Question

Can someone help me?

Answer 1

E. 997

Explanation:

NP :)

Answer 2

G. 1,494

Explanation:

We know that the special operation
`\mathcal{P}` gives the sum of all the whole numbers less than the number it operates on.

The example given by the question is:

`4\mathcal{P} = 3 + 2 + 1 + 0`

where 3, 2, 1, and 0 are added because they are all of the whole numbers less than 4, which is the number that
`\mathcal{P}` operated on.

Now, to the problem at hand:

First, let's just show the expanded representations of each term in the expression:

`(500\mathcal{P}) - (497\mathcal{P})`

`= (499 + 498 + 497 + 496 + 495 + ... +0) - (496 + 495 + 494 + ... + 0)`

I will call the terms within the parentheses subterms.

We can see that there is significant overlap between each term's subterms; actually, the entirety of
`497\mathcal{P}`'s subterms are within
`500\mathcal{P}`. So, when we subtract the former from the latter, we are just left with the terms that aren't part of the overlap.

We can identify these non-overlapping subterms as:

`499 + 498 + 497`

which can be simplified to get the answer:

G. 1,494