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23 Mar 2022, 05:30
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A
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Difficulty:
55%
(hard)
Question Stats:
57% (02:13) correct
43%
(02:17)
wrong
based on 164
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Is the sum of a sequence of n consecutive integers even?
(1) n = 6
(2) The n digit number formed by the series is a multiple of nine.
(1) n = 6
(2) The n digit number formed by the series is a multiple of nine.
23 Mar 2022, 14:17
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Bunuel
Breaking Down the Info:
Set the first element of the sequence as x. Then the sequence goes from x to x + n - 1.
Statement 1 Alone:
The sequence goes from x to x + 5, and the sum is \(6*(x + 2.5) = 6x + 15\). This is guaranteed to be odd, so statement 1 alone is sufficient.
Statement 2 Alone:
We know that the series must have only single digits since n numbers create an n-digit number. We can let the sum of the digits be equal to 9 with {4, 5} or {9}, or we could let the sum of digits be equal to 18 with {5, 6, 7}. Then the sum could be odd or even, so statement 2 alone is insufficient.
Answer: A
