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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

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MEDIUM
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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 \(\mathrm{w}\)?

A
34%
B
40%
C
50%
D
60%
E
66%
Solution
  1. 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.
  2. Express all variables in terms of a common base: Express both w and z in terms of y to compare directly.
  3. Set up the percentage comparison: Compute percent increase = \(\frac{z - w}{w} \times 100\%\).
  4. 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%
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