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.
Answer =
(A) Mike
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Mike McGarry
Magoosh Test PrepEducation is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)