Both Betty and Wilma earn annual salaries of more than $50,000.

Question

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 $50,000 than Wilma's is.

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

ID 05386

Bunuel · Accepted Answer

Both Betty and Wilma earn annual salaries of more than $50000. Is Wilma's annual salary greater than Betty's?

Notice that we are told that  both Betty and Wilma earn annual salaries of more than $50,000 .

(1) Betty's annual salary is closer to $50,000 than is Wilma's.

----$50,000---(Betty)----(Wilma)---- So, as you can see Wilma's annual salary is greater than Betty's. Sufficient.

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

$35,000----$50,000---(Betty)----(Wilma)---- Again Wilma's annual salary is greater than Betty's. Sufficient.

Answer: D.

Hope it's clear.

manulath · Answer

I believe that OA is wrong.
It should be D.

Kindly check the OA and edit it.

Bunuel - Your explanation is spot on.

ethnix · Answer

I am sorry, but the official answer does not make any sense for Statement 1. It is simply mathematically wrong.

Mathematically spoken the statement says: |Betty-50.000|<|Wilma-50.000| and not Betty-50.000 < Wilma-50.000
Let me make a numerical example. Betty earns 49.999 an Wilma earns 70.000. Obviously Betty's salary is closer than 50.000 though Wilma earns more. And the over way around: Let Betty earn 50.001 and Wilma 40.000, now still Betty's wage is closer to 50.000 though she now earns more than Wilma.

Stating that 1) is sufficient is simply wrong and I'm actually quite astonished people get away with such an answer so easily.

p.s.: The same argumentation holds for 2), so the correct answer must be C, as you can deduct from both statements that both wages must lie above 50.000; something you can't predict earlier.

Bunuel · Answer

Welcome to GMAT Club.

Your examples are not correct because we are told that "both Betty and Wilma earn annual salaries of  more than $50000 ".

Hope it's clear.

ethnix · Answer

OMG, thanks. I suppose reading the question would avoid to most of my wrong answers :D

janxavier · Answer

Hey guys just one small question.

If the test makers intended to say that Betty and Wilma's annual salaries put together was more than 50000 how could they have framed the question. I am non-native speaker so it kinda took me a while to know that they meant Betty > 50000 and Wilma > 50000. Plz help

Bunuel · Answer

It would be something like "combined salary of Betty and Wilma is more than $50000" or "together Betty and Wilma earn annual salary of more than $50000".

rakshithbabu · Answer

I got the answer correct, but got completely confused with statement 2. Took a while to understand, but both scenarios led to the same answer, so was lucky here.
My doubt here is between the two interpretations of statement 2. Namely,
1) Distance between Betty's salary and $35,000 < Distance between Betty's salary and Wilma's salary
1) Distance between Betty's salary and $35,000 < Distance between $35,000 and Wilma's salary

Bunuel  , Please help decipher these kind of statements.

ENGRTOMBA2018 · Answer

Let me try to help.

First of, do not waste time in doubting the official questions. I agree the placement of "it" is kind of ambiguous but both the versions (it=Betty's and it=35000) will lead to the same conclusion of Betty's salary < Wilma's salary as we are given that both the salaries are >50000.

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Both Betty and Wilma earn annual salaries of more than $50000. Is Wilma's annual salary greater than Betty's?

(1) Betty's annual salary is closer to $50,000 than is Wilma's. 
(2) Betty's annual salary is closer to $35,000 than it is to Wilma's annual salary.

In the original condition, we can let Betty's annual salary=b, Wilma's annual salary=w. Then, there are 2 variables and 3 equations from the question and the conditions, so there is high chance (D) will be our answer.
Condition 1 is sufficient as it answers the question 'yes'
Condition 2 is also sufficient for the same reason, so the answer becomes (D).

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

bumpbot · Answer

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Both Betty and Wilma earn annual salaries of more than $50,000.

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GMAT Data Sufficiency (DS) Questions

Both Betty and Wilma earn annual salaries of more than $50,000.

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