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

It is currently 21 Jun 2018, 03:34

Close

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If the average arithmetic mean of the five numbers x, 7, 2,

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

Hide Tags

Intern
Intern
avatar
Joined: 25 Sep 2010
Posts: 18
If the average arithmetic mean of the five numbers x, 7, 2, [#permalink]

Show Tags

New post 19 Oct 2010, 00:58
11
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

64% (01:07) correct 36% (01:02) wrong based on 431 sessions

HideShow timer Statistics

If the average (arithmetic mean) of the five numbers x, 7, 2, 16 and 11 is equal to the median of five numbers, what is the value of X

(1) 7 < x < 11
(2) x is the median of the five numbers

first statement is definitely sufficient, but in the second statement, if X is the median, it can take three numbers, 10. 9, 8, so ...how is it sufficient, i might be missing some basic point here,,,,so need help,,,,as the second statement is also sufficient for this problem
1 KUDOS received
Manager
Manager
User avatar
Joined: 08 Sep 2010
Posts: 201
Location: India
WE 1: 6 Year, Telecom(GSM)
Re: ds question [#permalink]

Show Tags

New post 19 Oct 2010, 03:22
1
satishreddy wrote:
if the average arithmetic mean of the five numbers X, 7,2,16.11 is equal to the median of five numbers, what is the value of X

1) 7<X<11
2) X is the median of five numbers

first statement is definitely sufficient, but in the second statement, if X is the median, it can take three numbers, 10. 9, 8, so ...how is it sufficient, i might be missing some basic point here,,,,so need help,,,,as the second statement is also sufficient for this problem



For finding out median you have to arrange the numbers in increasing or decresing order, then only you have to take the middle term as median.
So now the order will be 2,7,x,11,16
And in that way ,you will have the same median value i.e, 9.

So answer is D.


Please consider KUDOS if it is helpful to u .
Senior Manager
Senior Manager
avatar
Joined: 06 Jun 2009
Posts: 317
Location: USA
WE 1: Engineering
Re: ds question [#permalink]

Show Tags

New post 19 Oct 2010, 11:26
satishreddy wrote:
if the average arithmetic mean of the five numbers X, 7,2,16.11 is equal to the median of five numbers, what is the value of X

1) 7<X<11
2) X is the median of five numbers

first statement is definitely sufficient, but in the second statement, if X is the median, it can take three numbers, 10. 9, 8, so ...how is it sufficient, i might be missing some basic point here,,,,so need help,,,,as the second statement is also sufficient for this problem


Both statements are saying the SAME thing !

(X + 7 + 2 + 16 + 11) / 5 = MEDIAN

if it is given that X = Median, then

(X + 7 + 2 + 16 + 11) / 5 = X

(7 + 2 + 16 + 11) = 4X ....... and so on.
_________________

All things are possible to those who believe.

Manager
Manager
avatar
Joined: 25 Aug 2010
Posts: 68
Re: ds question [#permalink]

Show Tags

New post 20 Oct 2010, 06:24
satishreddy wrote:
if the average arithmetic mean of the five numbers X, 7,2,16.11 is equal to the median of five numbers, what is the value of X

1) 7<X<11
2) X is the median of five numbers

first statement is definitely sufficient, but in the second statement, if X is the median, it can take three numbers, 10. 9, 8, so ...how is it sufficient, i might be missing some basic point here,,,,so need help,,,,as the second statement is also sufficient for this problem


I am not convinced with the above answers...

from 1 ) 7 < X< 11 === > X is like 7.1, or 7.2 or 7.5 or 8,8.1 or 9 0r 9.5 ...

there are so many possibilites so i can not take only 8,9,10 as X

so i can not decide from 1

from 2) X is the median of five numbers then === > X, 7,2,16,11 ....

==> how can i arrange if i dont know the value of X in either descending or ascending..

so from the both also it wont be possible to get the ans i believe...
So ans E ...

Do let me know if i am wrong....
Expert Post
6 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46250
Re: ds question [#permalink]

Show Tags

New post 20 Oct 2010, 08:46
6
4
vitamingmat wrote:
satishreddy wrote:
if the average arithmetic mean of the five numbers X, 7,2,16.11 is equal to the median of five numbers, what is the value of X

1) 7<X<11
2) X is the median of five numbers

first statement is definitely sufficient, but in the second statement, if X is the median, it can take three numbers, 10. 9, 8, so ...how is it sufficient, i might be missing some basic point here,,,,so need help,,,,as the second statement is also sufficient for this problem


I am not convinced with the above answers...

from 1 ) 7 < X< 11 === > X is like 7.1, or 7.2 or 7.5 or 8,8.1 or 9 0r 9.5 ...

there are so many possibilites so i can not take only 8,9,10 as X

so i can not decide from 1

from 2) X is the median of five numbers then === > X, 7,2,16,11 ....

==> how can i arrange if i dont know the value of X in either descending or ascending..

so from the both also it wont be possible to get the ans i believe...
So ans E ...

Do let me know if i am wrong....


There is one more thing we know from the stem: "the average arithmetic mean of the five numbers x, 7, 2, 16, 11 is equal to the median of five numbers" --> \(\frac{x+2+7+11+16}{5}=median\). As there are odd number of terms then the median is the middle term when arranged in ascending (or descending) order but we don't know which one (median could be x, 7 or 11).

(1) 7 < x < 11 --> when ordered we'll get 2, 7, x, 11, 16 --> \(\frac{x+2+7+11+16}{5}=median=x\) --> \(\frac{x+36}{5}=x\) --> \(x=9\). Sufficient.

(2) x is the median of five numbers --> the same info as above: \(\frac{x+2+7+11+16}{5}=median=x\) --> \(\frac{x+36}{5}=x\) --> \(x=9\). Sufficient.

Answer: D.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

3 KUDOS received
Current Student
avatar
B
Joined: 31 Mar 2013
Posts: 68
Location: India
GPA: 3.02
Re: If the average arithmetic mean of the five numbers x, 7, 2, [#permalink]

Show Tags

New post 09 Oct 2013, 11:17
3
The above set is not evenly spaced. Is it possible to have a non-evenly spaced set where \(mean=median\)?

Thank you for your help.
Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46250
Re: If the average arithmetic mean of the five numbers x, 7, 2, [#permalink]

Show Tags

New post 10 Oct 2013, 02:43
2
2
Senior Manager
Senior Manager
avatar
Joined: 15 Aug 2013
Posts: 272
Re: ds question [#permalink]

Show Tags

New post 13 Jun 2014, 20:19
Bunuel wrote:
vitamingmat wrote:
satishreddy wrote:
if the average arithmetic mean of the five numbers X, 7,2,16.11 is equal to the median of five numbers, what is the value of X

1) 7<X<11
2) X is the median of five numbers

first statement is definitely sufficient, but in the second statement, if X is the median, it can take three numbers, 10. 9, 8, so ...how is it sufficient, i might be missing some basic point here,,,,so need help,,,,as the second statement is also sufficient for this problem


I am not convinced with the above answers...

from 1 ) 7 < X< 11 === > X is like 7.1, or 7.2 or 7.5 or 8,8.1 or 9 0r 9.5 ...

there are so many possibilites so i can not take only 8,9,10 as X

so i can not decide from 1

from 2) X is the median of five numbers then === > X, 7,2,16,11 ....

==> how can i arrange if i dont know the value of X in either descending or ascending..

so from the both also it wont be possible to get the ans i believe...
So ans E ...

Do let me know if i am wrong....


There is one more thing we know from the stem: "the average arithmetic mean of the five numbers x, 7, 2, 16, 11 is equal to the median of five numbers" --> \(\frac{x+2+7+11+16}{5}=median\). As there are odd number of terms then the median is the middle term when arranged in ascending (or descending) order but we don't know which one (median could be x, 7or 16).

(1) 7 < x < 11 --> when ordered we'll get 2, 7, x, 11, 16 --> \(\frac{x+2+7+11+16}{5}=median=x\) --> \(\frac{x+36}{5}=x\) --> \(x=9\). Sufficient.

(2) x is the median of five numbers --> the same info as above: \(\frac{x+2+7+11+16}{5}=median=x\) --> \(\frac{x+36}{5}=x\) --> \(x=9\). Sufficient.

Answer: D.


Hi Bunuel,

Two questions:

1) Why do you say that the median could be x, 7 or 16 -- couldn't it also be 11?
2) Isn't statement 1 and 2 saying the same thing or am I missing something?
1 KUDOS received
Intern
Intern
avatar
Joined: 29 May 2014
Posts: 17
Concentration: Finance, Strategy
GPA: 3.8
Re: If the average arithmetic mean of the five numbers x, 7, 2, [#permalink]

Show Tags

New post 13 Jun 2014, 20:48
1
russ9

1) I believe that it can also be 11 since if x was 11 the median in fact would be 11 (but the median could never be 16 since if x=16, then you'd have 2, 7, 11, 16, 16 and the median would be 11 not 16).

2) Statement 1 and 2 are essentially saying the say thing, since the constraint "the mean is equal to the median" and that is the only value [9] that satisfies that constraint -- therefore it is D.

Please Kudos if this helped!
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46250
Re: If the average arithmetic mean of the five numbers x, 7, 2, [#permalink]

Show Tags

New post 14 Jun 2014, 01:39
andrewwal wrote:
russ9

1) I believe that it can also be 11 since if x was 11 the median in fact would be 11 (but the median could never be 16 since if x=16, then you'd have 2, 7, 11, 16, 16 and the median would be 11 not 16).

2) Statement 1 and 2 are essentially saying the say thing, since the constraint "the mean is equal to the median" and that is the only value [9] that satisfies that constraint -- therefore it is D.

Please Kudos if this helped!


Correct. 15 was a typo there. Edited.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Status: Difficult Roads often lead to beautiful destinations !!!
Joined: 29 Jul 2015
Posts: 15
Location: India
Concentration: Strategy, General Management
Schools: Ivey '19 (A)
GMAT 1: 660 Q49 V32
GPA: 3.7
WE: Supply Chain Management (Consulting)
Re: If the average arithmetic mean of the five numbers x, 7, 2, [#permalink]

Show Tags

New post 29 Mar 2016, 12:07
Dear Bunuel , I have a doubt on statement B

Statement B says - x is the median of the 5 no's. So x can be 7,8,9,10,11 . Then how can we determine the value of x using B alone ?
Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46250
Re: If the average arithmetic mean of the five numbers x, 7, 2, [#permalink]

Show Tags

New post 29 Mar 2016, 12:19
2
ThePlayer wrote:
Dear Bunuel , I have a doubt on statement B

Statement B says - x is the median of the 5 no's. So x can be 7,8,9,10,11 . Then how can we determine the value of x using B alone ?


This is explained above: if-the-average-arithmetic-mean-of-the-five-numbers-x-103134.html#p803613

There is one more thing we know from the stem: "the average arithmetic mean of the five numbers x, 7, 2, 16, 11 is equal to the median of five numbers" --> \(\frac{x+2+7+11+16}{5}=median\). As there are odd number of terms then the median is the middle term when arranged in ascending (or descending) order but we don't know which one (median could be x, 7 or 11).
(1) 7 < x < 11 --> when ordered we'll get 2, 7, x, 11, 16 --> \(\frac{x+2+7+11+16}{5}=median=x\) --> \(\frac{x+36}{5}=x\) --> \(x=9\). Sufficient.

(2) x is the median of five numbers --> the same info as above: \(\frac{x+2+7+11+16}{5}=median=x\) --> \(\frac{x+36}{5}=x\) --> \(x=9\). Sufficient.

Answer: D.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Board of Directors
User avatar
P
Joined: 17 Jul 2014
Posts: 2730
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Premium Member Reviews Badge
Re: If the average arithmetic mean of the five numbers x, 7, 2, [#permalink]

Show Tags

New post 09 Apr 2016, 13:54
oh man..I just had this question in my GMATPrep test, and I panicked and picked A...
quick question to Bunuel, can we consider only INTEGER values, knowing that the question stem tells that we have NUMBERS (aka any numbers)?

1. x has values 8, 9, 10.
we know that (36+x)/5 = x
36+x=5x
x=9
so only value if x=9

2. x is the median of the five
36+x=5x
x=9
yes, 9 is the median.

D

I dismissed B because I considered non-integer values for x...but still..illogical..because if we apply what we are given..we always get x=9...
Intern
Intern
avatar
B
Joined: 31 Jan 2017
Posts: 42
Re: If the average arithmetic mean of the five numbers x, 7, 2, [#permalink]

Show Tags

New post Updated on: 02 Aug 2017, 06:13
On Generalizing the question the equation we got
x+36=5M
so if x is the median then M=x then statement 2 will become sufficient


Sent from my HTC Desire 816G dual sim using GMAT Club Forum mobile app

Originally posted by arif24 on 02 Aug 2017, 05:52.
Last edited by arif24 on 02 Aug 2017, 06:13, edited 1 time in total.
Manager
Manager
avatar
G
Joined: 27 Jan 2016
Posts: 147
Schools: ISB '18
GMAT 1: 700 Q50 V34
Re: If the average arithmetic mean of the five numbers x, 7, 2, [#permalink]

Show Tags

New post 02 Aug 2017, 05:58
Q stem states that (2+7+11+16+x)/5 = median

Statement 1) only x=9 in the given range satisfies the condition - suff

Stmnt 2) (x+36)/5 = x -> x=9 - suff

Answer D
Senior Manager
Senior Manager
avatar
G
Joined: 26 Dec 2015
Posts: 277
Location: United States (CA)
Concentration: Finance, Strategy
WE: Investment Banking (Venture Capital)
Re: If the average arithmetic mean of the five numbers x, 7, 2, [#permalink]

Show Tags

New post 16 Sep 2017, 16:48
If the average (arithmetic mean) of the five numbers x, 7, 2, 16 and 11 is equal to the median of five numbers, what is the value of X

(1) 7 < x < 11
(2) x is the median of the five numbers


Important to note: This is a purely CONCEPTUAL problem. Meaning, there's HARDLY ANY MATH REQUIRED/INVOLVED. You should be able to eye this and take 30-45 seconds MAX. I'll show you how.

1- set up #s in increasing order (common step whenever you see the word "median"): 2, 7, 11, 16, x --> quickly see 2+7=9...9+11=20, 20+16=36.
2- average = \(\frac{sum of #s in a set}{total numbers in a set}\) --> \(\frac{36+x}{5}\)
3- set up question: \(\frac{36+x}{5}\) = median.
> key here is to find out what x is (or what the median is)!

1) TELLS US X=MEDIAN! How do you know this? Well, there are 5 terms in the set.
> 2 terms are BELOW 7.
> 2 terms are ABOVE 11.
-- Since there are only 5 terms in a set, the 3rd term (middle) = median. Bingo. Eliminate B, C, E.

2) SAME AS 1!
-- Elim A.

Ans: D
Intern
Intern
avatar
B
Joined: 10 May 2017
Posts: 5
Re: If the average arithmetic mean of the five numbers x, 7, 2, [#permalink]

Show Tags

New post 18 Oct 2017, 01:37
Bunuel wrote:
andrewwal wrote:
russ9

1) I believe that it can also be 11 since if x was 11 the median in fact would be 11 (but the median could never be 16 since if x=16, then you'd have 2, 7, 11, 16, 16 and the median would be 11 not 16).

2) Statement 1 and 2 are essentially saying the say thing, since the constraint "the mean is equal to the median" and that is the only value [9] that satisfies that constraint -- therefore it is D.

Please Kudos if this helped!


Correct. 15 was a typo there. Edited.

Bunuel
Hi Bunuel,
I understood the solution however,
Elementary doubt here. Since Mean=Median, Shouldn't the numbers in the set be consecutive, However I cannot seem understand the consecutive nature of the above mentioned set.
Thanks
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46250
Re: If the average arithmetic mean of the five numbers x, 7, 2, [#permalink]

Show Tags

New post 18 Oct 2017, 01:48
neilphilip10 wrote:
Bunuel
Hi Bunuel,
I understood the solution however,
Elementary doubt here. Since Mean=Median, Shouldn't the numbers in the set be consecutive, However I cannot seem understand the consecutive nature of the above mentioned set.
Thanks


For an evenly spaced set (arithmetic progression), the median equals to the mean. Though the reverse is not necessarily true. Consider {0, 1, 1, 2} --> median = mean = 1 but the set is not evenly spaced.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
B
Joined: 05 Mar 2015
Posts: 22
Re: If the average arithmetic mean of the five numbers x, 7, 2, [#permalink]

Show Tags

New post 22 May 2018, 12:05
Hi, I just found a mistake in a question and would like to let you know

You can answer the question even without looking at the statements 1 and 2 - the question stem itself gives sufficient information to find the value of x, which is 9

My reasoning:

if we order the numbers in an increasing order we get 2, 7, 11, 16. we also have x. Regardless of the value of x, the median will be a number that is 7≤X ≤11

The question also says that median equals the mean. (36+x)/5 is the mean, which is also median. (36+x)/5 this tells us that x cannot be 7, because 36/5 is already greater than 7. If x were 7 the median would not be equal to the mean.

If x were 8, the median would be 8, but the mean would be greater than mean. You can check all numbers that satisfies 7≤X ≤11. The only number that satisfies 7≤X ≤11 and also makes median equal to the mean is 9


You can answer the question without looking at the statements
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46250
Re: If the average arithmetic mean of the five numbers x, 7, 2, [#permalink]

Show Tags

New post 23 May 2018, 05:58
kablayi wrote:
Hi, I just found a mistake in a question and would like to let you know

You can answer the question even without looking at the statements 1 and 2 - the question stem itself gives sufficient information to find the value of x, which is 9

My reasoning:

if we order the numbers in an increasing order we get 2, 7, 11, 16. we also have x. Regardless of the value of x, the median will be a number that is 7≤X ≤11

The question also says that median equals the mean. (36+x)/5 is the mean, which is also median. (36+x)/5 this tells us that x cannot be 7, because 36/5 is already greater than 7. If x were 7 the median would not be equal to the mean.

If x were 8, the median would be 8, but the mean would be greater than mean. You can check all numbers that satisfies 7≤X ≤11. The only number that satisfies 7≤X ≤11 and also makes median equal to the mean is 9


You can answer the question without looking at the statements


That's not correct.

From the stem, x can be -1, 9 or 19.

If x = -1, then the set is {-1, 2, 7, 11, 16} --> median = mean = 7.
If x = 9, then the set is {-2, 7, 9, 11, 16} --> median = mean = 9.
If x = 19, then the set is {2, 7, 11, 16, 19} --> median = mean = 11.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Re: If the average arithmetic mean of the five numbers x, 7, 2,   [#permalink] 23 May 2018, 05:58
Display posts from previous: Sort by

If the average arithmetic mean of the five numbers x, 7, 2,

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


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.