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31 Mar 2016, 10:13
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
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Question Stats:
49% (01:50) correct
51%
(01:59)
wrong
based on 416
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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
(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
31 Mar 2016, 14:55
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robu
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.
Answer = (A)
Mike
01 May 2017, 22:17
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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
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
