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# What is the value of even positive integer n?

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Manager
Joined: 03 Dec 2014
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What is the value of even positive integer n?  [#permalink]

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31 Mar 2016, 10:13
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75% (hard)

Question Stats:

48% (01:52) correct 52% (02:04) wrong based on 276 sessions

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What is the value of even positive integer n?
(1) The number of ways to choose 2 items out of n distinct items is 28
(2) The number of ways to choose 2 prime numbers out of the first n/2 positive integers is 1
Magoosh GMAT Instructor
Joined: 28 Dec 2011
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What is the value of even positive integer n?  [#permalink]

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31 Mar 2016, 14:55
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robu wrote:
What is the value of even positive integer n?
(1) The number of ways to choose 2 items out of n distinct items is 28
(2) The number of ways to choose 2 prime numbers out of the first n/2 positive integers is 1

Dear robu,
I'm happy to respond. I'm quite curious about the source of this question, as it doesn't seem a particularly GMAT-like question.

Statement #1: combinations have a fixed pattern, so if we know nC2 = 28, there would be only one possibility for n. As it happens, n = 8, but that knowledge is not needed for this question. The first statement, alone and by itself, is sufficient.

Statement #2: the first two prime numbers are 2 and 3. These would be the only prime numbers among the first 3 positive integers or the first among the first 4 positive. This means n = 6 or n = 8. Two possible values. Not sufficient.

Mike
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Re: What is the value of even positive integer n?  [#permalink]

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01 May 2017, 22:17
The language of the question is tricky:

What is the value of even positive integer n?
(1) The number of ways to choose 2 items out of n distinct items is 28

nC2=28; n(n-1)=56; n=8 or n=7

given that n=even so n=8

Suff.

(2) The number of ways to choose 2 prime numbers out of the first n/2 positive integers is 1

Since the number of ways to choose 2 prime numbers is 1, we are looking at first two prime numbers i.e. 2 and 3.

The next prime number is 5.

We need 2 prime numbers out of the first n/2 positive integers ; we get that within first 3 positive integers or first 4 positive integers. If we consider first 5 positive integers then we have 2,3 and 5 and the number of ways to select 2 prime numbers from 3 won't be 1.

so n/2=3 or n/2=4

Two diff values. Not suffi.

Option A
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What is the value of even positive integer n?  [#permalink]

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12 Jan 2019, 11:29
robu wrote:
What is the value of even positive integer n?
(1) The number of ways to choose 2 items out of n distinct items is 28
(2) The number of ways to choose 2 prime numbers out of the first n/2 positive integers is 1

N = +ive Even Integer

(1)
nC2 => n(n-1)/2 = 28
n(n-1) = 56
Only one case possible 8*7.
Sufficient

(2) 2 prime numbers out of the first n/2 positive integers is 1
this can have multiple values for n, 6 or 10.

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What is the value of even positive integer n?   [#permalink] 12 Jan 2019, 11:29
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