The sum of three from the four numbers A,B,C,D are 3967, 3864, 4055 and 3687 .…
2024
The sum of three from the four numbers A,B,C,D are 3967, 3864, 4055 and 3687 . What is the largest of the numbers A, B, C, D?
- A.
1712
- B.
1650
- C.
1327
- D.
1504
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Correct answer: D
Solution: Find the four numbers and identify the largest.
Step 1: Add the four given sums (each omits one of the numbers): 3967 + 3864 + 4055 + 3687 = 15573. This equals 3(A + B + C + D).
Step 2: Divide by 3 to get the total of all four numbers: A + B + C + D = 15573 / 3 = 5191.
Step 3: Each original number equals the total minus the three-number sum that omits it. Using the given sums:
If B + C + D = 3864, then A = 5191 - 3864 = 1327.
If A + C + D = 4055, then B = 5191 - 4055 = 1136.
If A + B + D = 3687, then C = 5191 - 3687 = 1504.
If A + B + C = 3967, then D = 5191 - 3967 = 1224.
Answer: The four numbers are 1327, 1136, 1504 and 1224; the largest is 1504.