Question

The operation $\Rightarrow$ is defined by $x\Rightarrow y=x+(x+1)+(x+2)...+y$. For example, $3\Rightarrow 7=3+4+5+6+7$. Then what is the value of $(100\Rightarrow 150)-(125\Rightarrow 150)$?

• A. $2600$
• B. $3200$
• C. $2800$
• D. $3000$

Answer 1

The correct option is C $2800$

This problem contains two components: the sum of all the numbers from $100$ to $150$, and the sum of all the numbers from $125$ to $150$. Since you are finding the difference between these components,you are essentially finding just the sum of all the numbers from $100$ to $124$. You can think of this logically by solving a simpler problem: find the difference $(1\Rightarrow 5)-(3\Rightarrow 5)$.

$1+2+3+4+5$

$\underset{–}{-3+4+5}$

$1+2$

There are $25$ numbers from $100$ to $124(124-100+1)$. Remember to add $1$ before you are done! To find the sum of these numbers, multiply by the average term:

$\frac{100+124}{2}=112$

$25\times 112=2,800$