Number properties

[Viper83]

What is the value of

(2 to power X + 2 to power X)/(2 to power Y)?

(1) x - y = 8
(2) x/y = -3


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[Brian@VeritasPrep]

Hey Viper,

Love the question! Remember, with exponents there are really only a few things that you can do, and they usually require:

1) Common bases
2) Multiplication

Here, they give you the common base of 2, so you're good there. The numerator, however, uses addition. Because nearly all exponent rules are related to multiplication/division, you should try to turn that addition into multiplication (often by factoring). 2^x + 2^x can be rewritten as 2(2^x), and since we have a common base of 2 there, we can add the exponents, making the numerator:

2^(x+1)

So now we can express the fraction given to us a little bit more conveniently for our exponential purposes:

2^(x+1)/2^y

Because we have the same base, when dividing the numerator by the denominator we would then subtract the exponents (e.g. 2^3 / 2^1 = 2^2).

Statement 1 tells us exactly the result of that subtraction: if x - y = 8, then x + 1 - y = 9, so we know that the answer is 2^9. Statement 1 is sufficient.

Statement 2 leaves multiple possibilities for that subtraction. x/y = -3 could mean that:

x = 9, y = -3

or

x = -9, y = 3

This gives us a huge range of possibilities for the value of the fraction (in the first, we'd have 2^12, a pretty large number; in the second, we'd have 2^-12, an incredibly small fraction). Therefore, statement 2 is not sufficient, and the correct answer is A.


Remember - when dealing with exponents, try to find common bases and turn addition/subtraction into multiplication so that you can apply the exponent rules that you know!

[pradeepkaushal9518]

good question

[clawhammer]

Nice question, indeed.