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n is a positive integer less than 50. When n is divided by

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by Max@Math Revolution » Mon Aug 06, 2018 11:51 pm
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[Math Revolution GMAT math practice question]

n is a positive integer less than 50. When n is divided by 6, the remainder is 2, and when n is divided by 7, the remainder is 6. What is the remainder when n is divided by 8?

A. 1
B. 2
C. 3
D. 4
E. 5
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by swerve » Wed Aug 08, 2018 10:25 am
When n is divided by 6, the remainder is 2.
When n is divided by 7, the remainder is 6.
(7x+6)/6 should give remainder 2
x=2 satisfies the equation.

Hence, the general equation will be 7*6x + 20 = 42x+20.
Since n is less than 50. Put x=0. Then n=20.

20/8 will leave a remainder 4. Therefore, D is the correct answer. Regards!
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by Max@Math Revolution » Thu Aug 09, 2018 12:20 am
=>

The positive integers less than 50 that have a remainder of 2 when they are divided by 6 are n = 2, 8, 14, 20, 26, 32, 38 and 44.
The positive integers less than 50 that have a remainder of 6 when they are divided by 7 are n = 6, 13, 20, 27, 34, 41 and 48.
The only integer in both lists is n = 20.
20 has a remainder of 4 when it is divided by 8.

Therefore, the answer is D.
Answer: D
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Re: n is a positive integer less than 50. When n is divided by

by Scott@TargetTestPrep » Thu Mar 23, 2023 10:52 am
Max@Math Revolution wrote: ↑
Mon Aug 06, 2018 11:51 pm
 [Math Revolution GMAT math practice question]

n is a positive integer less than 50. When n is divided by 6, the remainder is 2, and when n is divided by 7, the remainder is 6. What is the remainder when n is divided by 8?

A. 1
B. 2
C. 3
D. 4
E. 5
Using the first piece of information, we see that n can be:

2, 8, 14, 20, 26…

Using the second pieice of information, we see that n can be:

6, 13, 20

Since 20 matches both lists, we can say n = 20.

Thus, 20/8 2 remainder 4.

Answer: D

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