|
Author |
Message |
|
TAGS:
|
|
|
Intern
Joined: 14 Jul 2005
Posts: 45
Location: California
Followers: 0
Kudos [?]:
0
[0], given: 0
|
If M and N are positive integers that have remainders of 1 [#permalink]
 16 Nov 2006, 22:10
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
Can anyone show me an easy way of solving this...
|
|
|
|
|
|
|
SVP
Joined: 08 Nov 2006
Posts: 1560
Location: Ann Arbor
Schools: Ross '10
Followers: 12
Kudos [?]:
155
[0], given: 1
|
M=6n1+1
N=6n2+3
M+N = 6(n1+n2)+4=6(x)+4
So, M+N will be a multiple of 6, + 4.
Except 86, all the other values meet this criteria.
hence the answer is 86.
|
|
|
|
|
|
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5134
Location: Singapore
Followers: 9
Kudos [?]:
87
[0], given: 0
|
M = 6n + 1
N = 6t + 3
M+n = 6(n+t) + 4 = 2(3(n+t) + 2)
A - (86/2) - 2 = 41 <-- not divisible by 3
B - (52/2) - 2 = 48 <-- divisible by 3
C - (34/2) - 2 = 15 <-- divisible by 3
D - (28/2) - 2 = 12 <-- divisible by 3
E - (10/2) - 2 = 3 <--- divisible by 3
Ans A
|
|
|
|
|
|
Manager
Joined: 03 Jul 2005
Posts: 199
Location: City
Followers: 1
Kudos [?]:
0
[0], given: 0
|
Another approach
(m + n) / 6 = x + 4
6x + 24 = 86, x = 7
All other numbers when tested are not divisibly by 6 hence A is the answer
|
|
|
|
|
|
Director
Joined: 06 Feb 2006
Posts: 912
Followers: 1
Kudos [?]:
16
[0], given: 0
|
My way:
Pick numbers
m=7
n=9
m+n=16...divide by 6....remainder is 4
Now look at the answer choices. Divide each value by 6 and look where the raimainder isn't 4.
A
|
|
|
|
|
|
SVP
Joined: 05 Jul 2006
Posts: 1565
Followers: 4
Kudos [?]:
63
[0], given: 34
|
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= 6x+1
n= 6y+3
m+n= 6x+6y+4
86/6= 14 2/6 ( remainder is 2 not 4
my answer is A
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
close
