SAT math question I don't understand

Test Preparation
1

<p>I saw somebody post a SAT math question and the answer, but I don't understand how they got the answer. This is the question:
"There are 25 trays ona table in the cafe. each tray contains a cup only, plate only, or both
if 15 contain cups and 21 contain plates
how many contain both ?" </p>

<p>Apparently the answer was 11, but I don't get how they got that.</p>

2

<p>First fill those 25 trays up with the 21 plates. Then you have 4 trays left for cups. You still have 11 cups left to group with plates. Therefore, 11 trays will have both cups and plates.</p>

3

<p>Each tray MUST contain SOMETHING. So if it doesn’t have a cup on it, it must have a plate, and vise-versa.</p>

<p>So you have 25 trays. There are 21 plates, so you know that there’s 4 trays that have no plate on them. Since those 4 trays don’t have a plate, they MUST have a cup. So if those 4 trays have a cup on them, the rest of the 15 cups are put on a tray that already has a plate.</p>

<p>Get it?</p>

4

<p>a: number of tray contain both
b: number of tray contain C
c: number of tray contain P
2a+b+c=15+21=36
and a+b+c=25
=> a=36-25=11</p>

5

<p>I get it now!!!</p>