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

 It is currently 21 Jan 2019, 14:09

### 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 January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### GMAT Club Tests are Free & Open for Martin Luther King Jr.'s Birthday!

January 21, 2019

January 21, 2019

10:00 PM PST

11:00 PM PST

Mark your calendars - All GMAT Club Tests are free and open January 21st for celebrate Martin Luther King Jr.'s Birthday.
• ### The winners of the GMAT game show

January 22, 2019

January 22, 2019

10:00 PM PST

11:00 PM PST

In case you didn’t notice, we recently held the 1st ever GMAT game show and it was awesome! See who won a full GMAT course, and register to the next one.

# If 1/2 + 1/3 + 1/4 = 13/x, which of the following must be an integer?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52344
If 1/2 + 1/3 + 1/4 = 13/x, which of the following must be an integer?  [#permalink]

### Show Tags

17 Sep 2018, 23:44
00:00

Difficulty:

15% (low)

Question Stats:

76% (00:42) correct 24% (00:49) wrong based on 101 sessions

### HideShow timer Statistics

If $$\frac{1}{2} + \frac{1}{3} + \frac{1}{4} = \frac{13}{x}$$, which of the following must be an integer?

I. $$\frac{x}{8}$$

II. $$\frac{x}{12}$$

III. $$\frac{x}{24}$$

A. I only
B. II only
C. I and III only
D. II and III only
E. I, II, and III

_________________
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2726
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: If 1/2 + 1/3 + 1/4 = 13/x, which of the following must be an integer?  [#permalink]

### Show Tags

18 Sep 2018, 00:05
Bunuel wrote:
If $$\frac{1}{2} + \frac{1}{3} + \frac{1}{4} = \frac{13}{x}$$, which of the following must be an integer?

I. $$\frac{x}{8}$$

II. $$\frac{x}{12}$$

III. $$\frac{x}{24}$$

A. I only
B. II only
C. I and III only
D. II and III only
E. I, II, and III

$$\frac{1}{2} + \frac{1}{3} + \frac{1}{4} = \frac{13}{x}$$
i.e. 13/12 = 13/x
i.e. x = 12

i.e. x will be divisible by ONLY 12 and every factor of 12 hence

_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2457
Re: If 1/2 + 1/3 + 1/4 = 13/x, which of the following must be an integer?  [#permalink]

### Show Tags

18 Sep 2018, 01:15

Solution

Given:
• $$\frac{1}{2} + \frac{1}{3} + \frac{1}{4} = \frac{13}{x}$$

To find:
• Which of the given options is always an integer?

Approach and Working:
• Multiplying the equation, $$\frac{1}{2} + \frac{1}{3} + \frac{1}{4} = \frac{13}{x}$$, by x on both sides gives,
o $$\frac{x}{2} + \frac{x}{3} + \frac{x}{4} = 13$$
o $$\frac{13x}{12} = 13$$
o Implies, x = 12

Thus, only II is true

Hence, the correct answer is option B.

_________________

Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Director
Joined: 04 Sep 2015
Posts: 527
Location: India
WE: Information Technology (Computer Software)
Re: If 1/2 + 1/3 + 1/4 = 13/x, which of the following must be an integer?  [#permalink]

### Show Tags

18 Sep 2018, 02:12
Bunuel wrote:
If $$\frac{1}{2} + \frac{1}{3} + \frac{1}{4} = \frac{13}{x}$$, which of the following must be an integer?

I. $$\frac{x}{8}$$

II. $$\frac{x}{12}$$

III. $$\frac{x}{24}$$

A. I only
B. II only
C. I and III only
D. II and III only
E. I, II, and III

1/2+1/3+1/4=13/12. Thus x=12.

Not just put 12 in place of x in all three options we get only 2 II to be an integer.

Option B.
Manager
Joined: 07 Aug 2018
Posts: 110
Location: United States (MA)
GMAT 1: 560 Q39 V28
GMAT 2: 670 Q48 V34
Re: If 1/2 + 1/3 + 1/4 = 13/x, which of the following must be an integer?  [#permalink]

### Show Tags

20 Sep 2018, 00:13
If the question used "COULD be true" instead of "must be true", would the answer be D?

Because we know that $$\frac{13}{12}$$ = $$\frac{13}{x}$$

So x could also be a multiple of 12, therefore $$\frac{x}{24}$$ could also be true.

Am I correct?
_________________

Flashcards Quant + Verbal:https://gmatclub.com/forum/gmat-flashcards-108651.html
Thursdays with Ron:https://gmatclub.com/forum/manhattan-s-thursdays-with-ron-consolidated-video-index-223612.html#p2138753

Manager
Joined: 24 Dec 2017
Posts: 181
Location: India
Concentration: Strategy, Real Estate
Schools: Johnson '21
If 1/2 + 1/3 + 1/4 = 13/x, which of the following must be an integer?  [#permalink]

### Show Tags

20 Sep 2018, 21:50
1/2 + 1/3 + 1/4 = 13/x

=>13/12 = 13/x
=>13x = 156
=>x = 156/13
=>x=12

A. 12/8 = 3/2 - Not an Integer
B. 12/12 = 1 - Integer
C. 12/24 = 1/2 - Not an integer

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4557
Location: United States (CA)
Re: If 1/2 + 1/3 + 1/4 = 13/x, which of the following must be an integer?  [#permalink]

### Show Tags

23 Sep 2018, 15:32
Bunuel wrote:
If $$\frac{1}{2} + \frac{1}{3} + \frac{1}{4} = \frac{13}{x}$$, which of the following must be an integer?

I. $$\frac{x}{8}$$

II. $$\frac{x}{12}$$

III. $$\frac{x}{24}$$

A. I only
B. II only
C. I and III only
D. II and III only
E. I, II, and III

Multiplying by 12x we have:

6x + 4x + 3x = 156

13x = 156

x = 12; thus, x/12 must be an integer.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: If 1/2 + 1/3 + 1/4 = 13/x, which of the following must be an integer? &nbs [#permalink] 23 Sep 2018, 15:32
Display posts from previous: Sort by