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# If integer m is not a multiple of 3, which of the following must be

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Math Expert
Joined: 02 Sep 2009
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If integer m is not a multiple of 3, which of the following must be  [#permalink]

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16 Nov 2016, 04:51
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If integer m is not a multiple of 3, which of the following must be true?

A. m(m+1) is a multiple of 3
B. m+2 is a multiple of 3
C. m is a multiple of 2
D. (m+1)(m-1) is a multiple of 2
E. (m+1)(m-1) is a multiple of 3

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Re: If integer m is not a multiple of 3, which of the following must be  [#permalink]

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16 Nov 2016, 06:23
Since m is not multiple of 3, m can be 4 or 5 or any other no.
Let us substitute values in the answer.
A - m=4, 4(4+1)=20 not multiple of 3.
B - m=5, 5+2 = 7 is not multiple of 3.
C - m=5 not multiple of 2
D - m=4, (m+1)(m-1) = (4+1)(4-1)=15, not multiple of 2.
E - m=4 or 5 satisfies the equation (m+1)(m-1) is a multiple of 3. Hence true.

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Re: If integer m is not a multiple of 3, which of the following must be  [#permalink]

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16 Nov 2016, 06:52
Bunuel wrote:
If integer m is not a multiple of 3, which of the following must be true?

A. m(m+1) is a multiple of 3
B. m+2 is a multiple of 3
C. m is a multiple of 2
D. (m+1)(m-1) is a multiple of 2
E. (m+1)(m-1) is a multiple of 3

m is not a multiple of 3
m=1, 2, 4, 5, 7, 8....

A. m(m+1) is a multiple of 3 let m=2, 2(3) is a multiple of 3
B. m+2 is a multiple of 3 let m=1,m+2=3 is a multiple of 3
C. m is a multiple of 2 let m=2, m is a multiple of 2
D. (m+1)(m-1) is a multiple of 2 let m=1, 0 is amultiple of 2
E. (m+1)(m-1) is a multiple of 3 let m=1, (m-1)(m+1)=0 multiple of 3, let m=2, (m+1)(m-1)=3 is a multiple of 3 Always true

So E
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Re: If integer m is not a multiple of 3, which of the following must be  [#permalink]

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17 Nov 2016, 06:14
1
m is not a multiple of 3
m=3K+1 or 3K+2

A. m(m+1) is a multiple of 3 let m=3K+1, (3K+1)*(3K+2) is not a multiple of 3
B. m+2 is a multiple of 3 let m=3K+2,m+2=3K+4 is a not a multiple of 3
C. m is a multiple of 2 let m=3K+2, m is a not always a multiple of 2
D. (m+1)(m-1) is a multiple of 2 let m=3K+2, (m+1)(m-1) = (3K+3)X(3K+1) is a not a multiple of 2
E. (m+1)(m-1) is a multiple of 3 let m=3K+2, (m-1)(m+1)= (3K+3)(3K+1) is always a multiple of 3, let m=3K+1, (m+1)(m-1)=(3K+2)*(3k) is a multiple of 3 Always true

So E
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Re: If integer m is not a multiple of 3, which of the following must be  [#permalink]

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18 Nov 2016, 08:05
Bunuel wrote:
If integer m is not a multiple of 3, which of the following must be true?

A. m(m+1) is a multiple of 3
B. m+2 is a multiple of 3
C. m is a multiple of 2
D. (m+1)(m-1) is a multiple of 2
E. (m+1)(m-1) is a multiple of 3

A) m(m+1) is a multiple of 3: This is not necessarily true. For instance, if m = 4, m(m+1) = 4 x 5 = 20 is not a multiple of 3.

B) m+2 is a multiple of 3: This is not necessarily true. For instance, if m = 5, m + 2 = 7 is not a multiple of 3.

C) m is a multiple of 2: This is not necessarily true. For instance, if m = 5, then m is not a multiple 2.

D) (m+1)(m-1) is a multiple of 2: This is not necessarily true. For instance, if m = 4, (m+1)(n-1) = 5(3) = 15 is not a multiple of 2.

E) (m+1)(m-1) is a multiple of 3: This is true.

Regardless of the values we select for m (keeping in mind that m can’t be a multiple of 3), (m+1)(m-1) will always be a multiple of 3.

Remember non-multiples of 3 are numbers such as:

1, 2, 4, 5, 7, 8…

Adding or subtracting 1 to any of the above numbers will ALWAYS result in a multiple of 3, and thus the product of (m - 1)(m + 1) will always be a multiple of 3.

For instance:

1 - 1 = 0 (a multiple of 3)

2 + 1 = 3 (a multiple of 3)

4 - 1 = 3 (a multiple of 3)

5 + 1 = 6 (a multiple of 3)

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Re: If integer m is not a multiple of 3, which of the following must be  [#permalink]

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01 Jan 2018, 01:06
Possible values of m = 1,2,4,5,6,7,....

A) not true for m = 1
B) not true if m = 2
C) not true is m = 1
D) not true if m = 4
E) Always true
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Re: If integer m is not a multiple of 3, which of the following must be   [#permalink] 01 Jan 2018, 01:06
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