Let x = # of tickets sold for FULL PRICE
So, 140-x = # of tickets sold for HALF PRICE (since 140 tickets were sold in total)

Let y = the FULL PRICE cost
So, y/2 = the HALF PRICE cost

A charity sells 140 benefit tickets for a total of $2001
We can write: (amount raised by FULL-price tickets) + (amount raised by HALF-price tickets) = $2001
Substitute values to get: xy + (y/2)(140 - x) = $2001
Expand to get: xy + 70y - xy/2 = $2001
Multiply both sides by 2 to get: 2xy + 140y - xy = $4002
Simplify to get: xy + 140y = $4002

How much money is raised by the full-price tickets?
IMPORTANT: xy = the money is raised by the full-price tickets.
So our goal is to find the value of xy

We already know that xy + 140y = $4002
Subtract 140y from both sides to get: xy = $4002 - 140y

Since we're told the price of a full-price ticket is an INTEGER value (i.e., "a whole dollar amount"), we know that the units digit of 140y is 0
So, xy = $4002 - (some number with units digit 0)
So, xy must have units digit 2
Check the answer choices ... only answer choice A has units digit 2

Answer: A

Cheers,
Brent
_________________

If it wasn't A I would definitely skip and move forward because this kind of question takes time if you aren't an algebric genius. I will share what I did to solve this.
No. of tickets: 140
Sales from tickets of a price that is a whole no.: Let's take A 782
Factorize 782: 2*17*23
The price cannot be 2 because 17*23 will far exceed the 140 no. of tickets so the tickets sold at a whole number can be either 34 tickets @ 23$ or 23 tickets @ 34$
When you sell 34 tickets @ 23$ the other number of tickets that is 106 would be sold @ 11.5 which gives 1219$
I chose A and it took me more than 3 minutes