sachinrelan wrote:
If j and k are positive integers where k > j, what is the value of the remainder when k is divided by j?
(1) There exists a positive integer m such that k = jm + 5.
(2) j > 5
Got the answer as E , can someone testify ..whether the answer ..i am getting is right or wrong and also post the explanation.
Thanks
Positive integer \(a\) divided by positive integer \(d\) yields a reminder of \(r\) can always be expressed as \(a=qd+r\), where \(q\) is called a quotient and \(r\) is called a remainder, note here that \(0\leq{r}<d\) (remainder is non-negative integer and always less than divisor).So according to above \(k\) is divided by \(j\) yields a remainder of \(r\) can be expressed as: \(k=qj+r\), where \(0\leq{r}<j=divisor\). Question: \(r=?\)
(1) There exists a positive integer m such that k = jm + 5 --> it's tempting to say that this statement is sufficient and \(r=5\), as given equation is very similar to \(k=qj+r\). But we don't know whether \(5<j\): remainder must be less than divisor.
For example:
If \(k=6\) and \(j=1\) then \(6=1*1+5\) and the remainder upon division 6 by 1 is zero;
If \(k=11\) and \(j=6\) then \(11=1*6+5\) and the remainder upon division 11 by 6 is 5.
Not sufficient.
(2) \(j > 5\) --> clearly insufficient.
(1)+(2) \(k = jm + 5\) and \(j > 5\) --> direct formula of remainder as defined above --> \(r=5\). Sufficient.
Or: \(k = jm + 5\) --> first term \(jm\) is clearly divisible by \(j\) and 5 divided by \(j\) as (\(j>5\)) yields remainder of 5.
Answer: C.