700 Algrbra! Need help again. Thanks so much!
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Source: Beat The GMAT — Data Sufficiency |
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sparky_paris
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for n=1, n squared -1 becomes 0 hence r is 0 which is also true for any odd n. Hence it works for 1
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jeffedwards
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I think your question lies in, what happens when zero is divided by another number...what is the remainder?
When zero is divided by another number the remainder is zero; you get zero as an answer....nothing is left.
I have heard people explain it like this. You have a pizza and want to divide it up between 10 friends, how much pizza does each person get? They get nothing, because you had nothing...thus zero.
When zero is divided by another number the remainder is zero; you get zero as an answer....nothing is left.
I have heard people explain it like this. You have a pizza and want to divide it up between 10 friends, how much pizza does each person get? They get nothing, because you had nothing...thus zero.
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ajith
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n^2-1 = (n+1)(n-1)YTT wrote:Could anyone explain to me why the number 1 would work in the first situation? I understand why 3, 5, 7 or others work. But why 1 works, too? Thank you so much for this great help!!
if n is an odd num (except 1) , either n+1 or n-1 is a multiple of 4 and other a multiple of 2
for example if you take 17 => 17^2-1 = (17+1)(17-1) = 18*16 ; now 18 is a multiple of 2 and 16 is a multiple of 4 hence 17^2-1 is a multiple of 8. the same is true for any positive odd integer except 1
in the case of n^2 -1 = 0 and zero is a multiple of any number- zero is a multiple of 8
https://www.beatthegmat.com/is-zero-to-b ... t4268.html
https://www.beatthegmat.com/mba/2009/08/ ... torization (see the comments)
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harsh.champ
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Well,basically the two imp. concepts used in this ques. areYTT wrote:Could anyone explain to me why the number 1 would work in the first situation? I understand why 3, 5, 7 or others work. But why 1 works, too? Thank you so much for this great help!!
0 is an even number
0 is divisible by 8
Now, for n=odd we have 1 as an odd number.Also,1 is not divisible by 8 as it leaves the remainder as 1.
Now,zero divided by 8 gives 0 as the remainder.
So, it is clear that 1 can be taken as an answer choice.
Also,I wanted to ask in which option choice did u have the doubt:-For option C,when we take both the statements together ?? or do you have doubt in any other option choice ??
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shashank.ism
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well i would like to solve your problem this wayYTT wrote:Could anyone explain to me why the number 1 would work in the first situation? I understand why 3, 5, 7 or others work. But why 1 works, too? Thank you so much for this great help!!
let odd no.be n=2k+1
so (2k+1)^2 -1 =4k^2 +4K +1 - 1 = 4k^2 +4K =4k(k + 1)
so it is clearly divisble by 4
Now either k or k+1 is even so it is divisible by 8 also
now coming for value n =1 it gives (n)^2 -1 = 0
so my friend YTT always remember 0 is divisible by any no. except itself
Hence A is suff.
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