Let w, x, y, and z be positive numbers such that w is 40 percent less than x, and x...
GMAT Word Problems : (WP) Questions
Source: Mock
...
...
Post a Query
Let \(\mathrm{w}\), \(\mathrm{x}\), \(\mathrm{y}\), and \(\mathrm{z}\) be positive numbers such that \(\mathrm{w}\) is 40 percent less than \(\mathrm{x}\), and \(\mathrm{x}\) is 40 percent less than \(\mathrm{y}\). If \(\mathrm{z}\) is 46 percent less than \(\mathrm{y}\), then \(\mathrm{z}\) is what percent greater than \(\mathrm{w}\)?
Solution
- Translate the problem requirements: We need to understand that 'w is 40% less than x' means \(w = 0.6x\), 'x is 40% less than y' means \(x = 0.6y\), and 'z is 46% less than y' means \(z = 0.54y\). We want to find what percent greater z is than w.
- Express all variables in terms of a common base: Express both w and z in terms of y to compare directly.
- Set up the percentage comparison: Compute percent increase = \(\frac{z - w}{w} \times 100\%\).
- Calculate the final percentage: Substitute values \(w = 0.36y, z = 0.54y\) to get 50%.
Calculation
Percent increase = \( \frac{0.54y - 0.36y}{0.36y} \times 100\% = 50\% \)
Answer
z is 50% greater than w.
Answer Choices Explained
A
34%
B
40%
C
50%
D
60%
E
66%
Rate this Solution
Tell us what you think about this solution
Forum Discussions
Start a new discussion
Post
Load More