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12 Sep 2017, 23:33
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Difficulty:
25%
(medium)
Question Stats:
70% (01:01) correct
30%
(01:22)
wrong
based on 120
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What is the value of \(\frac{4^{(a + b)}}{2^{(a - b)}}\) ?
(1) a = 7
(2) a + 3b = 5
(1) a = 7
(2) a + 3b = 5
13 Sep 2017, 00:16
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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)
\(\frac{4^{(a + b)}}{2^{(a - b)}}\) \(= \frac{2^{2(a + b)}}{2^{(a - b)}}\) \(= \frac{2^{(2a + 2b)}}{2^{(a - b)}}\) = \(2^{2a + 2b - a + b} = 2^{a + 3b}\)
(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)
