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# I encountered this on the powerprep. If set S consists of

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I encountered this on the powerprep. If set S consists of [#permalink]

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04 Apr 2010, 12:46
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I encountered this on the powerprep.

If set S consists of the numbers 1,5,-2,8 and n, is 0 < n < 7?

(1) The median of the numbers in S is less than 5
(2) The median of the numbers in S is greater than 5

The software says the correct answer is C. I thought it would be A. I can't figure out why we need (2) to determine the answer.

Thanks,
arl
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Re: Numbers problem [#permalink]

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04 Apr 2010, 21:39
arlgmat wrote:
I encountered this on the powerprep.

If set S consists of the numbers 1,5,-2,8 and n, is 0 < n < 7?

(1) The median of the numbers in S is less than 5
(2) The median of the numbers in S is greater than 5

The software says the correct answer is C. I thought it would be A. I can't figure out why we need (2) to determine the answer.

Thanks,
arl

n can be 1,2,3,4,5,6
1: Not enough if median is less than 5, then n can be any value less than 5 so n<5 even negative so the condition 0<n<7 is not hold fully.
2: Not enough if median is more than 5, then n can be any value more than 5 so n>5 even more than 7.
I dont think you the choices can be combined.
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Re: Numbers problem [#permalink]

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04 Apr 2010, 23:40
arlgmat wrote:
I encountered this on the powerprep.

If set S consists of the numbers 1,5,-2,8 and n, is 0 < n < 7?

(1) The median of the numbers in S is less than 5
(2) The median of the numbers in S is greater than 5

The software says the correct answer is C. I thought it would be A. I can't figure out why we need (2) to determine the answer.

Thanks,
arl

stmt 2 doesn't sound right. Are you sure it's accurate.
If the series is 1,5,2,-8,n whatever n value might be median can't be greater than 5.
Since there are 5 elements the 3rd element in the ascending order should be the median.

If n <1 median =1
If 1<n<5 median =n
If n>5 median =5
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Re: Numbers problem [#permalink]

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05 Apr 2010, 08:52
Yeah, its a bug. How can the median simultaneously be > and < 5?
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Re: Numbers problem [#permalink]

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05 Apr 2010, 08:58
The second statement doesn't make sense... the median cant be greater than 5
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Median- Data Sufficiency- Gmat Prep [#permalink]

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17 Dec 2010, 10:47
Could anyone please provide a solution for this question?
Thanks.

OA:C
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Re: Median- Data Sufficiency- Gmat Prep [#permalink]

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17 Dec 2010, 11:09
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helloanupam wrote:
Can someone please give an explanation for this question?
Thanks.

Firs of all statement (2) should read: The median of the numbers in S is greater than 1.

If set S consists of the numbers 1, 5,-2, 8 and n, is 0 < n < 7?

Note that:
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 our set of 5 numbers: {-2, 1, 5, 8, n} must be the middle number, so it can be:
1 if $$n\leq{1}$$;
5 if $$n\geq{5}$$;
$$n$$ itself if $$1\leq{n}\leq{5}$$.

(1) The median of the numbers in S is less than 5 --> so either the median=1 and in this case $$n\leq{1}$$ so not necessarily in the range $$0<n<7$$ or median=n and in this case $$1\leq{n}<{5}$$ and in this case $$0<n<7$$ is always true. Not sufficient.

(2) The median of the numbers in S is greater than 1 --> again either the median=5 and in this case $$n\geq{5}$$ so not necessarily in the range $$0<n<7$$ or median=n and in this case $$1<{n}\leq{5}$$ and in this case $$0<n<7$$ is always true. Not sufficient.

(1)+(2) $$1<median<5$$ --> $$median=n$$ --> $$1<n<5$$, so $$0<n<7$$ is true. Sufficient.

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Re: Numbers problem [#permalink]

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17 Dec 2010, 12:22
Thankyou Bunuel. Super fast and super clear explanation.
Re: Numbers problem   [#permalink] 17 Dec 2010, 12:22
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# I encountered this on the powerprep. If set S consists of

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