Median trouble

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mj78ind: Master | Next Rank: 500 Posts; Posts: 265; Joined: Mon Dec 28, 2009 9:45 pmFollowed by: 2 members; Thanked: 26 times; GMAT Score:760

by mj78ind » Tue Aug 10, 2010 9:14 pm

A good question, I found:

Which of the following can not be the median of 3 positive numbers a,b and c:

1. a
2. (a+c)/4
3. (a+c)/7
4. b
5. a+c

[spoiler]Answer - 5
We can eliminate all four choices 1,2,3 and 4 by picking numbers. However,in choice 5 - a+c will be greater than a and c and if it has to be the median then b = a+c, but this can never be true since b> a and c hence, the median has to be either a or c, hence answer is 5. The tough part in the question was figuring out the logic of choice 5, eliminating the first four is easy.[/spoiler]

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Source: Beat The GMAT — Problem Solving | Tue Aug 10, 2010 9:14 pm

kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members; Thanked: 215 times

by kvcpk » Wed Aug 11, 2010 12:49 am

Median has to be either a or b or c
Observe the answer choices, they are all in tems of a and c. Which means question expects us to choose b as median.
Now going thru options:
a can be equal to b and be the median
a+c canequal 4b
a+c can equal 7b
b can equal b
a+c cannot equal b. because a+c will be greater than b [since a,b,c are positive.]

pick 5

"Once you start working on something,
don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC)

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mj78ind: Master | Next Rank: 500 Posts; Posts: 265; Joined: Mon Dec 28, 2009 9:45 pmFollowed by: 2 members; Thanked: 26 times; GMAT Score:760

by mj78ind » Wed Aug 11, 2010 1:09 am

kvcpk wrote:Median has to be either a or b or c
Observe the answer choices, they are all in tems of a and c. Which means question expects us to choose b as median.
Now going thru options:
a can be equal to b and be the median
a+c canequal 4b
a+c can equal 7b
b can equal b
a+c cannot equal b. because a+c will be greater than b [since a,b,c are positive.]

pick 5

@kvcpk ......... nice analysis .......one question though, why a + c > b has to be true? say a = 3, b = 8, c = 5 and the median is 5?

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kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members; Thanked: 215 times

by kvcpk » Wed Aug 11, 2010 1:18 am

mj78ind wrote:
kvcpk wrote:Median has to be either a or b or c
Observe the answer choices, they are all in tems of a and c. Which means question expects us to choose b as median.
Now going thru options:
a can be equal to b and be the median
a+c canequal 4b
a+c can equal 7b
b can equal b
a+c cannot equal b. because a+c will be greater than b [since a,b,c are positive.]

pick 5
@kvcpk ......... nice analysis .......one question though, why a + c > b has to be true? say a = 3, b = 8, c = 5 and the median is 5?

It is not given that a,b,c are in ascending order. My analysis above works when a,b,c are in ascending order. I just used this approach to eliminate choices.

When a,b,c are not in ascending order your example looks good. But, even in your case, a+c = 8 is not equal to median =5

Hope this helps!!

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mj78ind: Master | Next Rank: 500 Posts; Posts: 265; Joined: Mon Dec 28, 2009 9:45 pmFollowed by: 2 members; Thanked: 26 times; GMAT Score:760

by mj78ind » Wed Aug 11, 2010 1:21 am

kvcpk wrote:
mj78ind wrote:
kvcpk wrote:Median has to be either a or b or c
Observe the answer choices, they are all in tems of a and c. Which means question expects us to choose b as median.
Now going thru options:
a can be equal to b and be the median
a+c canequal 4b
a+c can equal 7b
b can equal b
a+c cannot equal b. because a+c will be greater than b [since a,b,c are positive.]

pick 5
@kvcpk ......... nice analysis .......one question though, why a + c > b has to be true? say a = 3, b = 8, c = 5 and the median is 5?
It is not given that a,b,c are in ascending order. My analysis above works when a,b,c are in ascending order. I just used this approach to eliminate choices.

When a,b,c are not in ascending order your example looks good. But, even in your case, a+c = 8 is not equal to median =5

Hope this helps!!

@kvcpk, Yup ....... I agree, I was just trying to point out that we can't use the strategy used by you to get an answer. However, we can eliminate all other choices using your analysis........

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kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members; Thanked: 215 times

by kvcpk » Wed Aug 11, 2010 1:54 am

mj78ind wrote: @kvcpk, Yup ....... I agree, I was just trying to point out that we can't use the strategy used by you to get an answer. However, we can eliminate all other choices using your analysis........

I agree. I used it for elimination. Cheers!!

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