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Math Expert V
Joined: 02 Sep 2009
Posts: 58395
If 2 is the remainder when m is divided by 5, what is the remainder  [#permalink]

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Difficulty:   5% (low)

Question Stats: 87% (00:40) correct 13% (00:59) wrong based on 154 sessions

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If 2 is the remainder when m is divided by 5, what is the remainder when 3m is divided by 5?

A. 0
B. 1
C. 2
D. 3
E. 4

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Math Expert V
Joined: 02 Aug 2009
Posts: 8004
Re: If 2 is the remainder when m is divided by 5, what is the remainder  [#permalink]

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Bunuel wrote:
If 2 is the remainder when m is divided by 5, what is the remainder when 3m is divided by 5?

A. 0
B. 1
C. 2
D. 3
E. 4

hi,
If 2 is the remainder when m is divided by 5, m can end with 7 or 2..
so 3m will end with.. 3*7 or 3*2 that is 1 or 6..
therefore any number with last digit 1 or 6 when divided by 5 will always leave 1 as remainder.
ans B
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Re: If 2 is the remainder when m is divided by 5, what is the remainder  [#permalink]

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Bunuel wrote:
If 2 is the remainder when m is divided by 5, what is the remainder when 3m is divided by 5?

A. 0
B. 1
C. 2
D. 3
E. 4

Let's find a number which when divided by 5 leaves remainder 2 = 5+2 = 7

i.e. one possible value of m = 7

value of 3m = 3*7 = 21

when em is divided by 5 then remainder = Rem (21/5) = 1

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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8024
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If 2 is the remainder when m is divided by 5, what is the remainder  [#permalink]

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Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.

If 2 is the remainder when m is divided by 5, what is the remainder when 3m is divided by 5?

A. 0
B. 1
C. 2
D. 3
E. 4

We can put m=5*k+2.
So 3*m=15*k+6 ---> 15*k+6 = 5*(3*m+1) +1 ---> The remainder is 1.

The answer is, therefore, (B).
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Re: If 2 is the remainder when m is divided by 5, what is the remainder  [#permalink]

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We can say

m=5a+2
.multiplying 3 on both side
3m=15a+6
Now divide by 5 through out m and 15a are multiples of 5 so remainder will be obtained from 6/5 remainder = 1
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Re: If 2 is the remainder when m is divided by 5, what is the remainder  [#permalink]

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2 is the remainder when m is divided by 5,
So 'm' will be 2, 7, 12 and so on.

what is the remainder when 3m is divided by 5..
putting all the values of m, we will get 1

Ans:B
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Re: If 2 is the remainder when m is divided by 5, what is the remainder  [#permalink]

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1
When 'm' is divided by 5 remainder is 2, also there must be a coefficient, say 'a'
So 'm' can be written as "m=5a+2"
To find remainder when 3m divided by 5, we can write (15a+6)/5
The term 15a being a multiple of 5 gives no remainder hence 6/5 is the only term which gives the remainder 1.
VP  P
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If 2 is the remainder when m is divided by 5, what is the remainder  [#permalink]

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if m/5 leaves a remainder of 2,
then 3m/5 leaves a remainder of 3*2-5=1
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Re: If 2 is the remainder when m is divided by 5, what is the remainder  [#permalink]

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_________________ Re: If 2 is the remainder when m is divided by 5, what is the remainder   [#permalink] 19 Jan 2018, 15:59
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