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Can someone help me?

Can someone help me?-example-1

2 Answers

3 votes

Answer:

E. 997

Explanation:

NP :)

User Stefan Weiser
by
8.3k points
2 votes

Answer:

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

User Nateirvin
by
9.1k points

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