GMAT PREP I MEDIAN/AVERAGE

Expert replies

pkw209: Master | Next Rank: 500 Posts; Posts: 266; Joined: Mon Oct 19, 2009 9:46 pm; Thanked: 8 times; GMAT Score:690

by pkw209 » Tue Dec 29, 2009 10:19 am

Hey all,

Couldn't figure this one out. I took this from Zuleron's 198 question doc. A brief explanation would be very much appreciated. Thanks!

26) If the average of five numbers, x, 7, 2, 16, and 11 = the median, what is x?

a. 7 < x > 11
b. x is median of the five numbers

Like this post

Source: Beat The GMAT — Data Sufficiency | Tue Dec 29, 2009 10:19 am

papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pmFollowed by: 252 members; Thanked: 653 times

by papgust » Tue Dec 29, 2009 6:43 pm

Are you sure that statement 1 is correct?

Like this post

pkw209: Master | Next Rank: 500 Posts; Posts: 266; Joined: Mon Oct 19, 2009 9:46 pm; Thanked: 8 times; GMAT Score:690

by pkw209 » Wed Dec 30, 2009 12:57 pm

I took this from zuleron's 198 gmat prep questions and it obviously didn't look right to me at first either.

I think a is supposed to be 7 < x < 11.

The answer is D and it makes sense.

the median=mean, therefore, x=9.

Like this post

anu009: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Fri Dec 11, 2009 10:15 am; Thanked: 2 times

by anu009 » Mon Jan 11, 2010 5:50 pm

hey what is the answer.According to my calulation is is D.

Like this post

vittalgmat: Legendary Member; Posts: 621; Joined: Wed Apr 09, 2008 7:13 pmFollowed by: 4 members; Thanked: 33 times

by vittalgmat » Mon Jan 11, 2010 9:40 pm

yep the answer is D.

the 5 numbers can be arranged as follows
2, 7, 11,16 and x.

Stmt 1 says x is between 7 and 11.
so the arrangement becomes
2, 7, x, 11, 16.

If u look at this seq carefully , u will notice 2 and 7, 11 and 16 are evenly spaced (diff = 5).
So we can ignore them in calculating the value of x.
so x cna be calculated simply as 7+11/2. = 9.
So sufficient.

Stmt 2 says the same

Hence ans is D.

HTHelps
-V

Like this post

taposh_dr: Senior | Next Rank: 100 Posts; Posts: 32; Joined: Tue Dec 09, 2008 1:37 am; Location: San Francisco; Thanked: 7 times

by taposh_dr » Tue Mar 02, 2010 11:23 pm

Well, if the st 1: is considered to be 7<x>11 which boils down to x> 11 then statement I is insufficient
and the answer will be "B"

as opposed to considering 7<x<11, where answer will be D.

Like this post

kstv: Legendary Member; Posts: 610; Joined: Fri Jan 15, 2010 12:33 amFollowed by: 2 members; Thanked: 47 times

by kstv » Wed Mar 03, 2010 8:26 am

In consecutive nos the Mean = Median. So can one conclude that if the no are arranged in ascending order 2 7 11 16 , x has to be the middle value ie.between 7 and 11. As mentioned before in this thread the diff between 7 & 2 = 11 & 16 = 5. Also the average of 2 7 11 and 16 is 9. So x cannot be in the beginning or end of the series.

Is 1 and 2 necessary as they are stating the obvious. Please point out the error in my reasoning.

Like this post

amittilak: Senior | Next Rank: 100 Posts; Posts: 34; Joined: Wed Nov 11, 2009 11:23 amFollowed by: 1 member; Thanked: 8 times

by amittilak » Wed Mar 03, 2010 9:24 am

Dear kstv,
you are right and wrong.
In consecutive nos the Mean = Median but the converse does not have to be true.
If mean = median, they don't have to be consecutive numbers.
Consider set A = 1, 9, 16, 25, 29 Clearly, 16 is the median
mean = (1+9+16+25+29)/5 = 16
Thus, mean = median and the numbers are not consecutive (or the set is not evenly spaced set, to be precise). Consecutive integers is special case of evenly spaced set.

kstv wrote:In consecutive nos the Mean = Median. So can one conclude that if the no are arranged in ascending order 2 7 11 16 , x has to be the middle value ie.between 7 and 11. As mentioned before in this thread the diff between 7 & 2 = 11 & 16 = 5. Also the average of 2 7 11 and 16 is 9. So x cannot be in the beginning or end of the series.

Is 1 and 2 necessary as they are stating the obvious. Please point out the error in my reasoning.

Like this post

kstv: Legendary Member; Posts: 610; Joined: Fri Jan 15, 2010 12:33 amFollowed by: 2 members; Thanked: 47 times

by kstv » Wed Mar 03, 2010 10:22 am

Thanks, using this can U disprove/elaborate what I have concluded about the options not being necessary.

Like this post

amittilak: Senior | Next Rank: 100 Posts; Posts: 34; Joined: Wed Nov 11, 2009 11:23 amFollowed by: 1 member; Thanked: 8 times

by amittilak » Wed Mar 03, 2010 11:22 am

26) If the average of five numbers, x, 7, 2, 16, and 11 = the median, what is x?

a. 7 < x < 11
b. x is median of the five numbers

Arranging terms in ascending order, we have,
2, 7, 11, 16 x can be any number.
It is given that mean = median. Depending on the value of x,
if x < 7, median = 7
7 < x < 11, median = x
x > 11, median = 11

Stmt. I
7 < x < 11
which gives us, median = mean = x
Hence, 2+7+11+16+x = 5*x
Solving, x = 9
Suff.

Stmt. II
x is the median of the five number. Essentially, this is the same info. as given in Stmt. I
Hence, Suff.

Answer is "D"

kstv,
This is a value question, which means we must find a definite value for "x". The theory for consecutive numbers does not really come into play here.

kstv wrote:Thanks, using this can U disprove/elaborate what I have concluded about the options not being necessary.

Like this post

kstv: Legendary Member; Posts: 610; Joined: Fri Jan 15, 2010 12:33 amFollowed by: 2 members; Thanked: 47 times

by kstv » Wed Mar 03, 2010 5:46 pm

was looking for the part which you explained

Arranging terms in ascending order, we have,
2, 7, 11, 16 x can be any number.
It is given that mean = median. Depending on the value of x,
if x < 7, median = 7
7 < x < 11, median = x
x > 11, median = 11

If x is 19 Mean = Median = 11.
so x does not necessarily lie between 7 and 11 if Mean = Median.

My doubt was whether the rule of cosecutive no applies universally to a ascending series. Thanks.

Like this post

ganesh prasath: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Sun Sep 12, 2010 9:09 pm

by ganesh prasath » Thu May 26, 2011 4:29 am

but the first stmt says that 7<x>11 so doesnt it mean that 7<11<x ? how have u written as 7<x<11 ??

Like this post

cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Fri May 27, 2011 5:04 pm

even if we use 7<x>11
this means x>11
and thus arranging in ascending order,
2,7,11,x,16 or 2,7,11,16,x (depends on whether x <16)
Median is still 11
and thus (2+7+11+x+6)/5 =11
and we get a single value of x.
Thus A is sufficient
also B is sufficient on its own.
Thus D

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review