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Let an infinite series of positive integers be termed "pure"

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Let an infinite series of positive integers be termed "pure"  [#permalink]

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New post 16 Apr 2018, 11:49
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Let an infinite series of positive integers be termed "pure" if it contains no numbers divisible by 3 or by 7. Is infinite series M "pure"?

1) M contains only prime numbers.
2) The ones digit of all members of M is either 3 or 7.

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Re: Let an infinite series of positive integers be termed "pure"  [#permalink]

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New post 16 Apr 2018, 21:34
itisSheldon wrote:
Let an infinite series of positive integers be termed "pure" if it contains no numbers divisible by 3 or by 7. Is infinite series M "pure"?

1) M contains only prime numbers.
2) The ones digit of all members of M is either 3 or 7.


So we need to know whether M has any integer divisible by either 3 or 7 (or both) or not.

(1) It contains only prime numbers, 3 and 7 are also prime, but we are not given whether it contains 3/7 or not. If M contains at least one of 3/7, then the answer to the question asked is NO, but otherwise, the answer to the question asked is YES. Not sufficient.

(2) Numbers whose ones digit is 3/7 might or might not be divisible by either 3 or 7, so we cant say. Eg, 63 ends in 3 and it is divisible by both 3 and 7. 53 ends in 3 but it is divisible by neither 3 nor 7. So we cant say. Not sufficient.

Combining the statements, M contains only prime numbers ending in either 3 or 7. But we still dont know whether it contains at least one number out of '3' and '7'. Because if it contains either 3 or 7, then the answer to the question asked is NO. But if M does not contain 3 or 7, then it contains prime numbers (except 3/7) which end in either 3 or 7. So M might contain one or more of :- 13, 17, 23, 37, 43, 47..etc, and in this case answer to the question asked will be YES.
Not sufficient. thus answer is E.
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Re: Let an infinite series of positive integers be termed "pure" &nbs [#permalink] 16 Apr 2018, 21:34
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Let an infinite series of positive integers be termed "pure"

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