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Is a>2?

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Is a>2? [#permalink]

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New post 29 Nov 2017, 13:03
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Question Stats:

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Is \(a>2\)

(1) \(\frac{1}{a} < \frac{1}{2}\)

(2) \(\sqrt{a} > \sqrt{2}\)

[Reveal] Spoiler:
Few questions:
1. if a>b, can we say 1/a <1/b
2. Can we square an inequality? Both sides should be +ve or both sides should be -ve?
[Reveal] Spoiler: OA

Last edited by Bunuel on 29 Nov 2017, 19:47, edited 1 time in total.
Edited the question and added the OA.

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Re: Is a>2? [#permalink]

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New post 29 Nov 2017, 21:23
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(1) 1/a < 1/2 or 2/a < 1
Now if 'a' is positive, we can multiply both sides by 'a' to get 2 < a
But if 'a' is negative, we will multiply both sides by 'a' to get 2 > a (sign of inequality will change)
So we cannot be sure. Eg, 'a' could take any negative value and thus 1/a < 1/2. But if 'a' is positive, all its values will be > 2.
Insufficient.

(2) √a > √2
Since its a square root sign, 'a' cannot be negative. 'a' has to be a non negative number.
So we can take square both sides to get
a > 2
Sufficient.

Hence B answer

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Re: Is a>2? [#permalink]

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New post 29 Nov 2017, 21:47
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lakers617 wrote:
Is \(a>2\)

(1) \(\frac{1}{a} < \frac{1}{2}\)

(2) \(\sqrt{a} > \sqrt{2}\)

[Reveal] Spoiler:
Few questions:
1. if a>b, can we say 1/a <1/b
2. Can we square an inequality? Both sides should be +ve or both sides should be -ve?


Adding, subtracting, squaring etc.: Manipulating Inequalities.

9. Inequalities



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Re: Is a>2? [#permalink]

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New post 30 Nov 2017, 06:49
Thanks a lot Bunnuel and amanvermagmat

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Re: Is a>2? [#permalink]

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New post 04 Dec 2017, 10:44
lakers617 wrote:
Is \(a>2\)

(1) \(\frac{1}{a} < \frac{1}{2}\)

(2) \(\sqrt{a} > \sqrt{2}\)


Statement One Alone:

1/a < 1/2

If a > 0, then a is indeed greater than 2. However, if a < 0, then a is less than 2. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

√a > √2

Squaring both sides we have: a > 2. Statement two alone is sufficient to answer the question.

Answer: B
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Re: Is a>2?   [#permalink] 04 Dec 2017, 10:44
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