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Number theory

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Number theory

by Gopi » Mon Jul 27, 2009 1:03 am
Hi All,

This is my first post, please let me know short-cut for this problem,


What is the remainder of the division of 14414*14416*14418 by 14?

A) 8
B) 3
C) 12
D) 10
E) 6



Thanks in advance
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by niraj_a » Mon Jul 27, 2009 6:35 am
is it D?

i didn't have scratch paper but i basically multiplied out the very last numbers since they are the only ones that change.

4 * 6 * 8 = a sequence of 24. 24/14 = 10 remainder.

if i had scratch paper, i probably would have multiplied out 14*16*18 and seen how that would have turned out.
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by sreak1089 » Mon Jul 27, 2009 6:46 am
4 * 6 * 8 = 192 / 14 gives remainder 10. But I am not sure if this method is correct to solve this problem.
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by prindaroy » Mon Jul 27, 2009 8:51 am
your method is correct but i don't think answer is.

14414/14 = remainder 8

14416/14 = remainder 10

14418/14 = remainder 12

so 8*10*12 = 960/14 = remainder 8

so A should be the answer.
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by vinayakdl » Mon Jul 27, 2009 10:01 am
Yes 8 is the answer...prindaroy's approach is correct.

Vinayak
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by ghacker » Mon Jul 27, 2009 1:20 pm
14420 is divisible by 14 so is 14406 then we can write 14406 as amultiple of 14

That is 14406 = 14K for some integer K

14414*14416*14418 /14 =(14K+8)(14K+10)(14K+12)/14


= (14(z)+8*10*12)/14 = Z+8*10*12/14

so the remainder is 8
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by xilef » Tue Jul 28, 2009 4:19 pm
what about taking the last 2 digits:

14/14 no remainder

16/14 remainder 2

18/14 remainder 4


2*4 = 8
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by Gopi » Sat Aug 08, 2009 12:08 am
prindaroy wrote:your method is correct but i don't think answer is.

14414/14 = remainder 8

14416/14 = remainder 10

14418/14 = remainder 12

so 8*10*12 = 960/14 = remainder 8

so A should be the answer.

Yes, The answer is A (8) and Thanks for reply
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