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# M70-05

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Math Expert
Joined: 02 Sep 2009
Posts: 59730

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03 Sep 2018, 02:20
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Difficulty:

35% (medium)

Question Stats:

75% (00:32) correct 25% (01:28) wrong based on 20 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.

The divisors of $$Y$$ are 1 and $$Y$$ and the divisors of 8 are 1, 2, 4, and 8. Then the divisors of $$8Y$$ are all combinations of these numbers: 1, 2, 4, 8, Y, 2Y, 4Y, 8Y. If $$Y = 2$$, then some of these divisors overlap: $$Y=2$$, $$2y=4$$ and $$4Y=8$$ so our list of divisors has only 5 distinct numbers: 1, 2, 4, 8, 16. If $$Y$$ is not 2, then all the numbers are distinct and we have 8 total divisors.

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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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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26 Sep 2018, 12:41
Bunuel wrote:
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.

Take a case of Y=11, in that case
8Y = 88 can have divisors(1,2,4,8,11,22,44,88) not equal to 5.
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02 Oct 2018, 05:51
1
If Y is a prime number greater than 2, 8Y will ALWAYS have 8 total factors, regardless of Y's actual value.

The only instance when 8Y does not have 8 total factors is when Y=2. This situation is remedied in both statements I and II. Hence the answer is D.
Re: M70-05   [#permalink] 02 Oct 2018, 05:51
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# M70-05

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