Practice GMAT Problem Solving Question
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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 (bc)/2?
Correct Answer: D
 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  At this point, there are two ways to manipulate the algebra.

Method 1
 Line up the two equations so that you can subtract them.
Equation 1: a+b = 180
Equation 2: a+c = 300  Notice that the equations are lined up such that if you subtract them, you end up with bc on the left and a number on the right. Since you are trying to find (bc)/2, this setup will get you most of the way to the answer.
 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.): bc = 120  With bc = 120, if you divide by two, you arrive at the equation that you are being asked for:
(bc)/2 = 120/2 = 60
 Line up the two equations so that you can subtract them.

Method 2
 Since the question asks for the value of (bc)/2, solve the two equations for the variable a so that they can be combined.
a = 180 – b
a = 300 – c  Combine the two equations by setting them equal to each other (since a = a) and manipulate them such that (bc)/2 is on one side of the equation and a number is on the other.
180 – b = 300 – c
180 – 300 = b – c
120 = bc
60 = (b – c)/2
 Since the question asks for the value of (bc)/2, solve the two equations for the variable a so that they can be combined.
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