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

Let x be the number of ticket sold at full price
Let y be the price of each ticket sold
Then, xy+(140-x)y/2 = 2001
xy/2 + 140y/2 = 2001
xy + 140y = 4002
xy = 4002 - 140y

Here , xy would be the total money earned from the sell of ticket sold at full price
Only for xy = 782 , y would be an integer and hence is an answer