Question

For all positive integer $j$ and $k$, let $j◊k$ be defined to be the sum of the $k$ consecutive integers beginning with $j$. For example,
$9◊4=9+10+11+12$

A B

$100◊99$

$99◊100$

• A. If the quantity in Column A is greater
• B. If the quantity in Column B is greater
• C. If the two quantities are equal
• D. If the relationship cannot be determined from the information given

Answer 1

The correct option is B If the quantity in Column B is greater

The value of quantity in column $1$ is $100+101+102+....\left(99terms\right)=100\times 99+\frac{99\times 100}{2}=9900+4950=14850$.

The value of quantity in column $2$ is $99+100+101+....\left(100terms\right)=100\times 99+\frac{101\times 100}{2}=9900+5050=14950$.

Therefore the quantity in column $2$ is greater.

So, the correct option is $B$.