If a and b are constants, is the expression

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AbeNeedsAnswers: Master | Next Rank: 500 Posts; Posts: 394; Joined: Sun Jul 02, 2017 10:59 amFollowed by: 5 members; Thanked: 1 times

by AbeNeedsAnswers » Wed May 08, 2019 7:46 pm

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

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

A

Source: Official Guide 2020

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Source: Beat The GMAT — Data Sufficiency | Wed May 08, 2019 7:46 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu May 09, 2019 8:06 am

AbeNeedsAnswers wrote:If a and b are constants, is the expression (x+b)/(âˆš(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/âˆš(-2+a)

There are two ways in which the expression(-2)+b/âˆš(-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 â‰¤ -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: https://www.gmatprepnow.com/module/gmat- ... cy?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

Brent Hanneson - Creator of GMATPrepNow.com

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by [email protected] » Thu May 09, 2019 3:43 pm

Hi All,

We're told that A and B are constants. We're asked if the expression (X+B)/(âˆš(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

Contact Rich at [email protected]

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SampathKp: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Wed Nov 13, 2019 9:42 pm

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by SampathKp » Sat Dec 21, 2019 4:24 am

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

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

A

Source: Official Guide 2020

Given expression (-2+b)/âˆš-2+a depends on value a rather b because âˆš-2+a has square root and in denominator. Square root of negative number is imaginary number and denominator if equal 0 will make number infinity.

from (1) a= 5 , denominator will be come âˆš3 which will make the given expression valid regardless of what value b takes in the numerator Hence this information is Sufficient
from (2) b=6 we cannot define anything about denominator. hence this information is NOT Sufficient.

Answer is A

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8139; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: If a and b are constants, is the expression

by Scott@TargetTestPrep » Wed May 12, 2021 8:10 am

AbeNeedsAnswers wrote: ↑
Wed May 08, 2019 7:46 pm
If a and b are constants, is the expression (x+b)/(âˆš(x+a)) defined for x = -2 ?

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

A

Source: Official Guide 2020

Solution:

Question Stem Analysis:

We need to determine whether the expression (x + b) / √(x + a) is defined for x = -2. Notice that the expression is defined when x + a is positive. Therefore, as long as (-2 + a) is positive, the expression will be defined.

Statement One Alone:

Since a = 5, then -2 + a = 3, which is positive. So the expression is defined. Statement one alone is sufficient.

Statement Two Alone:

Since we don’t know anything about the value of a, we can’t determine whether the expression is defined or not. Statement two alone is not sufficient.

Answer: A

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Founder and CEO
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