When the positive integer n is divided by 8, the remainder i

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Tue Jul 10, 2018 1:30 am

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[GMAT math practice question]

When the positive integer n is divided by 8, the remainder is 3, and when n is divided by 5, the remainder is 2. What is the remainder when the smallest possible value of n is divided by 6?

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

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Jul 10, 2018 3:57 am

Max@Math Revolution wrote:[GMAT math practice question]

When the positive integer n is divided by 8, the remainder is 3, and when n is divided by 5, the remainder is 2. What is the remainder when the smallest possible value of n is divided by 6?

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

When the positive integer n is divided by 8, the remainder is 3.
In other words, n is 3 more than a multiple of 8:
n = 8a + 3, where a is nonnegative integer.
Options for n:
3, 11, 19, 27...

When n is divided by 5, the remainder is 2.
In other words, n is 2 more than a multiple of 5:
n = 5b + 2, where b is nonnegative integer.
Options for n:
2, 7, 12, 17, 22, 27...

The smallest value common to the two lists is 27.
When 27 is divided by 6, the remainder is 3.

The correct answer is D.

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BTGmoderatorLU: Moderator; Posts: 2607; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Tue Jul 10, 2018 6:32 pm

n = 8p + 3
n = 5q + 2

8p+3 = 5q+2
p = (5q-1)/8

For p to be divisible by 8, q can be 5, 13...
Therefore, n = 27, 67...
Remainder when 27 (smallest value of n) is divided by 6 is 3.

Hence, D is the correct answer.

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Wed Jul 11, 2018 11:40 pm

=>

If n has remainder 3 when it is divided by 8, then n = 8a + 3 for some integer a. The possible positive integer values of n are 3, 11, 19, 27, 35, ... .
If n has remainder 2 when it is divided by 5, then n = 5b + 2 for some integer b. The possible positive integer values of n are 2, 7, 12, 17, 22, 27, 32, ... .
The smallest value of n that appears in both lists is 27. Therefore, the smallest possible value for n is 27.
27 = 6*4 + 3, 27 has remainder 3 when it is divided by 6.

Therefore, the answer is D.
Answer: D

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swerve: Legendary Member; Posts: 2579; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Fri Jul 13, 2018 9:06 am

Possible values when divided by 8 are {3, 11, 19, 27.............}
Possible values when divided by 5 are {2, 7, 12, 17, 22, 27.........}

Thus when 27 is divided by 6 we have the remainder as 3, the correct answer is D.

Regards!

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8207; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Fri Apr 26, 2019 2:38 pm

Max@Math Revolution wrote:[GMAT math practice question]

When the positive integer n is divided by 8, the remainder is 3, and when n is divided by 5, the remainder is 2. What is the remainder when the smallest possible value of n is divided by 6?

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

Since n/8 has a remainder of 3, n can be:

3, 11, 19, 27, ...

Since n/5 has a remainder of 2, n can be:

2, 7, 12, 17, 22, 27, ...

Thus, we see 27 is the smallest possible value of n, and 27/6 = 4 remainder 3.

Answer: D

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