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In the problem statement given it says n is an integer between 2 and 100 and square of n is an integer...does it mean square of n also lies between 2 and 100?How do we know that?

For ex can we say n = 4 and square of n = 16? and can we also say n =100 and square of n =10,000?

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.

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

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09 Jul 2011, 16:43

siddhans wrote:

In the problem statement given it says n is an integer between 2 and 100 and square of n is an integer...does it mean square of n also lies between 2 and 100?How do we know that?

For ex can we say n = 4 and square of n = 16? and can we also say n =100 and square of n =10,000?

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.

See the underline portion: n is square of an integer and lies b/w 2 n 100.

Stment 1: n could be 4 or 36, not sufficient. A & D out Stment 2: N is 64 (sq of 8 and cube of 8). Sufficient.

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09 Jul 2011, 17:05

In the problem statement given it says n is an integer between 2 and 100 and square of n is an integer...does it mean square of n also lies between 2 and 100?How do we know that?

N is between 2 and 100, but N square is between 3^2 and 99^2, inclusive.

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09 Jul 2011, 17:07

Yalephd wrote:

In the problem statement given it says n is an integer between 2 and 100 and square of n is an integer...does it mean square of n also lies between 2 and 100?How do we know that?

N is between 2 and 100, but N square is between 3^2 and 99^2, inclusive.

99^2 will be greater than 100 then so n can be greater than 100?

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09 Jul 2011, 17:32

Let's put it this way. If I say N is an integer greater than 4, but less than 6, you would know that N is 5, right? However, that wouldn't mean that N^2 is also less than 6. N^2 in this case is 25--5^2. I think you are trying to apply the limits established for N to N^2. Don't do that.

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09 Jul 2011, 17:42

2 < n < 100 n = x^2, where x is some integer

1) Not sufficient, various x^2 result in n between the bounds 2) n = y^3

n must be > 2, so y will be > 1 (and an integer, so lets start at 2)

y = 2, n = 8, no integer solution for x y = 3, n = 27, no integer solution for x y = 4, n = 64, x = 8 <--- fits all criteria y = 5, n = 125, out of bounds

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.