The average of three integers is 13. When a natural number n is included, the average of these four integers remains an odd integer. The minimum possible value of n is
Question:
The average of three integers is 13. When a natural number n is included, the average of these four integers remains an odd integer. The minimum possible value of n is
The average of three integers is 13. When a natural number n is included, the average of these four integers remains an odd integer. The minimum possible value of n is
Options
Answer: 5
Explanation:
Sum of three integers = 3×13 = 39. After adding n, average = an odd integer k, so (39 + n)/4 = k ⇒ 39 + n = 4k ⇒ n = 4k − 39. n must be a natural number ≥ 1, so 4k − 39 ≥ 1 ⇒ 4k ≥ 40 ⇒ k ≥ 10. The smallest odd integer ≥ 10 is 11. Thus n = 4×11 − 39 = 44 − 39 = 5. Minimum possible value of n = 5.
Explanation:
Sum of three integers = 3×13 = 39. After adding n, average = an odd integer k, so (39 + n)/4 = k ⇒ 39 + n = 4k ⇒ n = 4k − 39. n must be a natural number ≥ 1, so 4k − 39 ≥ 1 ⇒ 4k ≥ 40 ⇒ k ≥ 10. The smallest odd integer ≥ 10 is 11. Thus n = 4×11 − 39 = 44 − 39 = 5. Minimum possible value of n = 5.
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