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Divisibility/remainder problem

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Divisibility/remainder problem

by bubblynyg » Tue May 19, 2015 9:53 pm
For positive integers m and n, when m is divided by n the remainder is 4. Which of the following CANNOT be the value of n?

(A) 3 (B) 5 (C) 7 (D) 12 (E) 16

Can someone help with how to tackle this problem please. Thanks!
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by [email protected] » Tue May 19, 2015 10:09 pm
Hi bubblynyg,

This question is built around a Number Property rule that's tied to "Remainder" rules.

To have a remainder of 4, you have to divide by a number that is GREATER than 4.

For example....

11/5 = 2 remainder 1
12/5 = 2 remainder 2
13/5 = 2 remainder 3
14/5 = 2 remainder 4

If you divide by 4 or less, then the remainder CANNOT be 4.

11/4 = 2 remainder 3
12/4 = 3 remainder 0
13/4 = 3 remainder 1
14/4 = 3 remainder 2

Dividing by 3, 2 or 1 makes the maximum possible remainder even smaller.

Here, dividing by 3 means that the remainder can be 0, 1 or 2.....but not 4.

Final Answer: A

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by GMATGuruNY » Tue May 19, 2015 11:13 pm
bubblynyg wrote:For positive integers m and n, when m is divided by n the remainder is 4. Which of the following CANNOT be the value of n?

(A) 3 (B) 5 (C) 7 (D) 12 (E) 16
Rich's solution illustrates the following rule:
When a positive integer is divided by positive integer d, the greatest possible remainder is d-1.

Applying this rule to answer choice A, we get:
When positive integer m is divided by positive integer n=3, the greatest possible remainder is n-1 = 3-1 = 2.
Since n=3 cannot yield a remainder of 4, the value of n cannot be 3.

The correct answer is A.
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