GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 22 Jan 2020, 10:28 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # A set of integers consists of 2, 3, 5, 7, 11, 12, and x. If x increase

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 60600
A set of integers consists of 2, 3, 5, 7, 11, 12, and x. If x increase  [#permalink]

### Show Tags 00:00

Difficulty:   25% (medium)

Question Stats: 76% (01:35) correct 24% (01:23) wrong based on 79 sessions

### HideShow timer Statistics

A set of integers consists of 2, 3, 5, 7, 11, 12, and x. If x increases by 1, the median of the set stays unchanged. However, if x decreases by 1, the median of the set also decreases by 1. What is the value of x?

A. 6
B. 7
C. 8
D. 9
E. 10

_________________
Senior PS Moderator D
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 728
GMAT 1: 740 Q50 V40 GMAT 2: 770 Q51 V42 Re: A set of integers consists of 2, 3, 5, 7, 11, 12, and x. If x increase  [#permalink]

### Show Tags

This requires a little bit of number sense.

If we write down the numbers in ascending order and assume x to be somewhere. It is clear that x cannot be at the ends as we need to be able to influence the median. Since we have an odd number of numbers, the median will be the central number.

2, 3, 5, 7, x, 11, 12

Now, if x was 7, increasing it by one still maintains the median as 7. However, on decreasing it by 1, the new median is 6 which is 1 less than before. We are done.

x = 7.

Hence Option (B) does it.

Best,

Bunuel wrote:
A set of integers consists of 2, 3, 5, 7, 11, 12, and x. If x increases by 1, the median of the set stays unchanged. However, if x decreases by 1, the median of the set also decreases by 1. What is the value of x?

A. 6
B. 7
C. 8
D. 9
E. 10

_________________
Regards,

“Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back)
Manager  B
Joined: 16 Dec 2018
Posts: 66
Re: A set of integers consists of 2, 3, 5, 7, 11, 12, and x. If x increase  [#permalink]

### Show Tags

any other explanation ?
Board of Directors D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4862
Location: India
GPA: 3.5
Re: A set of integers consists of 2, 3, 5, 7, 11, 12, and x. If x increase  [#permalink]

### Show Tags

hudacse6 wrote:
any other explanation ?

Trying my bit

Median of the set of numbers - { 2, 3, 5, 7, 11, 12, and x. } must be 7

Now, try using the options -

(A) 2, 3, 5, 6 , 7, 11, 12 - Median = 6 ; If increased by 1 median increases by 1 , if decreased by 1 median decreases to 5
(B) 2, 3, 5, 7 , 7, 11, 12 - Median = 7 ; If increased by 1 median remains the same , if decreased by 1 median decreases to 6

Check with other options, only (B) works perfectly !!!
_________________
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 V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9095
Location: United States (CA)
Re: A set of integers consists of 2, 3, 5, 7, 11, 12, and x. If x increase  [#permalink]

### Show Tags

2
Bunuel wrote:
A set of integers consists of 2, 3, 5, 7, 11, 12, and x. If x increases by 1, the median of the set stays unchanged. However, if x decreases by 1, the median of the set also decreases by 1. What is the value of x?

A. 6
B. 7
C. 8
D. 9
E. 10

Since, when x increases by 1, the median of the set stays unchanged and when x decreases by 1, the median of the set also decreases by 1, it must be true that x is the median or is very close to the median. So let’s say x is the median, and we have:

2, 3, 5, x, 7, 11, 12

We see that, in this case, x could be 5, 6, or 7. Since 5 is not in the choices, let’s start with x = 6.

If x = 6 (i.e., the original median is 6), then x + 1 = 7, and the list becomes:

2, 3, 5, 7, 7, 11, 12

However, the median is now 7. Therefore, x can’t be 6 since the median is supposed to stay unchanged.

If x = 7 (i.e., the original median is 7), then x + 1 = 8, and the list becomes:

2, 3, 5, 7, 8, 11, 12

We see that the median is still 7. Furthermore, x - 1 = 6, and the list becomes:

2, 3, 5, 6, 7, 11, 12

We see that the median is 6, which is 1 less than the original median. Therefore, x must be 7.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

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

If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: A set of integers consists of 2, 3, 5, 7, 11, 12, and x. If x increase   [#permalink] 05 Dec 2019, 20:19
Display posts from previous: Sort by

# A set of integers consists of 2, 3, 5, 7, 11, 12, and x. If x increase  