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If x is an integer, what is the value of x? (3)

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Senior Manager
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If x is an integer, what is the value of x? (3) [#permalink]  17 May 2011, 12:00
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If √x is an integer, what is the value of √x?
(3) 11<x<17
(4) 2<√x<5
________________________________________________________________
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
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Re: DS - Value of SqRt x [#permalink]  17 May 2011, 12:12
IEsailor wrote:
If √x is an integer, what is the value of √x?
(1) 11<x<17
(2) 2<√x<5
________________________________________________________________
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

$$\sqrt{x}$$ is an integer means x is also an integer.
(1)
11<x<17
x can be 12,13,14,15,16.
But, only 16 will incur an integral root.
Thus; x=16 and $$\sqrt{x}=4$$
Sufficient.

(2)
2<$$\sqrt{x}$$<5
$$\sqrt{x}$$ can be either 3 or 4.
Not Sufficient.

Ans: "A"
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Re: DS - Value of SqRt x [#permalink]  17 May 2011, 12:29
From 1
what if sqrt x = -4, even then x is 16
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Re: DS - Value of SqRt x [#permalink]  17 May 2011, 12:49
IEsailor wrote:
From 1
what if sqrt x = -4, even then x is 16

Here's the rule:
Square root or any positive even root of a positive number will ALWAYS be positive.

$$\sqrt{16}=+4$$
$$\sqrt{36}=+6$$
$$\sqrt[4]{16}=+2$$

But, if $$x^2=16$$
x can be +4 or -4.
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Re: DS - Value of SqRt x [#permalink]  17 May 2011, 12:50
Thanks for that clarification Fluke ...
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Re: DS - Value of SqRt x [#permalink]  17 May 2011, 20:51
a. 16^(1/2) = 4 here.
b 3 or 4 are possible values.

As, (x^2)^1/2 = |x| meaning 4^(1/2) = 2 so, its always a positive value.
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Re: DS - Value of SqRt x [#permalink]  18 May 2011, 04:30
(1)

x = 16

Sufficient

(2)
x = 9 or 16

Insufficient

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Re: DS - Value of SqRt x [#permalink]  18 May 2011, 10:00
Thanks Fluke for clarification
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Re: DS - Value of SqRt x   [#permalink] 18 May 2011, 10:00
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