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bww: Senior | Next Rank: 100 Posts; Posts: 55; Joined: Sun Apr 29, 2007 6:25 am; Location: MA; Thanked: 1 times

prep question

by bww » Sun May 06, 2007 5:11 pm

Can someone give me a sanity check? I'm stuck. How can 10 be a possible value?

If M and N are positive integers that have remainders of 1 and 3, respectively, when divided by 6, which of the following could NOT be a possible value of M+N?
(A) 86
(B) 52
(C) 34
(D) 28
(E) 10

OA is E.

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Source: Beat The GMAT — Problem Solving | Sun May 06, 2007 5:11 pm

jayhawk2001: Community Manager; Posts: 789; Joined: Sun Jan 28, 2007 3:51 pm; Location: Silicon valley, California; Thanked: 30 times; Followed by:1 members

Re: prep question

by jayhawk2001 » Sun May 06, 2007 5:34 pm

bww wrote:Can someone give me a sanity check? I'm stuck. How can 10 be a possible value?

If M and N are positive integers that have remainders of 1 and 3, respectively, when divided by 6, which of the following could NOT be a possible value of M+N?
(A) 86
(B) 52
(C) 34
(D) 28
(E) 10

OA is E.

I'm getting A

M = 6x + 1
N = 6y + 3

M+N = 6 (x+y) + 4

A: 86-4 = 82 not divisible by 6
B: 52-4 = 48 divisible by 6
C: 30 divisible by 6
D: 24 divisible by 6
E: 6 divisible by 6

In fact if M = 1 and N = 9, we get M+N = 10 and this also satisfies
the remainder constraints.

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kookoo4tofu: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Mon May 07, 2007 5:23 am

by kookoo4tofu » Mon May 07, 2007 7:00 am

dont forget M and N MUST be positive integers so (x+y) must be greater than 1 no matter what, thus the sum must be greater than 10

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kookoo4tofu: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Mon May 07, 2007 5:23 am

by kookoo4tofu » Mon May 07, 2007 7:01 am

dont forget M and N MUST be positive integers so (x+y) must be greater than 1 no matter what, thus the sum must be greater than 10

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Cybermusings: Legendary Member; Posts: 559; Joined: Tue Mar 27, 2007 1:29 am; Thanked: 5 times; Followed by:2 members

by Cybermusings » Mon May 07, 2007 10:42 am

If M and N are positive integers that have remainders of 1 and 3, respectively, when divided by 6, which of the following could NOT be a possible value of M+N?
(A) 86
(B) 52
(C) 34
(D) 28
(E) 10

M can belong to the set {7,13,19,25,31,37....}
N belongs to the set {9,15,21,27,33,39,45...}

thus the least value of M+N can be 7+9 = 16
Hence 10 is clearly ruled out

So E