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03 Sep 2018, 02:20
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
65% (01:05) correct
35%
(01:18)
wrong
based on 31
sessions
History
Date
Time
Result
Not Attempted Yet
If \(Y\) is a prime number, how many divisors does \(8Y\) have?
(1) \(Y > 2\)
(2) \(Y\) is an odd integer.
(1) \(Y > 2\)
(2) \(Y\) is an odd integer.
03 Sep 2018, 02:20
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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
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
07 Sep 2018, 01:43
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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?
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?
