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# If √m is an integer, what is the value of √m?

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Math Expert
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If √m is an integer, what is the value of √m?  [#permalink]

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21 Sep 2018, 01:35
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If √m is an integer, what is the value of √m?

(1) 13 ≤ m ≤ 16
(2) 3 ≤ √m ≤ 4

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

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21 Sep 2018, 01:46
Bunuel wrote:
If √m is an integer, what is the value of √m?

(1) 13 ≤ m ≤ 16
(2) 3 ≤ √m ≤ 4

Given: $$√m = Integer$$

Question: what is the value of √m?

Statement 1: 13 ≤ m ≤ 16

i.e. $$√13 ≤ √m ≤ √16$$

i.e. $$3.6 ≤ √m ≤ 4$$

Only possible integer value of $$√m = 4$$
i.e. m = 16
SUFFICIENT

Statement 2: $$3 ≤ √m ≤ 4$$

i.e. m may be 9 or 16 and $$√m$$ may be 3 or 4 hence

NOT SUFFICIENT

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Re: If √m is an integer, what is the value of √m?  [#permalink]

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22 Sep 2018, 03:45
1

Solution

Given:
• √m is an integer

To find:
• The value of √m

Analysing Statement 1
From the information given in statement 1, 13 ≤ m ≤ 16.

• As √m is an integer, m must be a perfect square.
In the given range 13 ≤ m ≤ 16, only one perfect square exists, which is 16.

Therefore, we can find unique value of √m.

Hence, statement 1 is sufficient.

Analysing Statement 2
From the information given in statement 2, 3 ≤ √m ≤ 4.
• From this statement, we can say √m can be either 3 or 4.

Hence, statement 2 is not sufficient.

The correct answer is option A.

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Re: If √m is an integer, what is the value of √m?  [#permalink]

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22 Sep 2018, 09:45
But root m could be both +4 and -4. We wont get a unique solution. Why is A sufficient?
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If √m is an integer, what is the value of √m?  [#permalink]

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29 Jan 2019, 11:01
mitrakaushi wrote:
But root m could be both +4 and -4. We wont get a unique solution. Why is A sufficient?

I have the same confusion. Bunuel, Could you please clarify ?
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Posts: 58378
Re: If √m is an integer, what is the value of √m?  [#permalink]

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29 Jan 2019, 11:34
2
shaanaa22 wrote:
mitrakaushi wrote:
But root m could be both +4 and -4. We wont get a unique solution. Why is A sufficient?

I have the same confusion. Bunuel, Could you please clarify ?

$$\sqrt{...}$$ is the square root sign, a function (called the principal square root function), which cannot give negative result. So, this sign ($$\sqrt{...}$$) always means non-negative square root.

The graph of the function f(x) = √x

Notice that it's defined for non-negative numbers and is producing non-negative results.

TO SUMMARIZE:
When the GMAT provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the non-negative root. That is:

$$\sqrt{9} = 3$$, NOT +3 or -3;
$$\sqrt[4]{16} = 2$$, NOT +2 or -2;

Notice that in contrast, the equation $$x^2 = 9$$ has TWO solutions, +3 and -3. Because $$x^2 = 9$$ means that $$x =-\sqrt{9}=-3$$ or $$x=\sqrt{9}=3$$.
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Re: If √m is an integer, what is the value of √m?  [#permalink]

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30 Jan 2019, 08:52
Bunuel wrote:
shaanaa22 wrote:
mitrakaushi wrote:
But root m could be both +4 and -4. We wont get a unique solution. Why is A sufficient?

I have the same confusion. Bunuel, Could you please clarify ?

$$\sqrt{...}$$ is the square root sign, a function (called the principal square root function), which cannot give negative result. So, this sign ($$\sqrt{...}$$) always means non-negative square root.

The graph of the function f(x) = √x

Notice that it's defined for non-negative numbers and is producing non-negative results.

TO SUMMARIZE:
When the GMAT provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the non-negative root. That is:

$$\sqrt{9} = 3$$, NOT +3 or -3;
$$\sqrt[4]{16} = 2$$, NOT +2 or -2;

Notice that in contrast, the equation $$x^2 = 9$$ has TWO solutions, +3 and -3. Because $$x^2 = 9$$ means that $$x =-\sqrt{9}=-3$$ or $$x=\sqrt{9}=3$$.

Thank you so much for the response, Bunuel! It was really helpful.
Re: If √m is an integer, what is the value of √m?   [#permalink] 30 Jan 2019, 08:52
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