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14 Jan 2015, 02:35
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
68% (01:52) correct
32%
(01:59)
wrong
based on 424
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If y is an integer such that 2 < y < 100 and if y is also the square of an integer, what is the value of y ?
(1) y has exactly two distinct prime factors
(2) y is even.
(1) y has exactly two distinct prime factors
(2) y is even.
14 Jan 2015, 11:15
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First, let's rewrite the question stem. We know that y is a perfect square. Therefore \(2\leq\sqrt{y}\leq 9\), because \(2 < y < 100\).
Now, we can have a look at the 2 statements:
(1): We are told that y has exactly two prime factors. Since squaring an integer does not create any new prime factors and y can't be a prime itself, we know that \(\sqrt{y} = p_1* p_2\), where \(p_1\) and \(p_2\) are the two prime factors. Checking the integers between 2 and 9 inclusive, we see that the only number for which that is the case is 6. It has the prime factors 2 and 3. Therefore \(\sqrt{y}=6\) and \(y=36\).
This statement is sufficient.
(2): We are told that y is even. However, there are several perfect squares between 2 and 100: 4, 16, 36, 64. Therefore, this statement is not sufficient.
Answer A.
Now, we can have a look at the 2 statements:
(1): We are told that y has exactly two prime factors. Since squaring an integer does not create any new prime factors and y can't be a prime itself, we know that \(\sqrt{y} = p_1* p_2\), where \(p_1\) and \(p_2\) are the two prime factors. Checking the integers between 2 and 9 inclusive, we see that the only number for which that is the case is 6. It has the prime factors 2 and 3. Therefore \(\sqrt{y}=6\) and \(y=36\).
This statement is sufficient.
(2): We are told that y is even. However, there are several perfect squares between 2 and 100: 4, 16, 36, 64. Therefore, this statement is not sufficient.
Answer A.
14 Jan 2015, 11:17
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Bunuel
Question says, that y is between 2 and 100. And Y is square of an integer. In that case we have following squares below 100.
Y should be either of 4,9,16,25,36,49,64,81.
Statement-1 : It says Y has 2 DISTINCT Prime Factors. So eliminate all the odd numbers as they have only one prime factors(3 apart from prime factorization of 49 which has 7) in it.
We are left with even numbers(4,16,36,64)-- In this eliminate 4, 16 and 64. These got 2 has their only prime factor. But when we do prime factorization,
\(36= 2^2 * 3^2\). We get 2 distinct prime factors- 2 and 3.
So sufficient.
Statement-2 : Doesn't say anything other than y is even number. Not sufficient as we have 48 even numbers between 2 and 100,
So Statement-1 is sufficient. Answer is A.
Also, we can verify that our answer (y=36) is correct as statement-2 says y is even. And in GMAT DS, the statements never contradicts each other.
Bunuel, Please post your explanation
Hope i made my choice justifiable :D
