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If a,b, and c are positive integers with at least one of

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If a,b, and c are positive integers with at least one of  [#permalink]

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20 Jun 2018, 21:14
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95% (hard)

Question Stats:

41% (01:49) correct 59% (01:26) wrong based on 119 sessions

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If a,b, and c are positive integers with at least one of the three equal to 7, is the median of the set {a,b,c} greater than 7?
(1) a<7
(2) c>7

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Re: If a,b, and c are positive integers with at least one of  [#permalink]

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20 Jun 2018, 23:03
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chetan2u wrote:
If a,b, and c are positive integers with at least one of the three equal to 7, is the median of the set {a,b,c} greater than 7?
(1) a<7
(2) c>7

New question

At least one of the three = 7.

(1) a < 7
So at least one integer = 7, and one integer < 7.
If third integer = 7, then since two integers = 7, median of these three = 7
If third integer < 7, then since two integers < 7, median of these three < 7
If third integer > 7, then the median of these three = 7

So the median will either be = 7 or < 7, but never > 7. So this gives NO as an answer to the question asked. Sufficient.

(2) c > 7
So at least one integer = 7, and one integer > 7
If third integer = 7, then since two integers = 7, median of these three = 7
If third integer > 7, then since two integers > 7, median of these three > 7

So the median might be = 7 or greater than 7 also. This doesnt give a definite YES or NO to the question asked. Not Sufficient.

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Re: If a,b, and c are positive integers with at least one of  [#permalink]

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21 Jun 2018, 04:34

Solution

Given:

• a, b, and c are positive integers.
• At least one of a, b, and c is 7.

To find:

• Is the median of the set {a,b,c} greater than 7?

Statement-1: “a<7 “

If a is less than 7 then there can be three cases in which numbers will be arranged.
• a, 7, greater than 7
o In this case, median is 7.

• a, (less than 7 and greater than a), 7
o In this case, median is certainly less than 7.

• Less than a, a, 7
o In this case, median is a which is less than 7.

In all the cases median is less than 7.
Hence, Statement 1 alone is sufficient to answer the question.

Statement-2: “c>7 “

If c is greater than 7 then there can be some cases in which numbers will be arranged.

• 7, c, greater than c
o In this case, median is c which is greater than 7.

• Less than 7, ,7 c,
o In this case, median is 7.

Since we do not have a unique answer from the two cases, we do not need to check for rest of the cases.
Statement 2 alone is not sufficient to answer the question.

Hence, the correct answer is option A.

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Re: If a,b, and c are positive integers with at least one of  [#permalink]

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20 Jul 2018, 21:52
Chetan2u

Could you please check OA for same
I also got answer as A but OA given is D

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Re: If a,b, and c are positive integers with at least one of  [#permalink]

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24 Jul 2018, 07:44
I think the definition of median is middle number. You can conclusively say 7 of both I and II are provided

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Re: If a,b, and c are positive integers with at least one of  [#permalink]

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15 Aug 2018, 00:13
chetan2u
While posting solutions,Everyone has assumed this series to be an evenly spaced series or set. However, this is not mentioned in the question stem. Does this conclusively apply to gmat questions too ? Please suggest !
Re: If a,b, and c are positive integers with at least one of   [#permalink] 15 Aug 2018, 00:13
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