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DS - remainders: p² - n² divided by 10

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by Xbond » Sun Oct 04, 2009 7:55 am
Hi there,

Could you help me to resolve this PS and explain the step of resolution

If p and n are positive integers ans p>n, what is the remainder when p²-n² is divided by 15 ?

1) The remainder when p+n is divided by 5 is 1

2) The remainder when p-n is divided by 3 is 1
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Source: — Data Sufficiency |
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by life is a test » Sun Oct 04, 2009 10:16 am
E?
(P^2 + n^2) / (3 *5 )= (p+n)(p-n)/3*5
1: one of the numerators could be 6, 11, 16, 21...
2: one of the other numerators could 4, 7, 10, 13 ...

1 and 2 together doesn't give single remainder, e.g. when you take 6*4/15, remainder is 9 but when you take 11*7/15, the remainder is 2.
Whats the OA?
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by life is a test » Sun Oct 04, 2009 10:18 am
sorry I misread the denominator to be 15 for some reason...I still think same answer and same logic applies though.
life is a test wrote:E?
(P^2 + n^2) / (3 *5 )= (p+n)(p-n)/3*5
1: one of the numerators could be 6, 11, 16, 21...
2: one of the other numerators could 4, 7, 10, 13 ...

1 and 2 together doesn't give single remainder, e.g. when you take 6*4/15, remainder is 9 but when you take 11*7/15, the remainder is 2.
Whats the OA?
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by mehravikas » Sun Oct 04, 2009 3:29 pm
Answer should be E.
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by Dobrov » Wed Oct 14, 2009 10:55 am
Definitely E.
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by imanemekouar » Mon Dec 28, 2009 6:58 am
Can you please explain this.

In the arithmetic sequence t1,t2,t3,......tn......, t1 = 23 and tn = tn-1 - 3 for each n>1. What is the value of n when tn = -4
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