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# Is √ 1 4 s 2 an integer? s 1 2 is an integer. s 2 is an i

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VP
Joined: 11 Feb 2015
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Is √ 1 4 s 2 an integer? s 1 2 is an integer. s 2 is an i  [#permalink]

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07 Aug 2019, 21:15
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72% (01:09) correct 28% (01:17) wrong based on 46 sessions

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Is $$\sqrt{s^2/4}$$ an integer?

1) s/(1/2) is an integer.

2) s/2 is an integer.

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Manish
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Joined: 01 Jun 2019
Posts: 6
Is √ 1 4 s 2 an integer? s 1 2 is an integer. s 2 is an i  [#permalink]

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07 Aug 2019, 21:40
my pick is - option "B"
as s/2 is integer then s can only be a no. divisible by 2
eg - 2/2, 4/2, ....use this to solve the question - rootS^2/2 = root2^2/2 = 1 (INTEGER)
root4^2/2 = 2 (INTEGER)
( NOTE - "0" is also a valid value in this situation )

Alternative : - the question is simply asking is s/2 an integer.
option B directly says this.
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Joined: 20 Mar 2018
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Is √ 1 4 s 2 an integer? s 1 2 is an integer. s 2 is an i  [#permalink]

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07 Aug 2019, 21:46
Is (s^2/4)^(1/2) =Integer?
Is (s/2)^2^(1/2)= Integer?
Is s/2 =Integer?

(1) s/(1/2) = Integer
2s =Integer —> s= Integer/2
Now when s= 1/2
(s^2/4)^1/2 not an integer
Again, s= 4
(s^2/4)^1/2 is an integer
(Not sufficient)

(2) s/2 is an integer

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Veritas valet et vincet
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Joined: 20 Apr 2019
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Re: Is √ 1 4 s 2 an integer? s 1 2 is an integer. s 2 is an i  [#permalink]

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09 Aug 2019, 00:50
CAMANISHPARMAR wrote:
Is $$\sqrt{s^2/4}$$ an integer?

1) s/(1/2) is an integer.

2) s/2 is an integer.

We are looking whether s is divisable by 2 or not.

I don't understand why 1) is not sufficient. It is clear that 2) is sufficient, but why not 1)? Can someone help please?

1) 2s = integer
If s * 2 is an integer then it must also be divisable by 2 or why not?
Re: Is √ 1 4 s 2 an integer? s 1 2 is an integer. s 2 is an i   [#permalink] 09 Aug 2019, 00:50

# Is √ 1 4 s 2 an integer? s 1 2 is an integer. s 2 is an i

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