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

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

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New post 21 Sep 2018, 01:35
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A
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  45% (medium)

Question Stats:

57% (00:47) correct 43% (00:54) wrong based on 51 sessions

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

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New post 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

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

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New post 22 Sep 2018, 03:45

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

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New post 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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Re: If √m is an integer, what is the value of √m? &nbs [#permalink] 22 Sep 2018, 09:45
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If √m is an integer, what is the value of √m?

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