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N is the sum of X consecutive positive integers, is N divisible by 5?

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amanvermagmat
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N is the sum of X consecutive positive integers, is N divisible by 5? [#permalink] New post   16 Jul 2018, 11:18
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N is the sum of X consecutive positive integers, is N divisible by 5?

(1) X = 5.

(2) N is divisible by 10.
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D
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u1983
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Re: N is the sum of X consecutive positive integers, is N divisible by 5? [#permalink] New post   16 Jul 2018, 12:42
amanvermagmat wrote:
N is the sum of X consecutive positive integers, is N divisible by 5?

(1) X = 5.

(2) N is divisible by 10.


Statement 02: If N is divisible by 10 .... Definitely it will be divisible by 5..........SUFFICINT
Statement 01: x=5, say the numbers be n, n+2 , n+4 , n+6 , n+8 (n=1,2......)
hence, N=n + n+2 + n+4 + n+6 + n+8 =5n+20
hence N/5=n+4......... hence N is divisivle by 5........................................SUFFICIENT ...... Ans D.
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N is the sum of X consecutive positive integers, is N divisible by 5? [#permalink] New post   09 Nov 2020, 10:04
u1983 wrote:
amanvermagmat wrote:
N is the sum of X consecutive positive integers, is N divisible by 5?

(1) X = 5.

(2) N is divisible by 10.


Statement 02: If N is divisible by 10 .... Definitely it will be divisible by 5..........SUFFICINT
Statement 01: x=5, say the numbers be n, n+2 , n+4 , n+6 , n+8 (n=1,2......)
hence, N=n + n+2 + n+4 + n+6 + n+8 =5n+20
hence N/5=n+4......... hence N is divisivle by 5........................................SUFFICIENT ...... Ans D.



N = sum of consecutive integers (n, n+1, n+2, n+3, n+4), but why are you taking only the even or odd numbers (n, n+2...

I agree that any series in an A.P with a C.D of 1, 2, or 3 would lead to the same answer. But is there a specific reason you took those nos, considering the question is specifically asking for consecutive positive integers?
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Re: N is the sum of X consecutive positive integers, is N divisible by 5? [#permalink] New post   08 May 2022, 20:08
Statement 1:
X=5 means 5 consecutive integers
Eg: x,(x+1),(x+2),(x+3),(x+4)
Summation = 5x+10 = 5(x+2)
5(x+2) is divisible by 5

For understanding let us take some other consecutive integers
Eg: (x+42),(x+43),(x+44),(x+45),(x+46)
Summation= 5x+220 = 5(x+44)
5(x+44) is divisible by 5

Concept: If you take any 5 consecutive integers then the summation will always have the effect of 5.

Statement 1 is sufficient alone


Statement 2:
Concept: If a number is divisible by 10 then it is also divisible by 5

Statement 2 is sufficient alone

So, answer is D
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Re: N is the sum of X consecutive positive integers, is N divisible by 5? [#permalink]
08 May 2022, 20:08
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