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# 2>3a>0

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2>3a>0 [#permalink]  04 Jul 2019, 07:11
Expert's post
00:00

Question Stats:

89% (00:27) correct 10% (00:14) wrong based on 48 sessions
$$2>3a>0$$

 Quantity A Quantity B $$a$$ $$a^2$$

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Kudos [?]: 3975 [0], given: 65

Re: 2>3a>0 [#permalink]  04 Jul 2019, 09:57
Expert's post
Carcass wrote:
$$2>3a>0$$

 Quantity A Quantity B $$a$$ $$a^2$$

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

We can solve this question using matching operations

Given:
Quantity A: $$a$$
Quantity B: $$a^2$$

Since we're told $$a$$ is POSITIVE, we can safely divide both quantities by $$a$$ to get:
Quantity A: $$1$$
Quantity B: $$a$$

Now take the given information: $$2>3a>0$$

Divide all parts by 3 to get: $$\frac{2}{3}>a>0$$

Since $$a<\frac{2}{3}$$, it must be the case that $$a<1$$

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Kudos [?]: 20 [1] , given: 14

Re: 2>3a>0 [#permalink]  30 Jun 2020, 02:56
1
KUDOS
Here is my solution.
Notice that 2>3a>0, a here must be fraction.
QA a
QB a^2
when squaring a fraction it gets smaller, answer must be A.
Re: 2>3a>0   [#permalink] 30 Jun 2020, 02:56
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