X is 30% less than Z and Y is 35% less than Z. By what percentage is Y less than X?

Introduction / Context:
Comparative percentage questions require expressing both numbers relative to the same base and then comparing. Here both X and Y are defined as percentage reductions from Z; we must find the percent by which Y is below X.

Given Data / Assumptions:

• X = 30% less than Z ⇒ X = 0.70Z.
• Y = 35% less than Z ⇒ Y = 0.65Z.
• Compute % difference relative to X: (X − Y)/X * 100%.

Concept / Approach:
Use the common base Z to write both values, then take the ratio. Plug the expressions and simplify the fraction to get an exact percentage. Recognize 0.05/0.70 = 1/14 for a clean fractional percentage 7 1/7%.

Step-by-Step Solution:

Verification / Alternative check:
Assume Z = 100. Then X = 70 and Y = 65. Difference = 5. Percent below X = 5/70 * 100% = 7 1/7%, confirming.

Why Other Options Are Wrong:

• 30%, 20%, 15%: These are common distractors when comparing to Z instead of to X, or mixing percentage points with percent differences.

Common Pitfalls:
Comparing Y to Z instead of to X, or computing (Y − X)/X which would produce a negative sign and confusion.

Final Answer: