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rss GMAT Practice Question (One of Hundreds)
The average (arithmetic mean) of a and b is 90; the average (arithmetic mean) of a and c is 150; what is the value of (b-c)/2?
Correct Answer: D
Translate this into algebra. 90 = (a + b)/2
  1. Translate the question into algebra, using the formula that the average equals the sum of the terms divided by the number of terms.
    90 = (a + b)/2
    Multiply by 2: 180 = a + b

    150 = (a + c)/2
    Multiply by 2: 300 = a + c
  2. At this point, there are two ways to manipulate the algebra.
  3. Method 1
    1. Line up the two equations so that you can subtract them.
      Equation 1: a+b = 180
      Equation 2: a+c = 300
    2. Notice that the equations are lined up such that if you subtract them, you end up with b-c on the left and a number on the right. Since you are trying to find (b-c)/2, this setup will get you most of the way to the answer.
    3. Subtract the two equations:
      Equation 1: a+b = 180
      Equation 2: a+c = 300
      Equation 1 - 2: a - a + b - c = 180 - 300 = -120
      Equation 1 - 2 (cont.): b-c = -120
    4. With b-c = -120, if you divide by two, you arrive at the equation that you are being asked for:
      (b-c)/2 = -120/2 = -60
  4. Method 2
    1. Since the question asks for the value of (b-c)/2, solve the two equations for the variable a so that they can be combined.
      a = 180 – b
      a = 300 – c
    2. Combine the two equations by setting them equal to each other (since a = a) and manipulate them such that (b-c)/2 is on one side of the equation and a number is on the other.
      180 – b = 300 – c
      180 – 300 = b – c
      -120 = b-c
      -60 = (b – c)/2