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# If A and B are positive is A greater than B ?

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Intern
Joined: 05 Mar 2018
Posts: 33
If A and B are positive is A greater than B ?  [#permalink]

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Updated on: 03 Sep 2018, 19:41
00:00

Difficulty:

25% (medium)

Question Stats:

83% (00:59) correct 17% (01:02) wrong based on 22 sessions

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If A and B are positive is A greater than B ?

(1) A=5
(2) 2A = 5B

Originally posted by Nirenjan on 03 Sep 2018, 07:39.
Last edited by Bunuel on 03 Sep 2018, 19:41, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
GMATH Teacher
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Re: If A and B are positive is A greater than B ?  [#permalink]

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03 Sep 2018, 14:03
Nirenjan wrote:
If A and B are positive is A greater than B ?

1) A = 5
2) 2A = 5B

$$A,B\,\,\, > 0$$

$$A\,\,\mathop > \limits^? \,B$$

$$\left( 1 \right)\,\,A = 5\,\,\,\left\{ \begin{gathered} \,{\text{If}}\,\,\,\,B = 1\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{YES}}} \right\rangle \hfill \\ \,{\text{If}}\,\,\,\,B = 5\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{NO}}} \right\rangle \hfill \\ \end{gathered} \right.$$

$$\left( 2 \right)\,\,2A = 5B\,\,\,\, \Rightarrow \,\,\,\,A = \frac{5}{2}B\,\,\mathop > \limits^{\left( * \right)} \,\,B\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{YES}}} \right\rangle$$

$$\left( * \right)\,\,\,\frac{5}{2} > 1\,\,\,\,\mathop \Rightarrow \limits^{ \cdot \,B\,\,\left( {B\, > \,0} \right)} \,\,\,\frac{5}{2}\left( B \right) > 1 \cdot B\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\frac{5}{2}B > B\,$$

Conclusion: the right answer is (B).

The above follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.
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Re: If A and B are positive is A greater than B ?  [#permalink]

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04 Sep 2018, 09:45
From statement 1:

Hence insufficient.

From statement 2:

2A = 5B
Or A = 2.5B
Clearly A is greater than B.
2 is sufficient.

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Re: If A and B are positive is A greater than B ?  [#permalink]

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04 Sep 2018, 09:48
Stat 1 is not sufficient
In stat 2 A=2.5*B
And since both are positive integers A will be greater
B should be correct choice
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Re: If A and B are positive is A greater than B ?   [#permalink] 04 Sep 2018, 09:48
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