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# 0 < a < b/2 < 9

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0 < a < b/2 < 9 [#permalink]  12 Aug 2018, 09:46
Expert's post
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Question Stats:

70% (00:56) correct 29% (01:41) wrong based on 58 sessions
$$0 < a < \frac{b}{2} < 9$$

 Quantity A Quantity B $$9-a$$ $$\frac{b}{2} - a$$

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

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[Reveal] Spoiler: OA

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Re: 0 < a < b/2 < 9 [#permalink]  13 Aug 2018, 06:30
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Note that inequalities have many rules similar to equations, and thus we can balance the inequality by subtracting everything by a:

0 < a < b/2 < 9

-a < 0 < b/2 - a < 9 - a

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Re: 0 < a < b/2 < 9 [#permalink]  17 Aug 2018, 13:00
Romang67 wrote:
Note that inequalities have many rules similar to equations, and thus we can balance the inequality by subtracting everything by a:

0 < a < b/2 < 9

-a < 0 < b/2 - a < 9 - a

If it's not too much trouble, could you explain what you mean by balancing the inequality, and why we subtract everything by a to do that? Thank you!
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Re: 0 < a < b/2 < 9 [#permalink]  18 Aug 2018, 02:25
Expert's post
- He actually simplified the inequality and for each term subtracted a.

$$0 < a < \frac{b}{2} < 9$$

using -a

$$-a < 0 < \frac{b}{2} - a < 9 - a$$

As you can see inside the inequality $$\frac{b}{2} - a < 9 - a$$
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Re: 0 < a < b/2 < 9 [#permalink]  18 Aug 2018, 05:48
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Expert's post
Carcass wrote:
$$0 < a < \frac{b}{2} < 9$$

 Quantity A Quantity B $$9-a$$ $$\frac{b}{2} - a$$

GIVEN: 0 < a < b/2 < 9
Subtract a from all sides to get: 0 - a < a - a < b/2 - a < 9 - a
Simplify: -a < 0 < b/2 - a < 9 - a

If we ignore the first two values, we can see that: b/2 - a < 9 - a
Since 9 - a is GREATER THAN b/2 - a, the correct answer is A

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Re: 0 < a < b/2 < 9 [#permalink]  18 Aug 2018, 12:09
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We can easily eliminate -a from the inequality since it's on both the sides. After that, only 9 and b/2 are left, and 9 is bigger is given in the question.
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Re: 0 < a < b/2 < 9 [#permalink]  23 Sep 2018, 21:32
I got this correct! I am improving my quant score.! Gotta top GRE
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Re: 0 < a < b/2 < 9 [#permalink]  12 Jan 2019, 06:59
Adding +a in both the quantities,
Quantity A = 9
Quantity B= b/2
Given that,
b/2 <9, hence Quantity A > Quantity B
Re: 0 < a < b/2 < 9   [#permalink] 12 Jan 2019, 06:59
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