These principles aren't quite right. Say you have two numbers, and the remainder is 5 when you divide the first number by 7, and the remainder is 2 when you divide the second number by 7. If you multiply these two numbers, the remainder will not be 5*2 = 10 when you divide the product by 7, since 10 is too large - when you divide anything by 7, the remainder must be between 0 and 6 inclusive. Instead you need, as the final step, to take the remainder when you divide 10 by 7; the remainder is 3 when you divide this product by 7.knight247 wrote:One Important principal u may wanna keep in mind.
Suppose a number A*B divided by a number x leaves a certain remainder, that remainder is equal to the product of remainders produced when A is divided by x and B is divided by x individually.
Variation....If A divided by x leaves a certain remainder 'm' and B divided by x leaves a certain remainder 'n', then when A*B is divided by x the remainder is the product of m*n
Stewart is absolutely correct. I misinterpreted my solution right at the end. With the algebraic solution to this, the remainder comes to (rs)/q which means the remainder could still be anything. The only way remainder is rs is when q is 1 and that is not a precondition with the question. Do the algebra, it will actually show you very quickly what's wrong with assumptions defined by knight247Ian Stewart wrote:These principles aren't quite right. Say you have two numbers, and the remainder is 5 when you divide the first number by 7, and the remainder is 2 when you divide the second number by 7. If you multiply these two numbers, the remainder will not be 5*2 = 10 when you divide the product by 7, since 10 is too large - when you divide anything by 7, the remainder must be between 0 and 6 inclusive. Instead you need, as the final step, to take the remainder when you divide 10 by 7; the remainder is 3 when you divide this product by 7.knight247 wrote:One Important principal u may wanna keep in mind.
Suppose a number A*B divided by a number x leaves a certain remainder, that remainder is equal to the product of remainders produced when A is divided by x and B is divided by x individually.
Variation....If A divided by x leaves a certain remainder 'm' and B divided by x leaves a certain remainder 'n', then when A*B is divided by x the remainder is the product of m*n
So in the question in the original post, we're dividing by q. We can easily get a 'yes' answer to the question, using both statements, by letting r and s be 0, say, or 1. But if r*s is bigger than q, which can easily happen, then r*s can never be a remainder when you divide by q, since when you divide by q, the remainder must be smaller than q. So the answer is E.
Not exactly. The remainder is not rs/q. The remainder is the same as the remainder you would get if you divided rs by q. Make sure you see the difference.chufus wrote:
Stewart is absolutely correct. I misinterpreted my solution right at the end. With the algebraic solution to this, the remainder comes to (rs)/q which means the remainder could still be anything. The only way remainder is rs is when q is 1 and that is not a precondition with the question. Do the algebra, it will actually show you very quickly what's wrong with assumptions defined by knight247
knight247 wrote: Variation....If A divided by x leaves a certain remainder 'm' and B divided by x leaves a certain remainder 'n', then when A*B is divided by x the remainder is equal to the remainder left when the product of m*n is divided by x
Yea bang on.. I guess that is what i meant but just conveyed it in the wrong manner. Thanks for pointing the subtle difference out.GmatMathPro wrote:Not exactly. The remainder is not rs/q. The remainder is the same as the remainder you would get if you divided rs by q. Make sure you see the difference.chufus wrote:
Stewart is absolutely correct. I misinterpreted my solution right at the end. With the algebraic solution to this, the remainder comes to (rs)/q which means the remainder could still be anything. The only way remainder is rs is when q is 1 and that is not a precondition with the question. Do the algebra, it will actually show you very quickly what's wrong with assumptions defined by knight247
Thus, it is not true that q has to be 1 for the remainder to be rs. The remainder will always be rs as long as rs is less than q. For example, 11 divided by 9 leaves a remainder of 2. 12 divided by 9 leaves a remainder of 3. 12*11=132, which leaves a remainder of 6 when divided by 9, which is the same as 2*3, the product of the remainders of 12 and 11 divided by 9. If we tried to use "the remainder is rs/q", we would get a remainder of 6/9 or 2/3, which clearly does not make sense.
knight247's principle can be salvaged with a slight modification:
knight247 wrote: Variation....If A divided by x leaves a certain remainder 'm' and B divided by x leaves a certain remainder 'n', then when A*B is divided by x the remainder is equal to the remainder left when the product of m*n is divided by x
