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# M15-09

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Math Expert
Joined: 02 Sep 2009
Posts: 58333

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16 Sep 2014, 00:55
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Difficulty:

5% (low)

Question Stats:

92% (01:19) correct 8% (01:51) wrong based on 48 sessions

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If the value of fraction $$\frac{A}{B}$$ ($$A \lt B$$) will not change if $$A$$ grows by 6 and $$B$$ grows by 15, which of the following is equal to $$\frac{B}{A}$$?

A. 2.0
B. 2.1
C. 2.5
D. 2.8
E. 3.0

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Math Expert
Joined: 02 Sep 2009
Posts: 58333

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16 Sep 2014, 00:55
1
Official Solution:

If the value of fraction $$\frac{A}{B}$$ ($$A \lt B$$) will not change if $$A$$ grows by 6 and $$B$$ grows by 15, which of the following is equal to $$\frac{B}{A}$$?

A. 2.0
B. 2.1
C. 2.5
D. 2.8
E. 3.0

$$\frac{A}{B} = \frac{A + 6}{B + 15}$$. From here $$B(A + 6) = A(B + 15)$$ or $$6B = 15A$$ or $$\frac{B}{A} = \frac{15}{6} = 2.5$$.

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Joined: 08 Jun 2015
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Location: India
GMAT 1: 640 Q48 V29
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09 Jan 2017, 05:58
Given that A/B=(A+6)/(B+15), cross multiply to get the ratio between B and A. The answer comes out to be 2.5 i.e. option C
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" The few , the fearless "
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Joined: 30 Apr 2013
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22 Nov 2017, 00:00
Can we back solve this question anyway?
Manager
Joined: 28 Jun 2018
Posts: 130
Location: Bouvet Island
GMAT 1: 490 Q39 V18
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05 Nov 2018, 10:37
santro789 wrote:
Can we back solve this question anyway?

Hey santro789

Sure u can! But it is just too time consuming.

When back solving always remember to start from the middle option so that you know wether u should test higher values or lower values.
Luckily in this question 2.5 is the middle value and we can arrive at the AC quick.
So since it is a fraction it wont matter if u take A/B as 2/5 or 200/500. Just make sure B/A is equal to 2.5 because we are testing for it.
You will see that by adding the A and B with 6 and 15 will always give us $$\frac{2}{5}$$.
Example - $$\frac{2}{5}$$ is $$\frac{2+6}{5 +15}$$ = $$\frac{8}{20}$$ = $$\frac{2}{5}$$.
Hence C is the option.

Hope it helps!
Intern
Joined: 02 Feb 2018
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23 Nov 2018, 11:29
Bunuel How can we get from 6B=15A to B/A=15/6 without knowing that A is not 0? Thanks!
Intern
Joined: 15 Dec 2018
Posts: 6

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15 Jun 2019, 23:26
Hi Bunuel,

Is the below approach correct.

As mentioned in the question the ratio will not change if 6 is added to A and 15 is added to B.
Thus 6/15 will have the same ratio as A/B.
So to find B/A => just do 15/6 =2.5

Thanks
Re: M15-09   [#permalink] 15 Jun 2019, 23:26
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# M15-09

Moderators: chetan2u, Bunuel