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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7465
GMAT 1: 760 Q51 V42
GPA: 3.82

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27 Dec 2017, 01:02
00:00

Difficulty:

25% (medium)

Question Stats:

73% (00:54) correct 27% (01:57) wrong based on 70 sessions

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[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 $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Intern Joined: 08 Oct 2017 Posts: 1 9^{a+2b}/3^{a+3b}=? [#permalink] ### Show Tags 27 Dec 2017, 04:35 $$\frac{9^{a+2b}}{3^{a+3b}}$$=$$\frac{3^{2(a+2b)}}{3^{a+3b}}$$=$$3^{2a+4b-a-3b}$$= $$3^{a+b}$$ 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: 7465 GMAT 1: 760 Q51 V42 GPA: 3.82 9^{a+2b}/3^{a+3b}=? [#permalink] ### Show Tags 28 Dec 2017, 22:51 => 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 _________________ 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$149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
9^{a+2b}/3^{a+3b}=?   [#permalink] 28 Dec 2017, 22:51
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