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# M70-05

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Math Expert
Joined: 02 Sep 2009
Posts: 49258

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03 Sep 2018, 02:20
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80% (00:22) correct 20% (00:20) wrong based on 5 sessions

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If $$Y$$ is a prime number, how many divisors does $$8Y$$ have?

(1) $$Y > 2$$

(2) $$Y$$ is an odd integer.

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Joined: 02 Sep 2009
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03 Sep 2018, 02:20
Official Solution:

We’ll go for PRECISE because all the numbers we need are in the question.

Divisors of $$Y$$ are 1 and $$Y$$. Divisors of 8 are 1, 2, 4 and 8. Divisors of $$8Y$$ are all the divisors of 8 and $$Y$$ put together. Since 1 is a divisor of both 8 and $$Y$$, we’ll count it only once. Similarly, if $$Y$$ were a divisor of 8, we’d count it only once too. Only 2 is a prime divisor of 8. Since $$Y$$ is prime, if $$Y$$ is 2, the total number of divisors of $$8Y$$ is 4. If $$Y$$ is not 2, the total number of divisors is 5.

Statement (1) tells us definitively that $$Y$$ isn’t equal to 2. Enough! (B), (C) and (E) are eliminated. Statement (2) also gives us the same information, since 2 is an even number. (A) is also eliminated.

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Joined: 28 Aug 2018
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07 Sep 2018, 01:43
For statement 2:
If Y=1, then 8Y=8, which has 4 divisors (1,2,4,8);
if Y=3, then 8Y=24, which has 8 divisors (1,2,3,4,6,8,12,24).
So how statement 2 is sufficient?
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07 Sep 2018, 01:45
nishantneuton wrote:
For statement 2:
If Y=1, then 8Y=8, which has 4 divisors (1,2,4,8);
if Y=3, then 8Y=24, which has 8 divisors (1,2,3,4,6,8,12,24).
So how statement 2 is sufficient?

We are told that y is a prime number. 1 is not a prime number.
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Re: M70-05 &nbs [#permalink] 07 Sep 2018, 01:45
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# M70-05

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