If (2^a)*3^(b-1) = (18^b)/2 where a and b are integers, what is the v

Question

GMATH  practice exercise (Quant Class 3)

If  {2^a} \cdot {3^{b - 1}} = {{{{18}^b}} \over 2}  , where  a  and  b  are integers, what is the value of  ab  ?

(A) -3
(B) -1
(C) 0
(D) 1
(E) 2

m1033512 · Answer

IMO E .

2^a)*3^(b-1) = (18^b)/2,
 = 2^b-1.3^2b

Cmpare the powers of 2 and 3 , we get

a=b-1 and b-1=2b
=> b=-1 and a = -2

So ab = 2

E.

Archit3110 · Answer

{2^a} \cdot {3^{b - 1}} = {{{{18}^b}} \over 2}

2^a*3^b-1= 3^2b*2^b-1

a=b-1
b-1=2b
b=-1
so
a=-2
ab= 2
IMO E

fskilnik · Answer

? = \,\,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.

If (2^a)*3^(b-1) = (18^b)/2 where a and b are integers, what is the v

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GMAT Problem Solving (PS) Questions

If (2^a)*3^(b-1) = (18^b)/2 where a and b are integers, what is the v

Prep Toolkit

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