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If a and b are constants, is the expression

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If a and b are constants, is the expression

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If a and b are constants, is the expression (x+b)/(√(x+a)) defined for x = -2 ?

(1) a = 5
(2) b = 6

A

Source: Official Guide 2020

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AbeNeedsAnswers wrote:
If a and b are constants, is the expression (x+b)/(√(x+a)) defined for x = -2 ?

(1) a = 5
(2) b = 6
Target question: Is the expression defined for x = -2?
This is a great candidate for rephrasing the target question.

If x = -2, then the expression becomes (-2)+b/√(-2+a)

There are two ways in which the expression(-2)+b/√(-2+a) is NOT defined:

case i) If a = 2, then the fraction's denominator is 0, which means the entire rational expression is NOT defined.
case ii) If a < 2, then the value inside the square root sign is NEGATIVE, in which case the denominator is NOT defined.
When we combine both cases, we see that the expression is NOT defined when a ≤ -2
Or we can say, the expression IS defined when a > -2

REPHRASED target question: Is a > -2?

Aside: Here’s a video with tips on rephrasing the target question: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100

Statement 1: a = 5
The answer to the REPHRASED target question is YES, a IS greater than -2
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: b = 6
This does not help us answer the REPHRASED target question.
Statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

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Hi All,

We're told that A and B are constants. We're asked if the expression (X+B)/(√(X+A)) is "defined" for x = -2. This is a YES/NO question and is a great 'concept' question - meaning that you don't have to do much math if you understand the concepts involved. For the given fraction to be 'defined', the denominator CANNOT be 0. As such, since we're given a value for X (re: -2), we need to know the value for A to answer this question.

1) A = 5

Fact 1 gives us the value of A. With the given value of X, we know that the denominator will be a POSITIVE number, so the fraction will be defined and the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

2) B = 6

Fact 2 gives us information to define the numerator of the fraction (re: -2 + 6 = +4), but not the denominator.
IF....
A = +2, then the answer to the question is NO
A = +3, then the answer to the question is YES
Fact 2 is INSUFFICIENT

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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