Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 25 Sep 2010
Posts: 18

If the average arithmetic mean of the five numbers x, 7, 2,
[#permalink]
Show Tags
19 Oct 2010, 00:58
Question Stats:
64% (01:08) correct 36% (01:04) wrong based on 454 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
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 49303

Re: ds question
[#permalink]
Show Tags
20 Oct 2010, 08:46
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? Extrahard Quant Tests with Brilliant Analytics




Manager
Joined: 08 Sep 2010
Posts: 189
Location: India
WE 1: 6 Year, Telecom(GSM)

Re: ds question
[#permalink]
Show Tags
19 Oct 2010, 03:22
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
Joined: 06 Jun 2009
Posts: 299
Location: USA
WE 1: Engineering

Re: ds question
[#permalink]
Show Tags
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
Joined: 25 Aug 2010
Posts: 66

Re: ds question
[#permalink]
Show Tags
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....



Current Student
Joined: 31 Mar 2013
Posts: 67
Location: India
GPA: 3.02

Re: If the average arithmetic mean of the five numbers x, 7, 2,
[#permalink]
Show Tags
09 Oct 2013, 11:17
The above set is not evenly spaced. Is it possible to have a nonevenly spaced set where \(mean=median\)?
Thank you for your help.



Math Expert
Joined: 02 Sep 2009
Posts: 49303

Re: If the average arithmetic mean of the five numbers x, 7, 2,
[#permalink]
Show Tags
10 Oct 2013, 02:43



Senior Manager
Joined: 15 Aug 2013
Posts: 258

Re: ds question
[#permalink]
Show Tags
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?



Intern
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
13 Jun 2014, 20:48
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!



Math Expert
Joined: 02 Sep 2009
Posts: 49303

Re: If the average arithmetic mean of the five numbers x, 7, 2,
[#permalink]
Show Tags
14 Jun 2014, 01:39



Intern
Status: Difficult Roads often lead to beautiful destinations !!!
Joined: 29 Jul 2015
Posts: 15
Location: India
Concentration: Strategy, General Management
GPA: 3.7
WE: Supply Chain Management (Consulting)

Re: If the average arithmetic mean of the five numbers x, 7, 2,
[#permalink]
Show Tags
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 ?



Math Expert
Joined: 02 Sep 2009
Posts: 49303

Re: If the average arithmetic mean of the five numbers x, 7, 2,
[#permalink]
Show Tags
29 Mar 2016, 12:19
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: iftheaveragearithmeticmeanofthefivenumbersx103134.html#p803613There 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? Extrahard Quant Tests with Brilliant Analytics



Board of Directors
Joined: 17 Jul 2014
Posts: 2683
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: If the average arithmetic mean of the five numbers x, 7, 2,
[#permalink]
Show Tags
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 noninteger values for x...but still..illogical..because if we apply what we are given..we always get x=9...



Intern
Joined: 31 Jan 2017
Posts: 48

Re: If the average arithmetic mean of the five numbers x, 7, 2,
[#permalink]
Show Tags
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
Joined: 27 Jan 2016
Posts: 144

Re: If the average arithmetic mean of the five numbers x, 7, 2,
[#permalink]
Show Tags
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
Joined: 26 Dec 2015
Posts: 268
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
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 3045 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
Joined: 10 May 2017
Posts: 5

Re: If the average arithmetic mean of the five numbers x, 7, 2,
[#permalink]
Show Tags
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. BunuelHi 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



Math Expert
Joined: 02 Sep 2009
Posts: 49303

Re: If the average arithmetic mean of the five numbers x, 7, 2,
[#permalink]
Show Tags
18 Oct 2017, 01:48
neilphilip10 wrote: BunuelHi 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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 05 Mar 2015
Posts: 49
Location: Azerbaijan
GMAT 1: 530 Q42 V21 GMAT 2: 600 Q42 V31 GMAT 3: 700 Q47 V38

Re: If the average arithmetic mean of the five numbers x, 7, 2,
[#permalink]
Show Tags
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



Math Expert
Joined: 02 Sep 2009
Posts: 49303

Re: If the average arithmetic mean of the five numbers x, 7, 2,
[#permalink]
Show Tags
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? Extrahard Quant Tests with Brilliant Analytics




Re: If the average arithmetic mean of the five numbers x, 7, 2, &nbs
[#permalink]
23 May 2018, 05:58






