Question

There are 20 balls which are red, blue or green. If 7 balls are green and the sum of red balls and green balls is less than 13, at most how many red balls are there?

• A. 4
• B. 5
• C. 6
• D. 7
• E.

Hint:

When dealing with inequalities and total counts, use the given conditions to set up equations and solve for the unknowns.

Answer 1

The Correct Option is B

Let the number of red balls be \( r \), blue balls be \( b \), and green balls be \( g = 7 \). Step 1: Since the total number of balls is 20, we can write: \[ r + b + g = 20 \] \[ r + b + 7 = 20 \quad \Rightarrow \quad r + b = 13 \] Step 2: It is given that the sum of red and green balls is less than 13: \[ r + 7<13 \] Step 3: Solving for \( r \): \[ r<13 - 7 \] \[ r<6 \] Step 4: Since \( r \) must be an integer, the maximum possible value for \( r \) is 5. Thus, the maximum number of red balls is 5. .