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# If n is an integer between 2 and 100 and if n is also the square of

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If n is an integer between 2 and 100 and if n is also the square of [#permalink]

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01 Jun 2011, 14:26
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If n is an integer between 2 and 100 and if n is also the square of an integer, what is the value of n?

(1) n is even

(2) The cube root of n is an integer

[Reveal] Spoiler:
1) Not sufficient because n could be 4, 16, 36, 64, etc.

2) Doesn't between 2 and 100 mean 3 to 99? (I thought between means do not include the end points). Statement 2 says the cube of root n is an integer. Woudln't the cube root of 27 be included? as well as the cube root of 64?

The OG guide says there is only one such value of n between 2 and 100, which is 64.

Thanks for help in advance.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-n-is-an-integer-between-2-and-100-and-if-n-is-also-the-sq-167846.html
[Reveal] Spoiler: OA
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Re: If n is an integer between 2 and 100 and if n is also the square of [#permalink]

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01 Jun 2011, 15:06
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KraZZyiE wrote:
Can someone please help me understand this question.

I have a question about statement 2.....

If n is an integer between 2 and 100 and if n is also the square of an integer, what is the value of n?

1) n is even

2) The cube root of n is an integer

1) Not sufficient because n could be 4, 16, 36, 64, etc.

2) Doesn't between 2 and 100 mean 3 to 99? (I thought between means do not include the end points). Statement 2 says the cube of root n is an integer. Woudln't the cube root of 27 be included? as well as the cube root of 64?

The OG guide says there is only one such value of n between 2 and 100, which is 64.

Thanks for help in advance.

The question stem says that the "n" is square of an integer; 27 is not a square of any integer. Leaves us with just 64, which is 8^2.
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Re: If n is an integer between 2 and 100 and if n is also the square of [#permalink]

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01 Jun 2011, 15:49
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possibilities 4 9 16 25 36 49 64 81

1. Not sufficient

4 or 16 or 36....

2. Sufficient

as 64 is the only number is the above list thats also a cube of an integer.

Answer is B.
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Re: If n is an integer between 2 and 100 and if n is also the square of [#permalink]

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02 Jun 2011, 13:53
thanks. great explanation
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Re: If n is an integer between 2 and 100 and if n is also the square of [#permalink]

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16 Aug 2011, 04:49
thanks for the explanation
according to the quant review and the gmat club error log it is question #110 in the DS section, quant review
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Re: If n is an integer between 2 and 100 and if n is also the square of [#permalink]

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16 Aug 2011, 11:06
wow..i got it rite...B it is
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Re: If n is an integer between 2 and 100 and if n is also the square of [#permalink]

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19 Jan 2016, 10:13
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Re: If n is an integer between 2 and 100 and if n is also the square of [#permalink]

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19 Jan 2016, 11:11
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KraZZyiE wrote:
If n is an integer between 2 and 100 and if n is also the square of an integer, what is the value of n?

(1) n is even

(2) The cube root of n is an integer

[Reveal] Spoiler:
1) Not sufficient because n could be 4, 16, 36, 64, etc.

2) Doesn't between 2 and 100 mean 3 to 99? (I thought between means do not include the end points). Statement 2 says the cube of root n is an integer. Woudln't the cube root of 27 be included? as well as the cube root of 64?

The OG guide says there is only one such value of n between 2 and 100, which is 64.

Thanks for help in advance.

If n is an integer between 2 and 100 and if n is also the square of an integer, what is the value of n?

Given: n is a perfect square between 2 and 100 (a perfect square is an integer that can be written as the square of some other integer, for example 16=4^2, is a perfect square).

(1) n is even --> n can be any even perfect square in the given range: 4, 16, 36, ... Not sufficient.

(2) The cube root of n is an integer --> so n is also a perfect cube between 2 and 100. There are 4 perfect cubes in this range: 2^3=8, 3^3=27 and 4^3=64 but only one of them namely 64 is also a perfect square, so n=64=8^2=4^3. Sufficient.

Answer: B.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-n-is-an-integer-between-2-and-100-and-if-n-is-also-the-sq-167846.html
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Re: If n is an integer between 2 and 100 and if n is also the square of   [#permalink] 19 Jan 2016, 11:11
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