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Is x > 6 ?

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Is x > 6 ? [#permalink]

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Is x > 6 ?

1) \(\sqrt{x} > 2.5\)

2) \(x > \sqrt{37}\)
[Reveal] Spoiler: OA

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Re: Is x > 6 ? [#permalink]

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New post 13 Mar 2016, 14:33
I understand that 1) is SUFFICIENT because x > 6.25 hence x > 6, but not sure why 2) is SUFFICIENT ?

37^1/2 can have two values -6.08 and +6.08. If I consider +6.08 then it is sufficient, but what about the negative value ?

If I take the negative value then x > -6.08 which means x is not > 6. Hence the answer should be A), but the OA is D)

I am sure I am making some mistake, kindly help me to understand if my interpretation of taking a -ve is wrong and why ?
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Is x > 6 ? [#permalink]

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New post 13 Mar 2016, 14:58
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akxshay wrote:
I understand that 1) is SUFFICIENT because x > 6.25 hence x > 6, but not sure why 2) is SUFFICIENT ?

37^1/2 can have two values -6.08 and +6.08. If I consider +6.08 then it is sufficient, but what about the negative value ?

If I take the negative value then x > -6.08 which means x is not > 6. Hence the answer should be A), but the OA is D)

I am sure I am making some mistake, kindly help me to understand if my interpretation of taking a -ve is wrong and why ?


The mistake you are making is that \(x^2 = 36\) has 2 roots \(\pm 6\) (as it is a second degree equation in x) but \(x=\sqrt{36}\) only has 1 solution = +6 as it is a linear equation in x

Thus, from statement 2, \(x > \sqrt{37}\) means that \(x > 6.aaa\) and NOT \(x > - 6.aaa\)

Remember this rule for GMAT.

Thus both statements are sufficient.

D is the correct answer.

Hope this helps.

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Re: Is x > 6 ? [#permalink]

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New post 13 Mar 2016, 15:14
Engr2012 wrote:
The mistake you are making is that \(x^2 = 36\) has 2 roots \(\pm 6\) (as it is a second degree equation in x) but \(x=\sqrt{36}\) only has 1 solution = +6 as it is a linear equation in x

Thus, from statement 2, \(x > \sqrt{37}\) means that \(x > 6.aaa\) and NOT \(x > - 6.aaa\)

Remember this rule for GMAT.

Thus both statements are sufficient.

D is the correct answer.

Hope this helps.



Got it, Thanks a lot ! It does make sense.

Cheers ! :)
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Re: Is x > 6 ? [#permalink]

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New post 13 Mar 2016, 21:01
akxshay wrote:
I understand that 1) is SUFFICIENT because x > 6.25 hence x > 6, but not sure why 2) is SUFFICIENT ?

37^1/2 can have two values -6.08 and +6.08. If I consider +6.08 then it is sufficient, but what about the negative value ?

If I take the negative value then x > -6.08 which means x is not > 6. Hence the answer should be A), but the OA is D)

I am sure I am making some mistake, kindly help me to understand if my interpretation of taking a -ve is wrong and why ?


The square root function cannot give negative result: \(\sqrt{nonnegative \ value}\geq{0}\). For example, \(\sqrt{4}=2\) (not +2 and -2). In contrast, the equation \(x^2=25\) has TWO solutions, +5 and -5, because both 5^2 and (-5)^2 equal to 25.
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Re: Is x > 6 ? [#permalink]

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Re: Is x > 6 ?   [#permalink] 21 Nov 2017, 07:27
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