Both Betty and Wilma

[rsarashi]

Both Betty and Wilma earn annual salaries of more than $50,000. Is Wilma's annual salary greater than Betty's?

1) Betty's annual salary is closer to $50000 than Wilma's is.

2) Betty's annual salary is closer to $35000 than it is to Wilma's annual salary.

OAD

Please explain.

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Hi rsarashi,

This question can be approached in a couple of different ways (and you might find it helpful to draw a Number Line so that you can visualize where each of the numbers is located relatively to the other numbers).

We're told that Betty and Welma both earn a salary greater than $50,000. We're asked IF Wilma's salary is greater than Betty's salary. This is a YES/NO question.

1) Betty's annual salary is closer to $50000 than Wilma's is.

Since we already know that BOTH of the salaries are GREATER than $50,000, and Fact 1 tells us that Betty's salary is CLOSER to $50,000, then it has to be LESS than Wilma's salary and the answer to the question is ALWAYS YES.

For example:
Betty = $51,000
Wilma = $51,001

Algebraically, this can be written as (B - 50,000) < (W - 50,000)...... B < W.

Fact 1 is SUFFICIENT

2) Betty's annual salary is closer to $35,000 than it is to Wilma's annual salary.

This Fact requires a bit more work than the information in Fact 1 did, but the concepts involved are essentially the same. Since Betty's salary is greater than $50,000, we know that the difference between that salary and $35,000 has to be GREATER THAN $15,000. We're told that THAT difference is LESS than the difference between Betty's salary and Wilma's salary (which means that Wilma's salary CAN'T be closer to $35,000 than Betty's is).

For example:
Betty = $51,000
Difference = 51,000 - 35,000 = 16,000
Wilma = MORE THAN 51,000 + 16,000 = MORE than $67,000

As the difference between Betty's salary and $35,000 increases, the difference between Betty's salary and Wilma's salary increases MORE (meaning that Wilma's salary MUST be greater than Betty's salary. Thus, the answer to the question is ALWAYS YES.

Fact 2 is SUFFICIENT

Final Answer: D

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

[GMATGuruNY]

Both Betty and Wilma earn annual salaries of more than $50,000. Is Wilma's annual salary greater than Betty's?

1) Betty's annual salary is closer to $50000 than Wilma's is.

2) Betty's annual salary is closer to $35000 than it is to Wilma's annual salary.

Statement 1: Betty's annual salary is closer to $50000 than Wilma's is.
On a number line:
-----50,000---B---W
Thus, W > B.
SUFFICIENT.

Statement 2: Betty's annual salary is closer to $35000 than it is to Wilma's annual salary.
Case 1: -----35,000-----50,000---B---W
Case 2: -----35,000-----50,000---W---B

In Case 2, B is closer to W than to 35,000.
Thus, Case 2 is not viable.
Since only Case 1 is viable, W > B.
SUFFICIENT.

The correct answer is D.

[Jay@ManhattanReview]

Both Betty and Wilma earn annual salaries of more than $50,000. Is Wilma's annual salary greater than Betty's?

1) Betty's annual salary is closer to $50000 than Wilma's is.

2) Betty's annual salary is closer to $35000 than it is to Wilma's annual salary.

OAD

Please explain.

The question can be solved logically. Since both earn more than $50,000, the one whose salary is relatively less close (farther) to 50,000/35,000 would earn more than the one whose salary is relatively closer to 50,000/35,000.

Hope this helps!

-Jay
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