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# 9^{a+2b}/3^{a+3b}=?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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27 Dec 2017, 00:02
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Difficulty:

35% (medium)

Question Stats:

63% (00:42) correct 37% (01:11) wrong based on 43 sessions

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[GMAT math practice question]

$$\frac{9^{a+2b}}{3^{a+3b}}=?$$

1) $$a+b=2$$
2) $$a-b=3$$
[Reveal] Spoiler: OA

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Intern
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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

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Math Revolution GMAT Instructor
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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.

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