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.

• A. 1120
• B. 880
• C. 7600
• D. 1000

Hint:

Instead of solving a complex system, subtract the "removed" sum from the total to isolate specific variables.

Answer 1

The Correct Option is D

Step 1: Use the grand total.
We know $A + B + C + D = 10600$. Each clue removes one variable and gives the average of the remaining three.
Step 2: Turn each average into a sum of three.
Remove A: $B + C + D = 3 \times 1000 = 3000$. Remove B: $A + C + D = 3 \times 3220 = 9660$. Remove C: $A + B + D = 3 \times 3180 = 9540$.
Step 3: Find A.
Since $B + C + D = 3000$, we get $A = 10600 - 3000 = 7600$.
Step 4: Find B.
Since $A + C + D = 9660$, we get $B = 10600 - 9660 = 940$.
Step 5: Find C.
Since $A + B + D = 9540$, we get $C = 10600 - 9540 = 1060$.
Step 6: Solve for D.
Now $D = 10600 - (A + B + C) = 10600 - (7600 + 940 + 1060) = 10600 - 9600 = 1000$.
\[ \boxed{1000} \]