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Remainder Prob

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mana6 Just gettin' started! Default Avatar
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Post Sat Jan 08, 2011 4:26 pm
i see my own mistake i misread statement one its n is odd. if i use this statement now i do get that r should be zero and this statement is then sufficient.

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Post Wed Mar 23, 2011 5:29 am
The answer is very clear A
With 2 we can say value of r can be 0 1 2 3 4 5 6 or 7
but with 1 we can say for sure it is 0
i.e.
n = 1 expr (1-1)/8 , r= 0
n = 3 expr (9-1)/8, r= 0
n = 5 expr (25-1)/8, r= 0

hence answer is A Smile

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Post Tue May 17, 2011 7:40 am
My answer is (A).
I see that in this case, it is quicker to use number properties to get the answer. But, I went around plugging in values, which was obviously more time consuming.
At the time I saw this question, it seemed to me a clear candidate for plugging values!

Is there any means by which I could have identified the mode of attack better?

Cheers!

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Post Wed May 18, 2011 4:05 am
Ian Stewart wrote:
zagcollins wrote:
If n is a positive integer and r is the remainder when n^2-1 is divided by 8, what is the value of r?

1)n is odd
2)n is not divisible by 8
You might notice that this is a difference of squares:

n^2 - 1 = (n+1)(n-1)

If n is odd, then n-1 and n+1 are consecutive even integers. If you take any two consecutive even integers, one of them will be divisible by 4, the other not, so their product must be divisible by 8. Thus, if we know n is odd, we can be certain that n^2 -1 will be divisible by 8, and r will be zero. 1) is sufficient. 2) is not; n might be even, or might be odd. A.
Hi Steward,
I have one stupid question about divisibility and remainder and it really confuses me.
I'll much appreciate your explanation.
About divisibility: It's clear that 10 is indivisible by 3 and the remainder is 1 (because 1/3 is infinitive)
However: Is 12 divisible by 8 as the result is 1.5 (4 is divided by 8)?
What does divisibility mean? (Does it refer to integer or infinity?)
Thanks so much in advance
Kelly

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Post Mon May 30, 2011 10:23 pm
A

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Post Mon Jun 06, 2011 8:03 pm
IMO - A

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Post Mon Jun 06, 2011 9:33 pm
If n is a positive integer and r is the remainder when n^2-1 is divided by 8, what is the value of r?

1)n is odd
2)n is not divisible by 8
(n-1)(n+1) divided by 8
a) n is odd, and thus (n-1),(n+1) are 2 consecutive even numbers. thus one of them is divisible by 4 and one of them is divisible by 2. Thus product is divisible by 8. Sufficient (r=0)
b)n is not divisible by 8. But it can be even and odd (even->2,odd->3)
Insufficient.
IMO A

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Post Mon Jun 06, 2011 9:43 pm
the answer is A

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Post Tue Jun 07, 2011 12:55 pm
coolly01 wrote:
I have one stupid question about divisibility and remainder and it really confuses me.
I'll much appreciate your explanation.
About divisibility: It's clear that 10 is indivisible by 3 and the remainder is 1 (because 1/3 is infinitive)
However: Is 12 divisible by 8 as the result is 1.5 (4 is divided by 8)?
What does divisibility mean? (Does it refer to integer or infinity?)
I just saw this now. We say that an integer x is divisible by an integer y if x/y is an integer. So 14 is divisible by 7, because 14/7 = 2, which is an integer. However 12 is *not* divisible by 8, since 12/8 = 1.5 is not an integer.

I think you might be confusing the concept of divisibility with that of terminating/repeating decimals. A number is only divisible by another if you get no decimal part at all when you divide.

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coolly01 Just gettin' started! Default Avatar
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Post Tue Jun 07, 2011 8:57 pm
Ian Stewart wrote:
coolly01 wrote:
I have one stupid question about divisibility and remainder and it really confuses me.
I'll much appreciate your explanation.
About divisibility: It's clear that 10 is indivisible by 3 and the remainder is 1 (because 1/3 is infinitive)
However: Is 12 divisible by 8 as the result is 1.5 (4 is divided by 8)?
What does divisibility mean? (Does it refer to integer or infinity?)
I just saw this now. We say that an integer x is divisible by an integer y if x/y is an integer. So 14 is divisible by 7, because 14/7 = 2, which is an integer. However 12 is *not* divisible by 8, since 12/8 = 1.5 is not an integer.

I think you might be confusing the concept of divisibility with that of terminating/repeating decimals. A number is only divisible by another if you get no decimal part at all when you divide.
I'm clear now.
Thanks so much Stewart
Kelly

theadityajamwal Just gettin' started! Default Avatar
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Post Thu Jul 14, 2011 2:58 am
n^2 - 1 can be represented as (n-1)(n+1).
now if n = odd n-1 and n+1 represent two consecutive even number.
so n - 1 = 2 * x where x = any integer
n + 1 = (n-1) + 2 = 2*x + 2 = 2 (x+1)

Case1: if x = odd, x+1 will be even. So n+1 will be divisible by 2 * (Even Number) which means 4
Also n-1 will be divisible by 2 only. since x = odd.
Combining (n-1)(n+1) will be divisible by 4*2 = 8.
Case2: If x = even, x+1 will be odd. So n+1 will be divisible only by 2.
n-1 will be divisible by 2 * Even Number = 4
Combining (n-1)(n+1) will be divisible by 4*2 = 8.

Hence A) is the correct answer.

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Post Thu Jul 14, 2011 10:40 am
As statement 1 says-- n is odd..so just pick any odd value of n & you will see that the reminder is 0.
for example. n is 5. N^2 1 is 24 which is divisible by 8.n is 7 n^2-1 is 48 which is also divisible by 8 with reminder of 0.so you know r is always 0..\
St2.does not tell us anything about r or more..

OA - A

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Post Sat Jul 16, 2011 5:38 pm
1) is insufficient because n can be any odd number
2) is insufficient because n can be any number not divisible by 8 but it does rule out 1 as a possiblity. 0 is divisble by 8.
Together they are sufficent because the remainder is always zero for any odd number squared minus 1 divided by 8. (Performed)operation with 4 consecutive odd numbers.
Therefore I chose C and my answer.

shingik Just gettin' started!
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Post Sat Jul 16, 2011 5:46 pm
shingik wrote:
1) is insufficient because n can be any odd number
2) is insufficient because n can be any number not divisible by 8 but it does rule out 1 as a possiblity. 0 is divisble by 8.
Together they are sufficent because the remainder is always zero for any odd number squared minus 1 divided by 8. (Performed)operation with 4 consecutive odd numbers.
Therefore I chose C and my answer.
Just noticed my own dumb mistake --- A is sufficient.

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Post Mon Aug 29, 2011 6:36 am
ANSWER: A

Should be correct this time around

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