GMATH.com.br (Portuguese version)
Course release PROMO : finish our test drive till 30/Nov with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount!

Re: Is positive integer x divisible by 24? &nbs [#permalink] 28 Aug 2018, 06:02
Display posts from previous: Sort by

# Is positive integer x divisible by 24?

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

 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®.