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# what is the least positive number which leaves a remainder

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Director
Joined: 01 Feb 2003
Posts: 838

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what is the least positive number which leaves a remainder [#permalink]

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06 Jul 2004, 08:14
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what is the least positive number which leaves a remainder of 1 when divided by 3, 2 when divided by 4 and 3 when divided by 5?

Kudos [?]: 130 [0], given: 0

Senior Manager
Joined: 01 May 2004
Posts: 335

Kudos [?]: 117 [0], given: 0

Location: USA

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06 Jul 2004, 08:37
x=1mod3
x=2mod4
x=3mod5

=> X=58mod60, =>x=60k+58, x= 58, 118, 178,....

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Intern
Joined: 29 Jun 2004
Posts: 25

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06 Jul 2004, 09:48
boksana,
i have worked this out manually and have got 58 too. but i am not sure what formula u have used can u please explain it wud save me time to work this out manually by going thru each number or multiple.
thanks

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Senior Manager
Joined: 01 May 2004
Posts: 335

Kudos [?]: 117 [0], given: 0

Location: USA

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06 Jul 2004, 09:56
It's modul arithmetic. Very useful to find remainders etc. But you need to know theory. I missed some steps before writing the final equation.

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Intern
Joined: 29 Jun 2004
Posts: 25

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06 Jul 2004, 10:05
gee that was quick !
I think i might have cracked this tell me if i am in the right lines

the difference between the divisor and the corresponding remainder is the same i.e. 3-1 =2
4-2=2
5-3=2

(3x4x5)-2 = 58
is this the approach

PS. is that ur pic in the profile..bcos if it is u r hot

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Senior Manager
Joined: 01 May 2004
Posts: 335

Kudos [?]: 117 [0], given: 0

Location: USA

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06 Jul 2004, 10:16
Please take a look at this dicsussion

http://www.gmatclub.com/phpbb/viewtopic ... light=eggs

P.S. My approach is different

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Director
Joined: 01 Feb 2003
Posts: 838

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07 Jul 2004, 10:57
Sid:

your approach is correct, and, to my knowledge that's the best

OA is 58

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Director
Joined: 05 Jul 2004
Posts: 893

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08 Jul 2004, 01:58
Sid/Vithal
Can you explain your approach mathematically?

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08 Jul 2004, 01:58
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