Practice GMAT Data Sufficiency Question
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15a + 6b = 30, what is the value of ab?
 b = 5 – 2.5a
 9b = 9a – 81
Correct Answer: B
 Be aware that simply because you have two equations with two unknowns does not mean that a solution exists. You must have two unique equations with two unknowns in order for a solution to exist.

Evaluate Statement (1) alone.
 There are two possible ways to solve this problem:
Method (1): Substitute b from Statement (1) into the original equation.
15a + 6(5 – 2.5a) = 30
15a + 30  15a = 30
30 = 30
0 = 0
Based upon this answer, the equation in Statement (1) is the equation in the original question solved for b. Consequently, we only have one equation and two unknowns. There is not enough information to determine ab.
Method (2): Rearrange the equation in Statement (1) and subtract this equation from the original equation.
b = 5 – 2.5a
b + 2.5a = 5
2.5a + b = 5
Multiply by 6 so b's cancel:15a + 6b = 30
This method also shows that the equation in Statement (1) is nothing more than the original equation rearranged. Consequently, we only have one equation and two unknowns. There is not enough information to determine ab.  Statement (1) is NOT SUFFICIENT.
 There are two possible ways to solve this problem:

Evaluate Statement (2) alone.
 Try to line up the two equations so that you can subtract them:
9b = 9a – 81
81 + 9b = 9a
81 = 9a  9b
Statement (2) Equation: 9a  9b = 81
Original Question Equation: 15a + 6b = 30
At this point, you can stop since you know that you have two unique equations and two unknowns. Consequently, there will be a solution for a and for b, which means there will be one unique value for ab. Statement (2) is SUFFICIENT.  If you want to solve to see this (Note: Do not solve this in a test as it takes too much time and is not necessary):
Multiply (2) by 4: 36a  36b = 324
Multiply Original by 6: 90a + 36b = 180
6*Original + 2*Statement(2): (90a + 36a) + (36b + 36b) = 180 + 324
126a = 204
a = 4
Solve for b:
9b = 9(4)  81 = 45
b = 5
a  b = 4  (5) = 4 + 5 = 9
 Try to line up the two equations so that you can subtract them:
 Since Statement (1) alone is NOT SUFFICIENT and Statement (2) alone is SUFFICIENT, answer B is correct.
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