GMATH practice exercise (Quant Class 3)
Answer: [spoiler]____(E)__[/spoiler]
If (2^a)*3^(b-1) = (18^b)/2, what is the value of ab?
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- fskilnik@GMATH
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$$? = \,\,ab$$
$${2^a} \cdot {3^{b - 1}} = {{{{18}^b}} \over 2}\,\,\,\,\,\mathop \Rightarrow \limits^{ \cdot \,2} \,\,\,\,\,{2^{a + 1}} \cdot {3^{b - 1}}\, = {\left( {2 \cdot {3^2}} \right)^b} = {2^b} \cdot {3^{2b}}$$
$${2^{a + 1 - b}} = {3^{2b - \left( {b - 1} \right)}}\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\left\{ \matrix{
\,a + 1 - b = 0 \hfill \cr
\,2b - \left( {b - 1} \right) = 0\, \hfill \cr} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left( {a,b} \right) = \left( { - 2, - 1} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 2$$
$$\left( * \right)\,\,\,{\rm{integer}}\,\,{\rm{exponents}}$$
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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