The sum of three from the four numbers A, B, C, D are 7564 , 7512 , 7458 and…
2026
The sum of three from the four numbers A, B, C, D are 7564 , 7512 , 7458 and 7781 . What is the largest of the numbers A, B, C, D?
Answer: D. 2647 — Key idea: add all four given three-number sums. Each original number appears in exactly three of those sums, so the total equals three times the sum of the…
- A.
2593
- B.
2634
- C.
2541
- D.
2647
Attempted by 301 students.
Show answer & explanation
Correct answer: D
Key idea: add all four given three-number sums. Each original number appears in exactly three of those sums, so the total equals three times the sum of the four numbers.
Compute the total of the four given sums: 7564 + 7512 + 7458 + 7781 = 30315. Divide by 3 to get the sum of the four numbers: 30315 ÷ 3 = 10105.
A = total − (b + c + d) = 10105 − 7512 = 2593
B = total − (a + c + d) = 10105 − 7458 = 2647
C = total − (a + b + d) = 10105 − 7781 = 2324
D = total − (a + b + c) = 10105 − 7564 = 2541
Therefore the largest of the four numbers is 2647.