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If y is an integer such that 2 < y < 100 and if y is also the square

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If y is an integer such that 2 < y < 100 and if y is also the square  [#permalink]

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New post 14 Jan 2015, 02:35
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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.

Kudos for a correct solution.

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Re: If y is an integer such that 2 < y < 100 and if y is also the square  [#permalink]

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New post 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.
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Re: If y is an integer such that 2 < y < 100 and if y is also the square  [#permalink]

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New post 14 Jan 2015, 11:17
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Bunuel wrote:
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.

Kudos for a correct solution.


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
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Re: If y is an integer such that 2 < y < 100 and if y is also the square  [#permalink]

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New post 07 Feb 2015, 11:30
Yes I did the same:

2<y<100
y = square of integer
y = 4,9,16,25,36,49,64,81.

[1] y has 2 distinct prime factors
Only the prime factorization of 36 has 2 different primes: 36 = 2*3*2*3. S

[2] y = even. NS

So, ANS A
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Re: If y is an integer such that 2 < y < 100 and if y is also the square  [#permalink]

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New post 19 May 2015, 10:24
A

Listed all squares below 100
4 9 ... 81
then did prime factorization keeping in mind 2 ,3, 5,7

arrived at 36

hence a is sufficient as its the only one.

using b) 4,16 ... are also included , hence not sufficient.
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Re: If y is an integer such that 2 < y < 100 and if y is also the square  [#permalink]

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New post 28 Jun 2018, 18:05
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Re: If y is an integer such that 2 < y < 100 and if y is also the square &nbs [#permalink] 28 Jun 2018, 18:05
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