card game - Cambridge

[arora007]

This is a card game problem from Cambridge.

[GMATGuruNY]

This is a card game problem from Cambridge.

The even integers 2, 4, 6, and 8 can be added to get any even integer from 2 to 20 (because 2 is the smallest possible even value, and 2+4+6+8 = 20 is the largest possible even sum).

Between 2 and 20 inclusive, the number of even integers = (biggest - smallest)/2 + 1 = (20-2)/2 + 1 = 10 possible even point totals.

If we add the 1 card to each of these even point totals, we get an additional 10 possible point totals.

The 1 card by itself gives us the smallest possible point total, which is 1.

Thus, 10 + 10 + 1 = 21 point totals are possible.

The correct answer is E.