$N$ is a positive integer which can be expressed as $57$

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swerve: Legendary Member; Posts: 2535; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Wed Oct 02, 2019 7:18 am

$N$ is a positive integer which can be expressed as $57 \cdot 10^p$, where $p$ is a positive integer. What is the remainder when $N$ is divided by 9?

A. 0
B. 3
C. 4
D. 6
E. 7

The OA is B

Source: e-GMAT

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Source: Beat The GMAT — Problem Solving | Wed Oct 02, 2019 7:18 am

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Wed Oct 02, 2019 8:36 pm

swerve wrote:$N$ is a positive integer which can be expressed as $57 \cdot 10^p$, where $p$ is a positive integer. What is the remainder when $N$ is divided by 9?

A. 0
B. 3
C. 4
D. 6
E. 7

The OA is B

Source: e-GMAT

Given that \N=(57 \cdot 10^p\), where $p$ is a positive integer, $N$ would be of the form 570000...

Note that the rule of the remainder when a number is divided by 9 is that "The remainder when the sum of the digits of the number is the remainder when the number is divided by 9."

Sum of digits of 570000... = 5 + 7 = 12. Remainder when 12 is divided by 9 is 3. Thus, the remainder when $N$ is divided by 9 is 3.

The correct answer: B

Hope this helps!

-Jay
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8139; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Sat Oct 05, 2019 3:36 pm

swerve wrote:$N$ is a positive integer which can be expressed as $57 \cdot 10^p$, where $p$ is a positive integer. What is the remainder when $N$ is divided by 9?

A. 0
B. 3
C. 4
D. 6
E. 7

The OA is B

Source: e-GMAT

If p = 1, we have N = 570 and 570/9 = 63 R 3.

Alternate solution:

The remainder when a positive integer is divided by 9 is the same as when the sum of the digits of that integer is divided by 9. Since N = 57 x 10^p, where p is a positive integer, N is the integer 57 followed by p zeros. Therefore, the sum of the digits of N is 5 + 7 + p x 0 = 12, and since 12 has a remainder of 3 when it's divided by 9, N also has a remainder of 3 when it's divided by 9.

Answer: B

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