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thesunnyguy
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Yes Bunuel, I got it in Official practice mock test 3.
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If Bill's salary is \(\frac{11}{14}\) of Elizabeth's salary, then Bill's salary is what percent less than the sum of both salaries?

A. 12%
B. 25%
C. 30%
D. 48%
E. 56%

Assuming Elizabeth's salary is $14, Bill's salary would be $11. The sum of their salaries is $25. Bill's salary, at $11, is more than 50% less than $25. Only E fits.

Answer: E.

P.S. Is this a GMAT Prep Focus question? Could you please provide a screenshot?

Thank you for the info! :thumbsup:
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A percent problem that can be a bit tricky if you don't set it up correctly. Let's break this down together and make it clear.

The Core Challenge
You need to find what percent less Bill's salary is compared to the combined salaries of both Bill and Elizabeth. Notice those two key words - "less" and "combined" - they're crucial here!

Let's solve this step by step:

Step 1: Choose Smart Numbers
Since Bill's salary is \(\frac{11}{14}\) of Elizabeth's salary, let's make our life easier. Set Elizabeth's salary = 14 (choosing the denominator keeps things clean).

So Bill's salary = \(\frac{11}{14} \times 14 = 11\)

Step 2: Find the Sum
Now let's add both salaries together:
- Elizabeth: 14
- Bill: 11
- Total: 14 + 11 = 25

Step 3: Calculate How Much Less
Here's what you need to see - Bill's salary (11) compared to the total (25):
- The difference: 25 - 11 = 14
- As a percentage: \(\frac{14}{25} \times 100\% = 56\%\)

The Answer: E. 56%

Think about it this way: Bill earns 11 out of 25 total, which is 44% of the combined amount. So his salary is 56% less than the combined total. This distinction between "percent of" and "percent less than" catches many students!

You can check out the step-by-step solution on Neuron by e-GMAT to master the systematic approach for all salary/percentage problems and learn the common trap patterns to avoid. You can also explore other GMAT official questions with detailed solutions on Neuron for structured practice here.
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