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If the remainder is 7 when positive integer n is divided by 18, what is the remainder when n is divided by 6?
A. 0 B. 1 C. 2 D. 3 E. 4
When positive integer n is dived by 18 the remainder is 7: \(n=18q+7=(18q+6)+1=6(3q+1)+1\) --> since first term \(6(3q+1)\) is divisible by 6 then the remainder will only be from the second term 1 --> 1 divided by 6 yields remainder of 1.
Re: If the remainder is 7 when positive integer n is divided by [#permalink]
30 Sep 2013, 07:19
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what if the question is reversed, example if 23 is the remainder when n is divided by 36, what is the remainder when n is divided by 72?
When you divide n by 36, you have groups of 36 balls each and 23 balls leftover. If you want to divide by 72 now, you will join two groups of 36 to make groups of 72. You don't know whether you have even number of groups or odd number of groups of 36. If the number of groups of 36 is even (quotient is even), you will be able to pair them all up to make groups of 72 such that remainder is 23 only. If the number of groups of 36 is odd (quotient is odd), you will not be able to pair them all up. One group will be leftover and the remainder will be 36+23 = 59. _________________
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