The average of 4 numbers is 52. The average of the first two numbers is thrice the average of the other two numbers. What is the sum of the first two numbers?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 156.
Let:
The first two numbers = a and b
The other two numbers = c and d
the average of the 4 numbers = 52
the total sum of the numbers = (a + b + c + d)/4 = 52
⇒ a + b + c + d = 52 × 4 = 208
⇒ c + d = 208 − (a + b) .............(1)
The average of the first two numbers is thrice the average of the other two numbers, so:
⇒ (a + b)/2 = 3 × (c + d)/2
⇒ a + b = 3(c + d)
⇒ a + b = 3(208 − (a + b)) ...............(From eq. 1)
⇒ a + b = 624 − 3(a + b)
⇒ a + b + 3(a + b) = 624
⇒ 4(a + b) = 624
⇒ a + b = 624/4 = 156