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Is the sum of 7th through 18th term in a sequence of integers even?

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Is the sum of 7th through 18th term in a sequence of integers even?  [#permalink]

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New post 09 Apr 2018, 14:41
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Is the sum of \(7^{th}\) through \(18^{th}\) term in a sequence of integers even?

(1) Every term in the sequence is 5 more than the previous term.
(2) The \(1^{st}\) term in the sequence is 5.

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Re: Is the sum of 7th through 18th term in a sequence of integers even?  [#permalink]

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New post 09 Apr 2018, 23:36
Sum= Sum of first 18 terms- Sum of first 6 terms
Sum of first 18 terms=9(2a+17d)
Sum of first 6 terms=3(2a+5d)
Sum=18a+153d-6a-15d= 12a+138d
Sum is even. I don't need any other info.

Please point out my mistake
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Re: Is the sum of 7th through 18th term in a sequence of integers even?  [#permalink]

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New post 10 Apr 2018, 22:38
We can also say that in all we want some of 12 terms i.e. from 7th to 18th

i)consider 7th term as odd
Then 6 terms will be odd and other will be even.
So sum would always be even as 6 odd terms always give even and other 6 even also give even so total sum would be even.

ii) if 7th term is odd then also 6 odd and 6 even terms.Same logic follows as above.

So A is answer as we need to know differnce between 2 terms.initial term does not matter

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Re: Is the sum of 7th through 18th term in a sequence of integers even?  [#permalink]

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New post 08 Jun 2019, 07:15
benejo wrote:
Is the sum of \(7^{th}\) through \(18^{th}\) term in a sequence of integers even?

(1) Every term in the sequence is 5 more than the previous term.
(2) The \(1^{st}\) term in the sequence is 5.

Source: ExpertsGlobal



(1) Every term in the sequence is 5 more than the previous term.

Let the 7th term = x
So terms from 7th till 18th (1.e, 12 terms) are x, x+5, x+10, . . . . . x+55
Sum of n terms of AP = \(\frac{n}{2}\)*(first term + last term)
= \(\frac{12}{2}\)*(x + x + 55)
= 6*(2x + 55)
Which is always even - Sufficient

(2) The \(1^{st}\) term in the sequence is 5.
Nothing can be said about the other terms using first term - Insufficient

So, Option A

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Re: Is the sum of 7th through 18th term in a sequence of integers even?  [#permalink]

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New post 08 Jun 2019, 12:55
The first statement doesn't make sense unless it excludes the first term (the first term of the sequence can't be five more than the previous term, because there is no previous term). If this were a real GMAT question, the wording would account for that.

Anyway, if we add 5 to get the next term each time, then the sequence will alternate: odd, even, odd, even, odd, even (or even, odd, even, odd...). We need to add twelve terms, so 6 terms will be even, 6 will be odd, and the sum will thus be even. So Statement 1 is sufficient, and Statement 2 is irrelevant, so the answer is A.
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Re: Is the sum of 7th through 18th term in a sequence of integers even?   [#permalink] 08 Jun 2019, 12:55
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