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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?

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by BTGModeratorVI » Wed Dec 16, 2020 12:35 pm

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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

Answer: E
Source: Manhattan prep
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Re: If n divided by 7 has a remainder of 2, what is the remainder when 3 times n is divided by 7?

by Brent@GMATPrepNow » Wed Dec 30, 2020 6:27 am
BTGModeratorVI wrote: ↑
Wed Dec 16, 2020 12:35 pm
 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

Answer: E
Source: Manhattan prep
----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

Answer: E


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Brent
Brent Hanneson - Creator of GMATPrepNow.com
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Re: If n divided by 7 has a remainder of 2, what is the remainder when 3 times n is divided by 7?

by swerve » Wed Dec 30, 2020 5:10 pm
BTGModeratorVI wrote: ↑
Wed Dec 16, 2020 12:35 pm
 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

Answer: E
Source: Manhattan prep
Let \(n=2\)

If \(\dfrac{2}{7}\) gives a remainder of \(2\)

Then \(\dfrac{2\cdot 3}{7}\) gives a remainder of \(6\)

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

by Scott@TargetTestPrep » Sat Jan 02, 2021 2:07 pm
BTGModeratorVI wrote: ↑
Wed Dec 16, 2020 12:35 pm
 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

Answer: E
Solution:

We can let n = 2. Thus:

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

Answer: E

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