When positive integer N is divided by 1463, the remainder is 41. What is the remainder when N is divided by 11?

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BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pmFollowed by: 1 member

by BTGModeratorVI » Wed Feb 03, 2021 10:34 am

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When positive integer N is divided by 1463, the remainder is 41. What is the remainder when N is divided by 11?

A) 4
B) 5
C) 6
D) 7
E) 8

Answer: E
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Source: Beat The GMAT — Problem Solving | Wed Feb 03, 2021 10:34 am

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Re: When positive integer N is divided by 1463, the remainder is 41. What is the remainder when N is divided by 11?

by Scott@TargetTestPrep » Fri Feb 19, 2021 10:11 am

BTGModeratorVI wrote: ↑
Wed Feb 03, 2021 10:34 am
When positive integer N is divided by 1463, the remainder is 41. What is the remainder when N is divided by 11?

A) 4
B) 5
C) 6
D) 7
E) 8

Answer: E

Solution:

Since 11 divides 1463 (notice that 1463/11 = 133), the remainder when N is divided by 11 is the same as when 41 is divided by 11. Since 41/11 = 3 R 8, the remainder is 8.

Alternate Solution:

One possible value for N is 1463 + 41 = 1504. (We know this is true because, when 1504 is divided by 1463, the quotient is 1 and the remainder is 41.)

Therefore, if we divide 1504 by 11, we get a quotient of 136 and a remainder of 8.

Answer: E

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