QUESTION 14 The average of the three numbers is 135.
Qualcomm technical mcq question, verified with a worked answer. Free to practise - no sign-up.
QUESTION 14
The average of the three numbers is 135. The largest number is 180 and the difference between the others is 25. The smallest number is
Show answer & explanation
Answer: A. 100
Let the three numbers be x (smallest), y (middle), and 180 (largest). From the average: x + y + 180 = 405. From the difference constraint: y - x = 25, so y = x + 25. Substituting: x + (x + 25) + 180 = 405 → 2x + 205 = 405 → x = 100. Therefore, the smallest number is 100.
Step-by-step Derivation:
Step 1: Set up equations from given information.
- Average of three numbers = 135
- Sum of three numbers = 135 × 3 = 405
- Largest number = 180
- Let smallest = x, middle = y
Step 2: Express relationships.
- x + y + 180 = 405
- y - x = 25 (difference between the other two)
Step 3: Solve the system.
- From equation 2: y = x + 25
- Substitute into equation 1: x + (x + 25) + 180 = 405
- Simplify: 2x + 205 = 405
- 2x = 200
- x = 100
Step 4: Verify.
- Smallest = 100, Middle = 125, Largest = 180
- Average = (100 + 125 + 180) / 3 = 405 / 3 = 135 ✓
- Difference between others = 125 - 100 = 25 ✓
- Largest = 180 ✓