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Math Expert V
Joined: 02 Sep 2009
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If n divided by 7 has a remainder of 2, what is the remainder when 3  [#permalink]

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If n divided by 7 has a remainder of 2, what is the remainder when 3 times n is divided by 7?

A. 1
B. 2
C. 3
D. 5
E. 6

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Current Student D
Joined: 12 Aug 2015
Posts: 2550
Schools: Boston U '20 (M)
GRE 1: Q169 V154 If n divided by 7 has a remainder of 2, what is the remainder when 3  [#permalink]

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2
As per question => N=7P+2 for some integer p
hence 3N => 21Q + 6 => remainder => 6 for some integer Q
Alternatively => N=2 > 3N=> 6 => 6 divided by 7 will leave a remainder 6
hence E
I hope it helps.
Peace Out ..
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Originally posted by stonecold on 21 Mar 2016, 09:02.
Last edited by stonecold on 02 Apr 2016, 12:02, edited 1 time in total.
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Re: If n divided by 7 has a remainder of 2, what is the remainder when 3  [#permalink]

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Chiragjordan wrote:
As per question => N=7P+2 for some integer p
hence 3N => &Q + 6 => remainder => 6 for some integer Q
Alternatively => N=2 > 3N=> 6 => 6 divided by 7 will leave a remainder 6
hence E
I hope it helps.
Peace Out ..
NO KUDOS NEEDED Is it ok to multiply the entire equation by 3, like you did. I plugged in the values and got the right answer because was not sure of the multiplication approach. Can this be used a s a rule?
Current Student D
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GRE 1: Q169 V154 Re: If n divided by 7 has a remainder of 2, what is the remainder when 3  [#permalink]

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MeghaP wrote:
Chiragjordan wrote:
As per question => N=7P+2 for some integer p
hence 3N => &Q + 6 => remainder => 6 for some integer Q
Alternatively => N=2 > 3N=> 6 => 6 divided by 7 will leave a remainder 6
hence E
I hope it helps.
Peace Out ..
NO KUDOS NEEDED Is it ok to multiply the entire equation by 3, like you did. I plugged in the values and got the right answer because was not sure of the multiplication approach. Can this be used a s a rule?

It is completely Fine to multiply the equation by any integer as long as it is not zero.
here since it is a P.S question you can plug in the values to.
However by using the basic mathematical logic => it can be done in a few seconds.
Now your approach is absolutely fine ; Although i would recommend using the above technique so that you become more familiar with the concept of remainders.
During the exam =>Use the approach that you feel is the easiest .
Feel free to ask any more Questions
Peace Out
S.C.S.A

If you feel I helped Go tap that lil Kudos button
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Re: If n divided by 7 has a remainder of 2, what is the remainder when 3  [#permalink]

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Chiragjordan wrote:
MeghaP wrote:
Chiragjordan wrote:
As per question => N=7P+2 for some integer p
hence 3N => &Q + 6 => remainder => 6 for some integer Q
Alternatively => N=2 > 3N=> 6 => 6 divided by 7 will leave a remainder 6
hence E
I hope it helps.
Peace Out ..
NO KUDOS NEEDED Is it ok to multiply the entire equation by 3, like you did. I plugged in the values and got the right answer because was not sure of the multiplication approach. Can this be used a s a rule?

It is completely Fine to multiply the equation by any integer as long as it is not zero.
here since it is a P.S question you can plug in the values to.
However by using the basic mathematical logic => it can be done in a few seconds.
Now your approach is absolutely fine ; Although i would recommend using the above technique so that you become more familiar with the concept of remainders.
During the exam =>Use the approach that you feel is the easiest .
Feel free to ask any more Questions
Peace Out
S.C.S.A

If you feel I helped Go tap that lil Kudos button

N=7P+2, Multiply by 3 -> 3N = 21Q + 6
Is this correct? I ask because you put & instead of 21. not sure if that is a typo?
Thanks
Current Student D
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Schools: Boston U '20 (M)
GRE 1: Q169 V154 Re: If n divided by 7 has a remainder of 2, what is the remainder when 3  [#permalink]

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exactly MeghaP that was a typo Regards
S.C.S.A
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Re: If n divided by 7 has a remainder of 2, what is the remainder when 3  [#permalink]

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What is the level of these question ?
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Re: If n divided by 7 has a remainder of 2, what is the remainder when 3  [#permalink]

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Bunuel wrote:
If n divided by 7 has a remainder of 2, what is the remainder when 3 times n is divided by 7?

A. 1
B. 2
C. 3
D. 5
E. 6

Least possible value of n = 2
Quote:
what is the remainder when 3 times n is divided by 7

Thus, the remainder will be 6

Hence, answer will be (E) 6

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If n divided by 7 has a remainder of 2, what is the remainder when 3  [#permalink]

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Bunuel wrote:
If n divided by 7 has a remainder of 2, what is the remainder when 3 times n is divided by 7?

A. 1
B. 2
C. 3
D. 5
E. 6

let n=2
if 2/7 gives a remainder of 2,
then (2*3)/7 gives a remainder of 6
E
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Re: If n divided by 7 has a remainder of 2, what is the remainder when 3  [#permalink]

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Hi All,

We're told that when N is divided by 7, the remainder is 2. We're asked for the remainder when 3N is divided by 7. This question can be solved rather easily by TESTing VALUES.

N can actually be lots of different values, so I'll list out the first several: N/7 = __ r 2...... N = 2, 9, 16, 23, 30, etc.

IF.... N=9...
3(9)/7 = 27/7 = 3 r 6

So the remainder is 6.

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Rich
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Re: If n divided by 7 has a remainder of 2, what is the remainder when 3  [#permalink]

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Top Contributor
Bunuel wrote:
If n divided by 7 has a remainder of 2, what is the remainder when 3 times n is divided by 7?

A. 1
B. 2
C. 3
D. 5
E. 6

----ASIDE-------------------------
When it comes to remainders, we have a nice rule that says:
If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.
-----------------------------

In this case we are told that n divided by 7 leaves a remainder of 2
So the possible values of n are: 2, 9, 16, 23, etc....

So let's say n equals 2
The question becomes "What is the remainder when 3 times 2 is divided by 7?"
In other words, "What is the remainder when 6 is divided by 7?"
7 divides into 6 zero times, leaving a remainder of 6

Cheers,
Brent

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GMAT 1: 690 Q50 V34 Re: If n divided by 7 has a remainder of 2, what is the remainder when 3  [#permalink]

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Bunuel wrote:
If n divided by 7 has a remainder of 2, what is the remainder when 3 times n is divided by 7?

A. 1
B. 2
C. 3
D. 5
E. 6

n= 7x+2
3n = 21x + 6

IMO E

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Re: If n divided by 7 has a remainder of 2, what is the remainder when 3  [#permalink]

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Bunuel wrote:
If n divided by 7 has a remainder of 2, what is the remainder when 3 times n is divided by 7?

A. 1
B. 2
C. 3
D. 5
E. 6

We can let n = 2. Thus:

(3 x 2)/7 = 6/7 = 0 remainder 6.

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