Question:
Say 10600 is divided into positive quantities A, B, C, and D. Use the following information to find the value of D: If you remove A, the average of the other 3 numbers is 1000. If you remove B, the average of the other 3 numbers is 3220. If you remove C, the average of the other 3 numbers is 3180.
Say 10600 is divided into positive quantities A, B, C, and D. Use the following information to find the value of D: If you remove A, the average of the other 3 numbers is 1000. If you remove B, the average of the other 3 numbers is 3220. If you remove C, the average of the other 3 numbers is 3180.
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Instead of solving a complex system, subtract the "removed" sum from the total to isolate specific variables.
Updated On: Jun 12, 2026
- 1120
- 880
- 7600
- 1000
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept:
Use the definition of an average (Sum / Count) to form equations based on the removal of each variable.
Step 2: Detailed Explanation:
1. Total Sum \( S = A+B+C+D = 10600 \).
2. Removing A: \( (B+C+D)/3 = 1000 \implies B+C+D = 3000 \).
3. Since \( A+B+C+D = 10600 \), then \( A = 10600 - 3000 = 7600 \).
4. Removing B: \( (A+C+D)/3 = 3220 \implies A+C+D = 9660 \).
5. Removing C: \( (A+B+D)/3 = 3180 \implies A+B+D = 9540 \).
6. Now we have a system for A, B, C, D:
- \( A+B+C+D = 10600 \)
- \( A+C+D = 9660 \implies B = 10600 - 9660 = 940 \).
- \( A+B+D = 9540 \implies C = 10600 - 9540 = 1060 \).
7. Solve for D: \( A+B+C+D = 7600 + 940 + 1060 + D = 10600 \).
- \( 9600 + D = 10600 \implies D = 1000 \).
Step 3: Final Answer:
The value of D is 1000.
Use the definition of an average (Sum / Count) to form equations based on the removal of each variable.
Step 2: Detailed Explanation:
1. Total Sum \( S = A+B+C+D = 10600 \).
2. Removing A: \( (B+C+D)/3 = 1000 \implies B+C+D = 3000 \).
3. Since \( A+B+C+D = 10600 \), then \( A = 10600 - 3000 = 7600 \).
4. Removing B: \( (A+C+D)/3 = 3220 \implies A+C+D = 9660 \).
5. Removing C: \( (A+B+D)/3 = 3180 \implies A+B+D = 9540 \).
6. Now we have a system for A, B, C, D:
- \( A+B+C+D = 10600 \)
- \( A+C+D = 9660 \implies B = 10600 - 9660 = 940 \).
- \( A+B+D = 9540 \implies C = 10600 - 9540 = 1060 \).
7. Solve for D: \( A+B+C+D = 7600 + 940 + 1060 + D = 10600 \).
- \( 9600 + D = 10600 \implies D = 1000 \).
Step 3: Final Answer:
The value of D is 1000.
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