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Exponent Problem Set

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by melguy » Sun Oct 23, 2016 4:02 am
Please help me with question below

Does a^2 + a^4 = a^6 for all values of a? (Manhattan #1 Pg 71 Q9)

I am a bit confused with the languague of the question and answer. If a = 0 then it stands true otherwise not. But the answer states : No, remember you cannot combine expenential expressions linked by addition.

The statement is true when a = 0 and not valid for other values but what is it to do with combining expressions?

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by [email protected] » Sun Oct 23, 2016 9:06 am
Hi melguy,

If this is part of a DS prompt, then your logic makes sense. However, it appears to be more of a 'teaching point' - the questions asks if that sum is equal for ALL values of A. And the answer is NO. It's equal when A=0, but it's NOT equal when A is anything else. The 'point' of the example is that you CANNOT sum two different exponents in that way.

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by Matt@VeritasPrep » Fri Oct 28, 2016 12:10 am
a² + a� = a�

a² * (a² + 1) = a�

a = 0 is a solution. To find any others, divide both sides by a²:

(a² + 1) = a�

0 = a� - a² - 1

This will have two real solutions as well, but I doubt the GMAT would request their exact form.
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