Let w , x , y , and z be positive numbers such that w is 40 percent less than x , and x is 40 percent less than y . If z is 46 percent less than y , then z is what percent greater than w ?

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

Word Problems

Percents

MEDIUM

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Notes

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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 \(\mathrm{w}\)?

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66%

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

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40%

50%

60%

66%

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