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If x is an integer, what is the value of x?

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If x is an integer, what is the value of x? [#permalink]

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If √x is an integer, what is the value of √x?

(1) 11 < x < 17
(2) 2 < √x < 5
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If x is an integer, what is the value of x? [#permalink]

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alokchaks wrote:
(1) The only perfect square in this range is 16. So √x can be +4 or -4. Not Sufficient.
(2) The possible values for √x are 3 and 4. Not sufficient.

Combining (1) and (2), we get √x = 4.
Ans C

Am I missing something?


Square root function cannot give negative result.

Any nonnegative real number has a unique non-negative square root called the principal square root and unless otherwise specified, the square root is generally taken to mean the principal square root.

When the GMAT provides the square root sign for an even root, such as \(\sqrt{x}\) or \(\sqrt[4]{x}\), then the only accepted answer is the positive root.

That is, \(\sqrt{25}=5\), NOT +5 or -5. In contrast, the equation \(x^2=25\) has TWO solutions, +5 and -5. Even roots have only non-negative value on the GMAT.

Odd roots will have the same sign as the base of the root. For example, \(\sqrt[3]{125} =5\) and \(\sqrt[3]{-64} =-4\).
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Re: If x is an integer, what is the value of x? [#permalink]

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Hi Bunuel

In statement 2 3 is not a perfect square and ques says sqrt x is an integer. Please clarify
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New post 02 Jun 2010, 11:41
ajitsah wrote:
If √x is an integer, what is the value of √x?

(1) 11 < x < 17
(2) 2 < √x < 5


If \(\sqrt{x}\) is an integer, what is the value of \(\sqrt{x}\)?

\(\sqrt{x}\) is an integer means that \(x\) is a perfect square.

(1) \(11<x<17\) --> the only perfect square in this range is 16. So \(\sqrt{x}=4\). Sufficient.

(2) \(2<\sqrt{x}<5\) --> \(\sqrt{x}\) can be 3 or 4. Two answers, hence not sufficient.

Answer: A.

Hope it's clear.
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Re: DS - Inequality [#permalink]

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New post 02 Jun 2010, 11:59
i: The only perfect square in this range is 16, so \(sqrt x = 4\); sufficient
ii: \(sqrt x\) can be 3 or 4. insufficient.

Answer is A.
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Re: DS - Inequality [#permalink]

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New post 02 Jun 2010, 18:28
(1) The only perfect square in this range is 16. So √x can be +4 or -4. Not Sufficient.
(2) The possible values for √x are 3 and 4. Not sufficient.

Combining (1) and (2), we get √x = 4.
Ans C

Am I missing something?
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If x is an integer, what is the value of x? (1) [#permalink]

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If √x is an integer, what is the value of √x?
(1) 11<x<17
(2) 2<√x<5
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Re: Square root [#permalink]

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New post 02 May 2011, 05:52
If sqrt(x) is integer then x is integer

From 1) x can be 12,13,14,15,16

Only sqrt(16) is integer. Hence sqrt(x) = 4. Sufficient.

From 2) sqrt(x) can be 3 or 4. x can be 9 or 16. Not sufficient.

Hence A.

jamifahad wrote:
If √x is an integer, what is the value of √x?
(1) 11<x<17
(2) 2<√x<5
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Re: Square root [#permalink]

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New post 02 May 2011, 06:22
Thanks. i was bit confused with (2). sqrt(x) is an integer not x itself hence sqrt(x) can be 3 or 4 with x non-integer and integer respectively.
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Re: Square root [#permalink]

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New post 03 May 2011, 21:04
for B, x^(1/2) = 3,4. Hence POE.
thus A.
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Re: If x is an integer, what is the value of x? (3) [#permalink]

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New post 17 May 2011, 13:12
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: If x is an integer, what is the value of x? (3) [#permalink]

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New post 17 May 2011, 13:29
From 1
what if sqrt x = -4, even then x is 16
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Re: If x is an integer, what is the value of x? (3) [#permalink]

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New post 17 May 2011, 13:49
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: If x is an integer, what is the value of x? (3) [#permalink]

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New post 17 May 2011, 21:51
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: If x is an integer, what is the value of x? (3) [#permalink]

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New post 18 May 2011, 05:30
(1)

x = 16

Sufficient

(2)
x = 9 or 16

Insufficient

Answer - A
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Re: If x is an integer, what is the value of x? (1) [#permalink]

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New post 22 May 2016, 13:00
jamifahad wrote:
If √x is an integer, what is the value of √x?
(1) 11<x<17
(2) 2<√x<5


√x is an integer or x is square of an integer.

(1) 11<x<17
In the given range, only 16 is a number that is square of an integer. Sufficient

(2) 2<√x<5

integers 3 and 4 are between 2 and 5. So possible values van be √9 or √16. Not sufficient.

A is the answer
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Re: If x is an integer, what is the value of x? (1) [#permalink]

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New post 04 Aug 2016, 12:51
Divyadisha wrote:
jamifahad wrote:
If √x is an integer, what is the value of √x?
(1) 11<x<17
(2) 2<√x<5


√x is an integer or x is square of an integer.

(1) 11<x<17
In the given range, only 16 is a number that is square of an integer. Sufficient

(2) 2<√x<5

integers 3 and 4 are between 2 and 5. So possible values van be √9 or √16. Not sufficient.

A is the answer


if x = 16, why are we not considering \sqrt{x} = -4?
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Re: If x is an integer, what is the value of x? (1) [#permalink]

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New post 04 Aug 2016, 14:35
ajiteshdas wrote:
if x = 16, why are we not considering \sqrt{x} = -4?


In the GMAT, the square root refers to only the positive solution. This does not apply to the inverse.

\(\sqrt{16} = 4\\x^2 = 16 \implies x \in \{4,-4\}\)
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