For positive integer values of n, the operation . . . . .

[Vincen]

For positive integer values of n, the operation n# is defined as the sum of all integers from 1 to n, inclusive. For example, 4# = 1 + 2 + 3 + 4 = 10. If 15# - 14# = k#, what is the value of k#?

A. 1
B. 4
C. 5
D. 14
E. 15

The OA is the option E.

Is there an easy way to solve this PS question without making the whole calculation? I need your help experts. Thanks in advanced.

[EconomistGMATTutor]

Hello Vincen.

Let's take a look at your question.

We have to solve 15#-14#=k#. But, we have to notice that 15# = 15 + 14#.

Now, we can rewrite 15#-14#=k# as follows: $$ k\# = 15\#-14\#\ =\ 15\ +\ 14\#\ -\ 14\#\ =\ 15 .$$ Therefore, the correct answer is E.

I hope this explanation may help you.

I'm available if you'd like a follow-up.

Regards.