Deepthi Subbu wrote:2. 2.A painter intends to mixed two jars of paint to create a new color. He chooses one paint jar randomly from a display containing 2 red and 2 blue samples, and a second jar is chosen at random from a different display containing 3 red and 2 blue samples. If he plans on mixing the two chosen jars together, what is the probability that when mixed together, the result will be purple paint? (The color purple is created with 1 part red and 1 part blue.)

• 1. RED from 1st set, BLUE from 2nd
  • Number of ways to do it = (Number of ways to select 1 red from 1st set)*(Number of ways to select 1 blue from 1st set) = 2*2 = 4
  1. BLUE from 1st set, RED from 2nd
  • Number of ways to do it = (Number of ways to select 1 blue from 1st set)*(Number of ways to select 1 red from 1st set) = 2*3 = 6

Deepthi Subbu wrote:1. An alchemist discovered that the formula to turn ordinary metal into gold is , where G is the number of gold bars and M is the number of metal bars. If a metal bar weighs twice as much as a gold bar, how many metal bars will yield an equal weight of gold?

• Plug the options.
  A. 15 --> G = (3/2)*15 + 15 --> NOT integer
  B. 10 --> G = (3/2)*10 + 15 = 30 --> Weight mismatch
  B. 40 --> G = (3/2)*40 + 15 = 75 --> Weight mismatch
  B. 30 --> G = (3/2)*30 + 15 = 60 --> CORRECT

• Say, required number of metal bar = n and weight of each metal bar = 2w. Hence, total weight of metal bars = 2nw and weight of each gold bar = w.
  
  Now, from the formula, if M = n, Number of gold bars, G = (3n/2) + 15
  => Total weight of gold bars = Gw = [(3n/2) + 15]w
  
  According to the problem, Gw = 2nw
  => (3n/2) + 15 = 2n
  => n = 30