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Set A contains n distinct positive integers, all greater than 1. If th

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Set A contains n distinct positive integers, all greater than 1. If th  [#permalink]

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GMATbuster's Weekly Quant Quiz#10 Ques #6


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Set A contains n distinct positive integers, all greater than 1. If the number of even integers in the set is 5 and the set also contains 4 odd prime numbers, what is the value of n?
(1) The set contains 2 odd composite numbers.
(2) The set contains 6 composite numbers.

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Re: Set A contains n distinct positive integers, all greater than 1. If th  [#permalink]

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New post 24 Nov 2018, 09:59
A.
in the question statement we are given about even numbers and odd prime numbers. The only thing missing is number of odd composite numbers.
So statement one will be sufficient for that.

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Re: Set A contains n distinct positive integers, all greater than 1. If th  [#permalink]

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New post 24 Nov 2018, 10:21
Given: No. of even integers in the set = 5, no. of odd primes = 4

(1) Set contains 2 odd composite numbers, so total odd numbers = total odd comp + total odd prime = 2 + 4 = 6
Total even numbers = 5
So, total numbers = 5 + 6 = 11, Hence Sufficient.

(2) Set has 6 composite numbers. Now here we can have two cases:
2 is a prime number and even. So out of 5 even integers, we can have the following cases:
Case 1: All 5 even integers are composite, i.e. 2 is not a part of the set. Then, remaining 6-5 = 1 composite integer is odd.
So, total odd = 1 composite + 4 prime = 5
total even = 5
Total numbers = 5 + 5 = 10

Case 2: 4 even integers are composite and the other even integer is 2 which is prime.
Then, remaining 6 - 4 = 2 composite numbers are odd.
So, total odd = 2 composite + 4 prime = 6
total even = 5

Total numbers = 5 + 6 = 11

hence statement (2) is Insufficient.

Hence Option A!
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Re: Set A contains n distinct positive integers, all greater than 1. If th &nbs [#permalink] 24 Nov 2018, 10:21
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