Positive integer n leaves a remainder of 4 after division by 6 and a remainder of 3 after division by 5. If n is greater than 30, what is the remainder that n leaves after division by 40?  Choose the correct answer.
A) 3  B) 12  C) 18  D) 22  E) 30
The theory says:   if a # x is devided by y and leave the positive # r as the remainder then it can also leave negative # (r-y) as the remainder.   e.g:   9 when devided by 5 leves the remainder 4 : 9=5*1+4   it can also leave the remainder 4-5 = -1 : 9=5*2 -1   back to the original qtn:   n leaves a remainder of 4 after division by 6 and a remainder of 3 after division by 5   ==&gt; n leaves a remainder of -2 (i.e. 4-6) after division by 6 and a remainder of -2 (i.e. 3-5) after division by 5   ==&gt; n when devided by 5 and 6 leaves the same remainder -2.   what is n?   LCM (5,6)-2 = 30-2= 
<gadget id="calculator">30-2</gadget>
<output>28</output>
28   CHECK: 28 when devided by 6 leaves the remainder 4 and when devided by 5 leaves the remainder 3   However, the qtn says n &gt; 40   so what is the nex #, &gt; 28, that can give the said remainders when devided by 6 and 5   nothing but 28 + (some multiple of 6 and 5) as thissome multiple of 6 and 5will not give any remainder when devided by 5 or 6 but 28 will give the required remainders.   hence n could be anything that is in the form 28 + (some multiple of 6 and 5)   observe thatsome multiple of 6 and 5is always a multiple of 30 as LCM (5,6)= 30.   hence when n (i.e. 28 + some multiple of 6 and 5) is devided by 30 gives the remainder 28.   30
<result>E</result>
Positive integer n leaves a remainder of 4 after division by 6 and a remainder of 3 after division by 5. If n is greater than 30, what is the remainder that n leaves after division by 40?