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GmatTakerNo.1: Senior | Next Rank: 100 Posts; Posts: 37; Joined: Sat Apr 24, 2010 8:27 am

by GmatTakerNo.1 » Mon May 03, 2010 10:58 am

In the sequence of 7 positive integers 2, 3, k, r, 7, 7, 11 if the average equals the median, which is one of the members in the sequence. What is the average?
(1) r=6
(2) k=r

The answer is B, but I got A, because if r is 6 you have the median, and because median=average you have the average as well.
Am I wrong?

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Source: Beat The GMAT — Data Sufficiency | Mon May 03, 2010 10:58 am

iamseer: Master | Next Rank: 500 Posts; Posts: 170; Joined: Wed Jun 10, 2009 5:59 am; Thanked: 13 times

by iamseer » Mon May 03, 2010 11:24 am

average=median=value of one of the member element.

from statement 1:
IF r = 6, we have no information about k. Therefore we cannot find the average. NOT SUFFICIENT

from statement 2:
k=r
therefore average is (30+2k)/7. This greater than 2 or 3 for sure.
therefore (30+2k)/7 = k or 7 or 11
(30+2k)/7 = 7 not possible, since k is integer
(30+2k)/7 = 11 not possible, since k is integer

(30+2k)/7 = k gives 5k=30, k=6=r
So set is 2,3,6,6,7,7,11 .... median is 6, average is 6

answer B

"Choose to chance the rapids and dance the tides"

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GmatTakerNo.1: Senior | Next Rank: 100 Posts; Posts: 37; Joined: Sat Apr 24, 2010 8:27 am

by GmatTakerNo.1 » Mon May 03, 2010 11:45 am

But the question also says that the median is equal to the average. And because the numbers are ordered from small to big ones, actually itÂ´s clear that k is not bigger than r. So if r is 6, then the median is 6 which implies due to the question that the average is 6 as well.
Where is the flaw in my idea?

Can you maybe explain your way of solution a little bit more in detail?
Why do you check if (30+2k)/7 is 7 or 11?
And where do you get the term (30+2k)/7?

I have my Gmat tommorow and a strange feeling that I can use the knowledge to solve this

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liferocks: Legendary Member; Posts: 576; Joined: Sat Mar 13, 2010 8:31 pmFollowed by: 1 member; Thanked: 97 times

by liferocks » Mon May 03, 2010 6:31 pm

the average of the series is (30+r+k)/7 or 4+(2+r+k)/7

from 1 we get the average is 4+(2+6+k)/7 or 5+(1+k)/7
now for k=6 average is 6 and median 6...
now for k=13 average is 7 and median 7..

Not sufficient to conclude what is avarage

From 2
average 4+(2+k+k)/7 or 4+2*(1+k)/7
since the set is of integers median=average must be integer ..hence 1+k is a multiple of 7
for k=7n-1
when n=1,k=6 and median=average= 6
when n>1,k>=13 hence median 7..and average>=8
hence only solution is k=r=median=average=6
condition 2 is sufficient

ans B

"If you don't know where you are going, any road will get you there."
Lewis Carroll

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ssuarezo: Master | Next Rank: 500 Posts; Posts: 126; Joined: Wed Jun 24, 2009 1:12 pm; Location: Montreal; Thanked: 2 times; GMAT Score:510

by ssuarezo » Wed May 05, 2010 10:26 am

GmatTakerNo.1 wrote:In the sequence of 7 positive integers 2, 3, k, r, 7, 7, 11 if the average equals the median, which is one of the members in the sequence. What is the average?
(1) r=6
(2) k=r

The answer is B, but I got A, because if r is 6 you have the median, and because median=average you have the average as well.
Am I wrong?

Me too, anyone please tell me what's wrong with this: (I get D !! )

From the quest, I simplified to (Avg=Med): (30 + k)/6 = r --> since r is both the median and avg, and assuming the list is sorted (seems so). Maybe this is the mistake. If sorted:

Stm 1: r=6, and applied to (30 + k)/6 = 6, then k = 6 Suff.
Stm 2: k=r, and applied to (30 + r)/6 = r, then r =k=6 Suff

Maybe I dont understand the question: which is one of the members in the sequence, but I do got the average.

Please help !
Silvia

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liferocks: Legendary Member; Posts: 576; Joined: Sat Mar 13, 2010 8:31 pmFollowed by: 1 member; Thanked: 97 times

by liferocks » Wed May 05, 2010 5:55 pm

ssuarezo wrote:
GmatTakerNo.1 wrote:In the sequence of 7 positive integers 2, 3, k, r, 7, 7, 11 if the average equals the median, which is one of the members in the sequence. What is the average?
(1) r=6
(2) k=r

The answer is B, but I got A, because if r is 6 you have the median, and because median=average you have the average as well.
Am I wrong?
Me too, anyone please tell me what's wrong with this: (I get D !! )

From the quest, I simplified to (Avg=Med): (30 + k)/6 = r --> since r is both the median and avg, and assuming the list is sorted (seems so). Maybe this is the mistake. If sorted:

Stm 1: r=6, and applied to (30 + k)/6 = 6, then k = 6 Suff.
Stm 2: k=r, and applied to (30 + r)/6 = r, then r =k=6 Suff

Maybe I dont understand the question: which is one of the members in the sequence, but I do got the average.

Please help !
Silvia

here you have considered r as median which is not necessary correct.
if k=2 and r=1 then the series will be

r k 2 3 7 7 11-->median 3
don't consider that the series is in ascending order unless it is specified.

"If you don't know where you are going, any road will get you there."
Lewis Carroll

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

by kstv » Wed May 05, 2010 6:22 pm

(1) r = 6 so average = (36+k)/7
(36+k)/7 = median so (36+k)/7 hass to be a positive integer
the possible values of k are 6,13 etc
if k = 6,13 then the median & mean will be 6,7 respectively
so insuff
IMO B

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ssuarezo: Master | Next Rank: 500 Posts; Posts: 126; Joined: Wed Jun 24, 2009 1:12 pm; Location: Montreal; Thanked: 2 times; GMAT Score:510

by ssuarezo » Thu May 06, 2010 9:17 am

liferocks wrote:
ssuarezo wrote: Me too, anyone please tell me what's wrong with this: (I get D !! )

From the quest, I simplified to (Avg=Med): (30 + k)/6 = r --> since r is both the median and avg, and assuming the list is sorted (seems so). Maybe this is the mistake. If sorted:

Stm 1: r=6, and applied to (30 + k)/6 = 6, then k = 6 Suff.
Stm 2: k=r, and applied to (30 + r)/6 = r, then r =k=6 Suff

Maybe I dont understand the question: which is one of the members in the sequence, but I do got the average.

Please help !
Silvia
here you have considered r as median which is not necessary correct.
if k=2 and r=1 then the series will be

r k 2 3 7 7 11-->median 3
don't consider that the series is in ascending order unless it is specified.

Ok LR, if not specifically indicated that they are in ascending order, they are not (worse case).
Thanks for your patience.
Silvia

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