If x% of y = y% of x, then which of the following is true?

Question

If x% of y = y% of x, then which of the following is true?

1. A. x y
2. B. y x
3. C. y = x
4. D. Cannot be determined (Correct answer)

Correct Answer

Option D — D

Detailed Solution & Explanation

The correct answer is Option D.

Key Points

• The statement x% of y = y% of x expands to (x/100)·y = (y/100)·x, i.e. xy/100 = xy/100.
• This is always true for every x and y — it is an identity, not a condition.
• Because the equation holds no matter what x and y are, it tells us nothing about their relative sizes. x could be greater than y, less than y, or equal — all are consistent.
• So the relationship between x and y cannot be determined from this statement.

Exam Tip

• 'x% of y = y% of x' is a classic identity — recognise it instantly so you are not tricked into concluding x = y.

Additional Information

• Since (x/100)·y and (y/100)·x are both xy/100, the identity holds for all values of x and y — nothing special is required.
• The practical use is computational: 35% of 8 = 8% of 35 = 2.8, and swapping often makes the arithmetic far easier.
• Useful companions: 50% of x = x/2, 25% of x = x/4, 12.5% of x = x/8.