Is \(20\) the average (arithmetic mean) of \(a, b,\) and \(20?\)

[M7MBA]

Is \(20\) the average (arithmetic mean) of \(a, b,\) and \(20?\)

(1) \(a + b = 40\)
(2) \(a – b = 2\)

[spoiler]OA=A[/spoiler]

Source: GMAT Prep

[Brent@GMATPrepNow]

Is \(20\) the average (arithmetic mean) of \(a, b,\) and \(20?\)

(1) \(a + b = 40\)
(2) \(a – b = 2\)

[spoiler]OA=A[/spoiler]

Source: GMAT Prep

Target question: Is 20 the average (arithmetic mean) of a, b, and 20 ?
This is a good candidate for rephrasing the target question.
First recognize that we can write: Does (a + b + 20)/3 = 20 ?
Multiply both sides of that equation by 3 to get: Does a + b + 20 = 60 ?
Subtract 20 from both sides to get: Does a + b = 40 ?
REPHRASED target question: Does a + b = 40 ?

Aside: the video below has tips on rephrasing the target question

Statement 1: a + b = 40
Perfect!!
The answer to the REPHRASED target question is YES, a + b = 40
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: a – b = 2
Since we can not use this information to answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

If you aren't convinced, check out the following two cases:
Case a: a = 4 and b = 2 (this satisfies the condition that a - b = 2). In this case, the answer to the REPHRASED target question is NO, a + b does not equal 40
Case b: a = 21 and b = 19 (this also satisfies the condition that a - b = 2). In this case, the answer to the REPHRASED target question is YES, a + b = 40
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

VIDEO ON REPHRASING THE TARGET QUESTION:
https://www.gmatprepnow.com/module/gmat ... video/1100