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

 It is currently 24 Apr 2019, 05:18

### 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

# If x>100, what is the smallest value of x for which (3+x)/12 is an int

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 54493
If x>100, what is the smallest value of x for which (3+x)/12 is an int  [#permalink]

### Show Tags

23 Feb 2017, 06:39
00:00

Difficulty:

5% (low)

Question Stats:

93% (00:56) correct 7% (01:08) wrong based on 204 sessions

### HideShow timer Statistics

If x>100, what is the smallest value of x for which (3+x)/12 is an integer.

A. 102
B. 103
C. 104
D. 105
E. 106

_________________
Director
Joined: 05 Mar 2015
Posts: 999
Re: If x>100, what is the smallest value of x for which (3+x)/12 is an int  [#permalink]

### Show Tags

23 Feb 2017, 07:42
1
Bunuel wrote:
If x>100, what is the smallest value of x for which (3+x)/12 is an integer.

A. 102
B. 103
C. 104
D. 105
E. 106

means 3+x must be divisible by 3 &4 (since 3*4=12)

for divisible by 3 sum of all three digit of (3+x)should be divisible by 3
And for it tobe divisible by 4 ,last two digit of (3+x) must be divisible by 4

A) 102
3+x= 3+102=105....NO
B) 103
3+x= 3+103=106....NO
C) 104
3+x= 3+104=107....NO
D)105
3+x= 3+105=108....YES
E)106
3+x= 3+106=109....NO

Ans D
Intern
Joined: 08 Oct 2016
Posts: 20
Location: Nepal
Concentration: Finance, Marketing
WE: Account Management (Accounting)
Re: If x>100, what is the smallest value of x for which (3+x)/12 is an int  [#permalink]

### Show Tags

23 Feb 2017, 07:51
1
Bunuel wrote:
If x>100, what is the smallest value of x for which (3+x)/12 is an integer.

A. 102
B. 103
C. 104
D. 105
E. 106

For (3+x)/12 to be an integer (3+x) must be multiple of 12. We know x>100 so least multiple of 12 above 100 is 108. therefore we need to add 105 in order to make (3+x) a multiple of 12. so the ans is D.
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4426
Location: India
GPA: 3.5
Re: If x>100, what is the smallest value of x for which (3+x)/12 is an int  [#permalink]

### Show Tags

23 Feb 2017, 08:25
Bunuel wrote:
If x>100, what is the smallest value of x for which (3+x)/12 is an integer.

A. 102
B. 103
C. 104
D. 105
E. 106

12*9 = 108

Now, to make the numerator 108 , we must add 105 to 3

_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 5851
Location: United States (CA)
Re: If x>100, what is the smallest value of x for which (3+x)/12 is an int  [#permalink]

### Show Tags

27 Feb 2017, 11:46
Bunuel wrote:
If x>100, what is the smallest value of x for which (3+x)/12 is an integer.

A. 102
B. 103
C. 104
D. 105
E. 106

Since (3 + x)/12 must be an integer and x >100, we must find the smallest value of x greater than 100 that makes 3 + x a multiple of 12.

Since (105 + 3)/12 = 108/12 = 9, 105 is the smallest possible value of x.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

Director
Joined: 02 Sep 2016
Posts: 663
Re: If x>100, what is the smallest value of x for which (3+x)/12 is an int  [#permalink]

### Show Tags

03 Apr 2017, 05:41
To be divisible by 12 (2^2*3), (3+x) should be even and therefore x must be odd (odd+odd=even).
105 fits all the requirements.

105+3= 108

It's divisible by 3 (1+0+8=9)
Also 108 is a multiple of 12.
_________________
Help me make my explanation better by providing a logical feedback.

If you liked the post, HIT KUDOS !!

Don't quit.............Do it.
Intern
Joined: 05 Feb 2014
Posts: 22
GMAT 1: 700 Q45 V40
Re: If x>100, what is the smallest value of x for which (3+x)/12 is an int  [#permalink]

### Show Tags

08 Apr 2017, 07:34
Here's another way of looking at it :

(3+x)/12 => 3/12 + x/12

3/12 leaves a remainder of 3. Hence for the whole thing to be divisible by 12, the second part needs to leave a reminder 9.

105 leaves a remainder of 9 when divided by 12.
Director
Joined: 12 Nov 2016
Posts: 725
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Re: If x>100, what is the smallest value of x for which (3+x)/12 is an int  [#permalink]

### Show Tags

27 Jun 2017, 16:16
Bunuel wrote:
If x>100, what is the smallest value of x for which (3+x)/12 is an integer.

A. 102
B. 103
C. 104
D. 105
E. 106

Very simple- 12 x 9 = 108- this is the smallest number that satisfies x>100 so

3 + 105 /12 = 1

Thus
"D"
Intern
Joined: 22 Jun 2017
Posts: 6
Re: If x>100, what is the smallest value of x for which (3+x)/12 is an int  [#permalink]

### Show Tags

27 Jun 2017, 20:02
It's possible to use the following approaching:

You need the least multiple of 12 greater than 100.

You can get this quickly, using easy numbers:

12x5 = 60x2 = 120

120-12=108

3+x = 108
x = 105
Manager
Joined: 08 Oct 2016
Posts: 203
Location: United States
Concentration: General Management, Finance
GPA: 2.9
WE: Engineering (Telecommunications)
Re: If x>100, what is the smallest value of x for which (3+x)/12 is an int  [#permalink]

### Show Tags

03 Jul 2017, 12:33
It should be odd+odd=even to be divisible by an even so A,C,E eliminated now put values
Answer is: D is it right approach?
_________________
Got Q42,V17
Target#01 Q45,V20--April End
Re: If x>100, what is the smallest value of x for which (3+x)/12 is an int   [#permalink] 03 Jul 2017, 12:33
Display posts from previous: Sort by