GMAT Prep Question Exponents

[Yuke]

Here is the questions. Thanks for the help.

If xy=1, what is the value of

2^(x+y)^2 divided by 2^(x-y)^2

a) 2
b) 4
c) 8
d) 16
e) 32

[sankruth]

Simplifying the exponents you get...

2^[(x+y)^2 - (x-y)^2]

The exponent part can be ssimplified as follows:

[(x+y)+(x-y)].[(x+y)-(x-y)]

2x.2y = 4xy = 4 (B)

[cris]

I think is D.

What is the correcty answer??

[Yuke]

Yes its D. I was making a mulitplication error and things were not canceling out. I figured it out in my sleep last nite.

Thanks for the help.

[sibbineni]

2^(x+y)2/2^(x-y)2

=2^(x^2+y^2+2xy)/2^(x^2+y^2-2xy)


since a^x/a^-y=a^(x+y)

then 2^(x^2+y^2+2xy-x^2-y^2+2xy)

=2^(4xy)

since xy=1

=2^4
=16

Suggest me if iam wrong

[Stuart@KaplanGMAT]

Here is the questions. Thanks for the help.

If xy=1, what is the value of

2^(x+y)^2 divided by 2^(x-y)^2

a) 2
b) 4
c) 8
d) 16
e) 32

Alternately, we can just pick numbers... which will make our lives MUCH simpler.

We know that xy=1, so let's pick x=1 and y=1.

Now we have 2^2^2/2^0^2 = 2^4/2^0 = 16/1 = 16: choose (D)

[yalephd2007]

I choose D

[aj5105]

Yup, using numbers - the problem gets simpler.

Here is the questions. Thanks for the help.

If xy=1, what is the value of

2^(x+y)^2 divided by 2^(x-y)^2

a) 2
b) 4
c) 8
d) 16
e) 32

Alternately, we can just pick numbers... which will make our lives MUCH simpler.

We know that xy=1, so let's pick x=1 and y=1.

Now we have 2^2^2/2^0^2 = 2^4/2^0 = 16/1 = 16: choose (D)

[barnesthad]

If you pick numbers and x=0.5 and y=2 then the answer is 8 (C). If you pick x=1 and y=1 then the answer is 16 (D). Unless it is stated that x and y are integers it's not a "given." Guessing in this situation is risky. I would work the problem.

[Stuart@KaplanGMAT]

If you pick numbers and x=0.5 and y=2 then the answer is 8 (C). If you pick x=1 and y=1 then the answer is 16 (D). Unless it is stated that x and y are integers it's not a "given." Guessing in this situation is risky. I would work the problem.

There is absolutely 0 risk in picking numbers on this question.

Here's a fundamental rule of the GMAT:

Every question on the test has 1 right answer and 4 wrong answers. There has never been a GMAT question with more than 1 correct answer.

Here's a corollary to that rule:

If you ever find two right answers to a question, you have made a mistake.

And one more corollary for free questions that you find on the internet:

If a question does have two correct answers, then it is not a real GMAT question.

How do we know that picking numbers is safe on this particular question? Because all of the answer choices are numbers. Since it's impossible (by GMAT rules) to have more than one correct answer, as soon as we find a match, we know we've got the right choice.

I agree that, on this particular question, different numbers lead to different answers. I didn't even check any other numbers because the question is labeled as "GMAT Prep", a usually reliable source (since GMAT Prep should refer to questions from the official CATs composed of retired GMAT questions).

So, what should we take away from this experience?

1) if the answer choices are all numbers, it's 100% safe to pick numbers on that question (if one of the choices had been "it cannot be determined from the information given", then we'd have to try multiple numbers to be sure of our first result);

2) if you're posting a question on this board, please make sure to accurately cite the source and to properly reproduce the question; and

3) don't trust every question you find on the internet!

[Ian Stewart]

If you pick numbers and x=0.5 and y=2 then the answer is 8 (C). If you pick x=1 and y=1 then the answer is 16 (D). Unless it is stated that x and y are integers it's not a "given." Guessing in this situation is risky. I would work the problem.

There's only one answer to the problem. If you pick the numbers 0.5 and 2, you will also get 16:

2^(2 + 0.5)^2 / 2^(2 - 0.5)^2
= 2^(2.5)^2 /2^(1.5)^2
= 2^(2.5^2 - 1.5^2)
= 2^[(2.5 + 1.5)(2.5 - 1.5)]
= 2^(4*1)
= 16