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# Is c the median of a, b and c ? (1) b - c = a (2) c = a how

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Senior Manager
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Joined: 15 Sep 2010
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Is c the median of a, b and c ? (1) b - c = a (2) c = a how  [#permalink]

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19 Oct 2010, 09:11
1
00:00

Difficulty:

45% (medium)

Question Stats:

57% (00:52) correct 43% (00:51) wrong based on 145 sessions

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Is c the median of a, b and c ?

(1) b - c = a

(2) c = a

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I'm the Dumbest of All !!

Math Expert
Joined: 02 Sep 2009
Posts: 51185
Re: Is c the median of a, b and c ? (1) b - c = a (2) c = a how  [#permalink]

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19 Oct 2010, 09:29
1
shrive555 wrote:
Is c the median of a, b and c ?

(1) b - c = a

(2) c = a

how quickly you solve this ? write down ur timings.

If a set has odd number of terms the median of a set is the middle number when arranged in ascending or descending order;
If a set has even number of terms the median of a set is the average of the two middle terms when arranged in ascending or descending order.

So the median of the three numbers a, b and c would be the middle term, hence c would be the median in two cases: $$a\leq{c}\leq{b}$$ or $$a\geq{c}\geq{b}$$..

(1) b - c = a --> clearly insufficient. If b=10, c=1, a=9=median, then answer would be NO but if b=10, c=9=median, and a=1, then answer would be YES.

(2) c=a --> either the three numbers are c, c, b (in ascending order) --> media=c or the three numbers are b, c, c (in ascending order) --> median=c. Sufficient.

Similar question: ds6-93969.html?hilit=median

Hope it helps.
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Re: Is c the median of a, b and c ? (1) b - c = a (2) c = a how  [#permalink]

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20 Oct 2010, 13:14
B.

Solved in 10 seconds because I solved a similar problem a few minutes ago.

ds6-93969.html?hilit=median
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GMAT 1: 720 Q48 V41
Re: Is c the median of a, b and c ? (1) b - c = a (2) c = a how  [#permalink]

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21 Oct 2010, 08:55
B 20 sec... was just studying number theory and then saw this question :-p thought at first that i was making a mistake but read the line "how quickly you solve this ? write down ur timings" and was sure that i was right
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Re: Is c the median of a, b and c ? (1) b - c = a (2) c = a how  [#permalink]

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02 Dec 2018, 01:10

Official Solution:

For the value of c to be the median, it needs to be the middle number of those 3 numbers.

Statement 1: There are many possible situations arising from this statement. In some, c is the median, but in others, it is not. Here are some examples:

Yes, c is the median:

a = 2, c = 3, b = 5
b - c = a
5 - 3 = 2

No, c is not the median:

c = 2, a = 3, b = 5
b - c = a
5 - 2 = 3

This statement is insufficient.

Statement 2: If two out of the three numbers in a set are equal, then those two numbers must represent the median. For example:

2, 2, 3
c, c, b
or
1, 2, 2
b, c, c

The only way b could go in the middle is if it also equals c. However, if all three numbers in a set are equal, then they all must be the median. So if a = b = c, the value of c is still the median. For example:

2, 2, 2
c, b, c

But since b = c, that's really the same as:

2, 2, 2
c, c, c

Thus, from this statement, we know that the value of c is always the median. This statement alone is sufficient.
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Re: Is c the median of a, b and c ? (1) b - c = a (2) c = a how &nbs [#permalink] 02 Dec 2018, 01:10
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