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 ChallengeYou 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 NumbersSince 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 SumNow let's add both salaries together:
- Elizabeth: 14
- Bill: 11
- Total: 14 + 11 = 25
Step 3: Calculate How Much LessHere'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.