Which of the following statement (s) is/are TRUE? I. 199 + 299 + 399 + 499 + 599 is exactly divisible by 5. II. 3111 > 1714
Which of the following statement (s) is/are TRUE? I. 199 + 299 + 399 + 499 + 599 is exactly divisible by 5. II. 3111 > 1714 Correct Answer Only I, Only I
Statement I:
(an + bn) will be divisible by (a + b) if n is odd
With same logic, 199 + 499 will be divisible by (1 + 4) = 5
Let 199 + 499 = 5a
Also, 299 + 399 will be divisible by (2 + 3) = 5
Let 299 + 399 = 5b
⇒ 199 + 299 + 399 + 499 + 599 = 5a + 5b + 599
It is divisible by 5
⇒ Statement I is true
Statement II:
3111 < 3411
⇒ 3111 < (2 × 17)11
⇒ 3111 < 211 × 1711< 212 × 1711
⇒ 3111 < (24)3 × 1711
⇒ 3111 < 163 × 1711 < 173 × 1711
⇒ 3111 < 1714
⇒ Statement II is false
∴ Only statement 1 is true.
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Feb 20, 2025