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# When a positive integer is divided by 4, the remainder is r;

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SVP
Joined: 21 Jul 2006
Posts: 1512

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When a positive integer is divided by 4, the remainder is r; [#permalink]

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18 Aug 2008, 08:27
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When a positive integer is divided by 4, the remainder is r; when divided by 9, the remainder is R. What is the greatest possible value of $$r^2+R?$$

a) 23
b) 21
c) 17
d) 13
e) 11

Last edited by tarek99 on 18 Aug 2008, 13:21, edited 1 time in total.

Kudos [?]: 1014 [0], given: 1

Senior Manager
Joined: 19 Mar 2008
Posts: 351

Kudos [?]: 68 [0], given: 0

Re: PS: What is r^2+R? [#permalink]

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18 Aug 2008, 08:40
r can be 1,2,3
R can be 1,2,3,4,5,6,7,8,9
let k be the integer to be divided by 4 and 9.

when r = 3,
k can be 3,7,11,15,19,23,27,31,35

when k = 35, R = 8

So, max r^2 + R = 9 + 8 = 17

Kudos [?]: 68 [0], given: 0

SVP
Joined: 07 Nov 2007
Posts: 1792

Kudos [?]: 1065 [0], given: 5

Location: New York
Re: PS: What is r^2+R? [#permalink]

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18 Aug 2008, 10:12
tarek99 wrote:
When a positive integer is divided by 4, the remainder is r; when divided by 9, the remainder is R. What is the greatest possible value of $$r^2+R?$$

a) 23
b) 21
c) 17
d) 13
e) 11

divided by 4, the remainder is r--------> means -------> r<4
when divided by 9, the remainder is R ---means ------> R<9
Max possible values = 3*3 + 8=17
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Kudos [?]: 1065 [0], given: 5

SVP
Joined: 21 Jul 2006
Posts: 1512

Kudos [?]: 1014 [0], given: 1

Re: PS: What is r^2+R? [#permalink]

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18 Aug 2008, 13:48
thanks a lot guys! the OA is C.

Kudos [?]: 1014 [0], given: 1

Re: PS: What is r^2+R?   [#permalink] 18 Aug 2008, 13:48
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