The sum of two numbers is 20 and their difference is 4, then the numbers are:

Question

The sum of two numbers is 20 and their difference is 4, then the numbers are:

1. A. 10, 10
2. B. 16, 12
3. C. 12, 8 (Correct answer)
4. D. None of the above

Correct Answer

Option C — 12, 8

Detailed Solution & Explanation

The correct answer is 12, 8.

Key Points

• Let the numbers be x and y with x + y = 20 and x − y = 4.
• Adding the equations: 2x = 24, so x = 12.
• Substituting back: y = 8.
• Check: 12 + 8 = 20 ✓ and 12 − 8 = 4 ✓.

Additional Information

• The shortcut worth memorising: given a sum S and a difference D, the numbers are (S + D)/2 and (S − D)/2 — here (20+4)/2 = 12 and (20−4)/2 = 8.
• Option B fails the sum test (16 + 12 = 28) and option A fails the difference test, so both can be eliminated by inspection.
• Checking a candidate answer against both conditions is faster than solving whenever options are given.