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If (2^a)*3^(b-1) = (18^b)/2, what is the value of ab?

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by fskilnik@GMATH » Thu Feb 28, 2019 7:27 am

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Answers

A

B

C

D

E

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GMATH practice exercise (Quant Class 3)

Image

Answer: [spoiler]____(E)__[/spoiler]
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by fskilnik@GMATH » Thu Feb 28, 2019 12:13 pm
fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 3)

Image
$$? = \,\,ab$$
$${2^a} \cdot {3^{b - 1}} = {{{{18}^b}} \over 2}\,\,\,\,\,\mathop \Rightarrow \limits^{ \cdot \,2} \,\,\,\,\,{2^{a + 1}} \cdot {3^{b - 1}}\, = {\left( {2 \cdot {3^2}} \right)^b} = {2^b} \cdot {3^{2b}}$$
$${2^{a + 1 - b}} = {3^{2b - \left( {b - 1} \right)}}\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\left\{ \matrix{
\,a + 1 - b = 0 \hfill \cr
\,2b - \left( {b - 1} \right) = 0\, \hfill \cr} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left( {a,b} \right) = \left( { - 2, - 1} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 2$$
$$\left( * \right)\,\,\,{\rm{integer}}\,\,{\rm{exponents}}$$


The correct answer is (E).


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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