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# What is the value of 4^(a + b)/2^(a - b) ?

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Math Expert
Joined: 02 Sep 2009
Posts: 47219
What is the value of 4^(a + b)/2^(a - b) ?  [#permalink]

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12 Sep 2017, 23:33
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Difficulty:

35% (medium)

Question Stats:

70% (00:50) correct 30% (00:49) wrong based on 32 sessions

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What is the value of $$\frac{4^{(a + b)}}{2^{(a - b)}}$$ ?

(1) a = 7
(2) a + 3b = 5

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Joined: 31 Jan 2017
Posts: 48
Re: What is the value of 4^(a + b)/2^(a - b) ?  [#permalink]

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12 Sep 2017, 23:40
on simplifying the equation we 2^a+3b

S1: a=7 insuff
b could be 2,3,4 .....
S2: a+3b=5
2^5=32 Suff..
Ans B
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Joined: 26 Feb 2016
Posts: 2964
Location: India
GPA: 3.12
Re: What is the value of 4^(a + b)/2^(a - b) ?  [#permalink]

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13 Sep 2017, 00:16
The expression for which the value has to be found can be simplified as follows:

$$\frac{4^{(a + b)}}{2^{(a - b)}}$$ $$= \frac{2^{2(a + b)}}{2^{(a - b)}}$$ $$= \frac{2^{2a + 2b)}}{2^{(a - b)}}$$ = $$2^{2a + 2b - a + b} = 2^{a + 3b}$$

(1) a = 7
Just knowing the value of a,
we cannot find the value of the expression(Insufficient)

(2) a + 3b = 5
Since we have simplified the expression as $$2^{a + 3b}$$
knowing the value of$$a + 3b$$ is enough
to find the value of the expression (Sufficient) (Option B)
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Re: What is the value of 4^(a + b)/2^(a - b) ? &nbs [#permalink] 13 Sep 2017, 00:16
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