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# M12-05

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Math Expert
Joined: 02 Sep 2009
Posts: 58464

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16 Sep 2014, 00:46
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Difficulty:

45% (medium)

Question Stats:

66% (01:14) correct 34% (01:15) wrong based on 95 sessions

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If $$a, b, c$$ and $$d$$ are positive numbers, is $$\frac{a}{b} \lt \frac{(a + c)}{(b + d)}$$?

(1) $$\frac{a}{b} \lt \frac{c}{d}$$

(2) $$a + c \lt b + d$$

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Math Expert
Joined: 02 Sep 2009
Posts: 58464

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16 Sep 2014, 00:46
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Official Solution:

Is $$\frac{a}{b} \lt \frac{a+c}{b+d}$$? As all numbers are positive we can safely crossmultiply: is $$ab+ad \lt ab+bc$$? Or: is $$ad \lt bc$$? Or: is $$\frac{a}{b} \lt \frac{c}{d}$$?

(1) $$\frac{a}{b} \lt \frac{c}{d}$$. Directly gives the answer. Sufficient.

(2) $$a+c \lt b+d$$. Not sufficient.

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Joined: 17 Feb 2017
Posts: 5
Location: India
GMAT 1: 670 Q49 V32
GPA: 3.3

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24 Nov 2017, 16:31
Hi.

Sorry I didn't get this right and require further help.

Can you explain a bit and also provide me a link to practice such type of questions?

Thank you.
Math Expert
Joined: 02 Sep 2009
Posts: 58464

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24 Nov 2017, 23:57
jasanisanket24 wrote:
Hi.

Sorry I didn't get this right and require further help.

Can you explain a bit and also provide me a link to practice such type of questions?

Thank you.

Please be more specific when asking a question. Which part of the solution above is confusing?

9. Inequalities

For more check Ultimate GMAT Quantitative Megathread

Hope it helps.
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Joined: 21 Jan 2019
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28 Jan 2019, 01:46
Could you please explain more why (2) a+c<b+da+c<b+d is Not sufficient? Thank you!
Math Expert
Joined: 02 Sep 2009
Posts: 58464

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28 Jan 2019, 01:56
pero88 wrote:
Could you please explain more why (2) a+c<b+da+c<b+d is Not sufficient? Thank you!

The question asks: is $$ad \lt bc$$?

(2) says: $$a+c \lt b+d$$.

Pick numbers.

If $$a=d=c=1$$ and $$b=2$$, then $$ad \lt bc$$
If $$a=c=1$$, $$b=2$$, and $$d=3$$ then $$ad \gt bc$$
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Re: M12-05   [#permalink] 28 Jan 2019, 01:56
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# M12-05

Moderators: chetan2u, Bunuel