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

[BTGModeratorVI]

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

(1) a + b = 40
(2) a – b = 2

Answer: A
Source: GMAT prep

[deloitte247]

$$Is\ \frac{a+b+20}{3}=20\ ?$$
Rephrased as => Is a + b + 20 = 60
=> Is a + b = 60 - 20
=> Is a + b = 40 ?

Statement 1 => a + b = 40
$$\frac{40+20}{3}=20$$
$$\frac{60}{3}=20$$
$$20=20$$
This statement gives exact value of (a + b) and the mean of a, b and 20 is 20
Statement 1 is NOT SUFFICIENT

Statement 2 => a - b = 2
The information provided cannot be used to evaluate a + b; the exact value of a and b is unknown so the target question remains a mystery. Statement 2 is NOT SUFFICIENT.

Since only statement 1 is SUFFICIENT
Answer = A

[Brent@GMATPrepNow]

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

(1) a + b = 40
(2) a – b = 2

Answer: A
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: Here’s a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

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

Cheers,
Brent