Set $P$ consists of the first $n$ positive multiples of $3$ and set $Q$ consists of the first $m$ positive

Set $P$ consists of the first $n$ positive multiples of $3$ and set $Q$ consists of the first $m$ positive multiples of $5.$ The sum of all the numbers in set $P$ is equal to $R$ and the sum of all the numbers in set $Q$ is equal to $S.$ If $m$ and $n$ are positive integers, is the difference between $R$ and $S$ odd?

(1) $m$ is odd and $n$ is even.

(2) $m$ can be expressed in the form of $4x +3$ and $n$ can be expressed in the form of $2x,$ where $x$ is a positive integer.

Answer: E

Source: e-GMAT

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