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Bunuel
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If √m is an integer, what is the value of √m? 21 Sep 2018, 01:35
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64% (00:58) correct 36% (01:06) wrong based on 212 sessions

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

(1) 13 ≤ m ≤ 16
(2) 3 ≤ √m ≤ 4
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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

Answer: Option A
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If √m is an integer, what is the value of √m? 22 Sep 2018, 03:45
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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.

Answer: A
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If √m is an integer, what is the value of √m? 22 Sep 2018, 09:45
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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? 29 Jan 2019, 11:01
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mitrakaushi
But root m could be both +4 and -4. We wont get a unique solution. Why is A sufficient?
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I have the same confusion. Bunuel, Could you please clarify ?
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If √m is an integer, what is the value of √m? 29 Jan 2019, 11:34
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shaanaa22
mitrakaushi
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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\(\sqrt{...}\) 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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If √m is an integer, what is the value of √m? 30 Jan 2019, 08:52
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Bunuel
shaanaa22
mitrakaushi
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 \(x=\sqrt{9}=3\).
Show more


Thank you so much for the response, Bunuel! It was really helpful.
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