The average of fifteen numbers is 60. The average of the first seven numbers is 63 and the average of next five numbers is 59. The last number is half of the 13th number and the 14th number is four more than the last number. Which of the following is/are correct I. Average of the last three numbers is an integer II. Fourteenth number is divisible by 11 III. Average of 13th and 15th number is not 65?

LohaHridoy
  1. I, II and III
  2. I and II
  3. I and III
  4. II and III

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AhmedNazir

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Option 4 : II and III

Given:

Average of 15 numbers = 60

Average of the first seven numbers = 63

Average of next five numbers = 59

15th number = 1/2(13th number)

14th number = 4 + 15th number

Formula Used:

Average = Sum of values/Number of values

Calculation:

Let 13th, 14th, and 15th numbers are a, b, and c

c = a/2

b = 4 + c

⇒ 4 + a/2

Sum of the first seven numbers/7 = 63

⇒ Sum of the first seven numbers = 441

Sum of the next five numbers/5 = 59

⇒ Sum of the next five numbers = 295

Sum of 15 numbers/15 = 60

⇒ Sum of 15 numbers = 900

⇒ 441 + 295 + a + b + c = 900

⇒ 736 + a + b + c = 900

⇒ a + b + c = 164

⇒ a + 4 + a/2 + a/2 = 164

⇒ 2a = 160

⇒ a = 80

⇒ c = 40

⇒ b = 44

I. Average of the last three numbers is an integer

(80 + 44 + 40)/3 = 164/3

⇒ 54.67

This is not an integer.

⇒ I is not correct

II. Fourteenth number is divisible by 11

44 = 4 × 11

⇒ II is correct

III. Average of 13th and 15th number is not 65

(80 + 40)/2 = 120/2

⇒ 60

⇒ III is correct

∴ II and III are correct.

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