It is currently 15 Dec 2017, 13:59

# Decision(s) Day!:

CHAT Rooms | Olin (St. Louis) R1 | Tuck R1 | Ross R1 | Fuqua R1

### 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 June
Open Detailed Calendar

# Is x a multiple of 12?

Author Message
TAGS:

### Hide Tags

Manager
Joined: 24 Nov 2010
Posts: 197

Kudos [?]: 96 [1], given: 7

Location: United States (CA)
Concentration: Technology, Entrepreneurship
Schools: Ross '15, Duke '15
Is x a multiple of 12? [#permalink]

### Show Tags

19 Nov 2011, 13:27
1
KUDOS
1
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

60% (01:24) correct 40% (01:09) wrong based on 124 sessions

### HideShow timer Statistics

Is x a multiple of 12?

(1) $$\sqrt{x-3}$$ is odd
(2) x is a multiple of 3
[Reveal] Spoiler: OA

Last edited by Bunuel on 01 Oct 2017, 04:01, edited 2 times in total.
Renamed the topic, edited the question and added the OA.

Kudos [?]: 96 [1], given: 7

Manager
Joined: 31 May 2011
Posts: 85

Kudos [?]: 67 [1], given: 4

Location: India
GMAT Date: 12-07-2011
GPA: 3.22
WE: Information Technology (Computer Software)
Re: Is x a multiple of 12? [#permalink]

### Show Tags

19 Nov 2011, 23:08
1
KUDOS
I believe the answer should be C,
S1 tells us that X is an even number greater than 3 so we have 4,12,28. (As \sqrt{(x-3)} is also an odd number So not sufficient
S2 tells us that X is a multiple of 3. so we have 3,6,9... so not sufficient.

S1 and S2 tells us that X is an even multiple of 3 that is 12,36,

So IMO C.

What is the OA

Kudos [?]: 67 [1], given: 4

Manager
Joined: 24 Nov 2010
Posts: 197

Kudos [?]: 96 [0], given: 7

Location: United States (CA)
Concentration: Technology, Entrepreneurship
Schools: Ross '15, Duke '15
Re: Is x a multiple of 12? [#permalink]

### Show Tags

20 Nov 2011, 08:13
OA is C.

However, S1 says \sqrt{x-3} is odd. It does not however say that it is an integer or not.

for eg. the number 18 will satisfy both the both S1 and S2. As Sq root of 15 is odd and 18 is a multiple of 3. In fact sq of any odd number will be odd. Unless we assume that the statement "sq root of a number is odd" means that the number is a perfect sq.
Can someone please clarify if that this is a valid assumption that we can make for all gmat questions?

Kudos [?]: 96 [0], given: 7

Senior Manager
Joined: 23 Jun 2009
Posts: 360

Kudos [?]: 134 [0], given: 80

Location: Turkey
Schools: UPenn, UMich, HKS, UCB, Chicago
Re: Is x a multiple of 12? [#permalink]

### Show Tags

20 Nov 2011, 11:17
dreambeliever wrote:
OA is C.

However, S1 says \sqrt{x-3} is odd. It does not however say that it is an integer or not.

for eg. the number 18 will satisfy both the both S1 and S2. As Sq root of 15 is odd and 18 is a multiple of 3. In fact sq of any odd number will be odd. Unless we assume that the statement "sq root of a number is odd" means that the number is a perfect sq.
Can someone please clarify if that this is a valid assumption that we can make for all gmat questions?
Only an integer can be odd. i.e. if sqrt{x-3} is odd then it must be a number. So 18 do not satisfies.

Kudos [?]: 134 [0], given: 80

Manager
Joined: 24 Nov 2010
Posts: 197

Kudos [?]: 96 [0], given: 7

Location: United States (CA)
Concentration: Technology, Entrepreneurship
Schools: Ross '15, Duke '15
Re: Is x a multiple of 12? [#permalink]

### Show Tags

20 Nov 2011, 13:26
maliyeci wrote:
dreambeliever wrote:
OA is C.

However, S1 says \sqrt{x-3} is odd. It does not however say that it is an integer or not.

for eg. the number 18 will satisfy both the both S1 and S2. As Sq root of 15 is odd and 18 is a multiple of 3. In fact sq of any odd number will be odd. Unless we assume that the statement "sq root of a number is odd" means that the number is a perfect sq.
Can someone please clarify if that this is a valid assumption that we can make for all gmat questions?
Only an integer can be odd. i.e. if sqrt{x-3} is odd then it must be a number. So 18 do not satisfies.

hmm.. decimals cannot be even or odd.. thanks!

Kudos [?]: 96 [0], given: 7

Intern
Joined: 16 Oct 2011
Posts: 27

Kudos [?]: 3 [0], given: 5

GMAT 1: 640 Q44 V35
GMAT 2: 720 Q47 V42
Re: Is x a multiple of 12? [#permalink]

### Show Tags

21 Nov 2011, 04:20
Statement 1:

Let sqrt(x-3) =n with n being odd.
<=> x-3 = n^2 <=> x = n^2 + 3

Going through odd integers we get x = 4, 12, 28, 52, 84, 124, 172 etc.

=> INSUFF.

Statement 2: x is a multiple of 3 => INSUFF.

Both statements combined:

Looking at the list of possible values for x above, we see that all values that are divisible by 3 are divisible by 4, too. Therefore, these values are also a multiple of 12.

_________________

GMAT 720 Q47 V42 AWA 6.0, TOEFL 110.

Kudos [?]: 3 [0], given: 5

Intern
Joined: 26 Sep 2016
Posts: 35

Kudos [?]: 12 [0], given: 67

Re: Is x a multiple of 12? [#permalink]

### Show Tags

01 Oct 2017, 03:35
Hi,
the OA is given as "d" in this question however I think it should be "c" as others have also pointed out?

Kudos [?]: 12 [0], given: 67

Math Expert
Joined: 02 Sep 2009
Posts: 42618

Kudos [?]: 135755 [1], given: 12708

Re: Is x a multiple of 12? [#permalink]

### Show Tags

01 Oct 2017, 04:01
1
KUDOS
Expert's post
deucebigalow wrote:
Hi,
the OA is given as "d" in this question however I think it should be "c" as others have also pointed out?

_____________________
Edited the OA. Thank you.
_________________

Kudos [?]: 135755 [1], given: 12708

Senior Manager
Joined: 02 Jul 2017
Posts: 281

Kudos [?]: 108 [1], given: 66

GMAT 1: 730 Q50 V38
Re: Is x a multiple of 12? [#permalink]

### Show Tags

01 Oct 2017, 05:16
1
KUDOS
Is x a multiple of 12?

(1) $$\sqrt[]{x−3}$$ is odd
=> $$\sqrt[]{x−3}$$ = a => a= odd integer
=> $$x-3 = a^2$$
=> $$x= a^2+3$$

=> here x is an integer
For a as an odd integer, for a=1,3,5,7,9.... value of x = 4,12,28,52,84.......
Insufficient

(2) x is a multiple of 3
=> x is an integer and x =3b => here b is an integer => x=3,6,9,12,15,18,21,24......
Clearly Insufficient

1+2
$$x= a^2+3$$ and x =3b , here a is an odd integer and b is an integer
=> $$3b=a^2+3$$
=> b= $$\frac{a^2}{3}$$+1
Here as 'b' need to be an integer 'a' should be multiple of 3

=> a is odd and multiple pf 3
=> $$x= a^2+3$$ , a=3,9,15 => x=12,84,228......
=> x is multiple of 12

Kudos [?]: 108 [1], given: 66

Intern
Joined: 30 May 2017
Posts: 3

Kudos [?]: 0 [0], given: 0

Re: Is x a multiple of 12? [#permalink]

### Show Tags

04 Nov 2017, 07:21
Both taken together

As x is a multiple of 3, we need to see whether x is a also a multiple of 4.
Let's say $$\sqrt{x-3} = k$$
$$x = k^2 + 3 = (k - 1)(k+1) + 4$$

Because k is an odd number(we have that condition from $$\sqrt{x-3}$$ is an odd number), that means $$(k - 1)(k+1) + 4$$ is multiple of 4. So we have x is multiple of 3 and 4, so x is multiple of 12

Kudos [?]: 0 [0], given: 0

Re: Is x a multiple of 12?   [#permalink] 04 Nov 2017, 07:21
Display posts from previous: Sort by