Number theory

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Gopi: Junior | Next Rank: 30 Posts; Posts: 21; Joined: Sun Jul 26, 2009 9:54 pm; Location: Hyderabad

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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Source: Beat The GMAT — Problem Solving | Mon Jul 27, 2009 1:03 am

niraj_a: Legendary Member; Posts: 708; Joined: Sun Jun 01, 2008 4:59 amFollowed by: 1 member; Location: USA; Thanked: 13 times

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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sreak1089: Master | Next Rank: 500 Posts; Posts: 379; Joined: Wed Jun 03, 2009 3:05 amFollowed by: 1 member; Thanked: 19 times; GMAT Score:690

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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prindaroy: Master | Next Rank: 500 Posts; Posts: 113; Joined: Thu Jul 16, 2009 11:23 am; Thanked: 15 times; GMAT Score:730

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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vinayakdl: Master | Next Rank: 500 Posts; Posts: 131; Joined: Wed May 06, 2009 1:01 pm; Location: Chicago; Thanked: 7 times

by vinayakdl » Mon Jul 27, 2009 10:01 am

Yes 8 is the answer...prindaroy's approach is correct.

Vinayak

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ghacker: Master | Next Rank: 500 Posts; Posts: 148; Joined: Wed Jun 03, 2009 8:04 pmFollowed by: 1 member; Thanked: 18 times

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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xilef: Master | Next Rank: 500 Posts; Posts: 111; Joined: Thu Jan 31, 2008 4:05 pmFollowed by: 1 member; Thanked: 18 times

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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Gopi: Junior | Next Rank: 30 Posts; Posts: 21; Joined: Sun Jul 26, 2009 9:54 pm; Location: Hyderabad

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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