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M70-05

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M70-05  [#permalink]

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New post 03 Sep 2018, 01:20
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

100% (00:18) correct 0% (00:00) wrong based on 10 sessions

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Re M70-05  [#permalink]

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New post 03 Sep 2018, 01:20
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.


Answer: D
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Re: M70-05  [#permalink]

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New post 07 Sep 2018, 00:43
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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Re: M70-05  [#permalink]

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New post 07 Sep 2018, 00:45
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Re: M70-05  [#permalink]

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New post 26 Sep 2018, 11:41
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.
So answer is E
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Re: M70-05  [#permalink]

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New post 02 Oct 2018, 04:51
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.
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Re: M70-05 &nbs [#permalink] 02 Oct 2018, 04:51
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