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Dividing Polynomials

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by GMATGuruNY » Wed Sep 17, 2014 7:32 am
The problem should read as follows:
If xy=1, then what is the value of [2^(x+y)²]/ [2^(x-y)²]?

1)2
2) 4
3) 8
4) 16
5) 32
Let x=y=1.
Then:
2^(x+y)² / 2^(x-y)² = 2^(1+1)² / 2^(1-1)² = 2�/2� = 16/1 = 16.

The correct answer is D.
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by Brent@GMATPrepNow » Wed Sep 17, 2014 8:03 am
if xy=1 then what is the value of 2^(x+y)²/ 2^(x-y)²

1)2
2) 4
3) 8
4) 16
5) 32
2^(x+y)²/ 2^(x-y)² = 2^(x² + 2xy + y²)/ 2^(x² - 2xy + y²)
= 2^(4xy) [after we SUBTRACT exponents]
= 2^4 [since xy = 1]
= 16

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by [email protected] » Wed Sep 17, 2014 8:01 pm
Hi recentgradmsu,

From Mitch's and Brent's explanations, you'll notice that a number of different math rules are required to answer this question. Whether you're using GMAT tactics or more of a "math" approach to answer a question, you have to have a certain amount of knowledge (math rules, formulas, etc.) and pattern-matching skills.

For example, one of the exponent rules that appears in this prompt is the idea of dividing exponents (we have to subtract the exponents):

x�/x� = x²

This rule holds true whether the exponents are numbers or variables.

Another duo of rules that appear in this prompt are 2 Classic Quadratics:
(x+y)² = x² + 2xy + y²
(x-y)² = x² - 2xy + y²

The GMAT writers often find ways to test you on rules that you know, but in ways that you're not used to thinking about. When dealing with strange "looking" questions, be on the lookout for patterns/rules/language/etc. that you recognize - they should help you to figure out what to do to answer the question.

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