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• ### $450 Tuition Credit & Official CAT Packs FREE December 15, 2018 December 15, 2018 10:00 PM PST 11:00 PM PST Get the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### FREE Quant Workshop by e-GMAT! December 16, 2018 December 16, 2018 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score. # 9^{a+2b}/3^{a+3b}=?  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6639 GMAT 1: 760 Q51 V42 GPA: 3.82 9^{a+2b}/3^{a+3b}=? [#permalink] ### Show Tags 27 Dec 2017, 00:02 00:00 Difficulty: 25% (medium) Question Stats: 74% (00:55) correct 26% (02:05) wrong based on 64 sessions ### HideShow timer Statistics [GMAT math practice question] $$\frac{9^{a+2b}}{3^{a+3b}}=?$$ 1) $$a+b=2$$ 2) $$a-b=3$$ _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Joined: 08 Oct 2017
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9^{a+2b}/3^{a+3b}=?  [#permalink]

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27 Dec 2017, 03:35
$$\frac{9^{a+2b}}{3^{a+3b}}$$=$$\frac{3^{2(a+2b)}}{3^{a+3b}}$$=$$3^{2a+4b-a-3b}$$= $$3^{a+b}$$

1) a+b=2
Hence $$3^{a+b}$$ = $$3^2$$
Data (1) itself sufficient to sole the problem

2) a−b=3

Data (2) itself is insufficient to sole the problem

Hence the answer is A
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6639
GMAT 1: 760 Q51 V42
GPA: 3.82
9^{a+2b}/3^{a+3b}=?  [#permalink]

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28 Dec 2017, 21:51
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.

Modifying the question:
$$\frac{9^{a+2b}}{3^{a+3b}}=?$$
$$⇔ \frac{(3^2)^{a+2b}}{3^{a+3b}}=?$$
$$⇔ \frac{3^{2a+4b}}{3^{a+3b}}=?$$
$$⇔ 3^{a+b}=?$$

Condition 1)
Since the exponent is $$a + b$$, this condition is sufficient.

Condition 2)
The value of $$a – b$$ does not tell us anything about the value of $$a + b$$.
For example, if $$a = 6$$ and $$b = 3$$, $$a + b = 9$$; and if $$a = 7$$ and $$b = 4, a + b = 11$$.
Since there is no unique answer, condition 2) is NOT sufficient.

Therefore, the answer is A.

Answer: A
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9^{a+2b}/3^{a+3b}=? &nbs [#permalink] 28 Dec 2017, 21:51
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# 9^{a+2b}/3^{a+3b}=?

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