What is the value of ab? (1) (a - 2) (b - 3) = 0 (2) b = 2

(1) (a-2)(b-3)=0
Not Sufficient

(2) b=2, a can be anything
Not Sufficient

(1)+(2) b=2, therefore a=2
ab =4
Sufficient

Answer: C

BrentGMATPrepNow, Could you please resolve this one?

I think you are a scholar dealing with all levels of learners at ease. Your pleasant personality pleases all. You are not getting praised here; you deserve respect and honor.

Target question: What is the value of ab?

Statement 1: (a - 2)(b - 3) = 0
There are infinitely many pairs of values that satisfy statement 1. Here are two:
Case a: a = 2 and b = 1. To show that these values satisfy statement 1, we can take the equation (a - 2) (b - 3) = 0, replace a and b with 2 and 1 to get: (2 - 2) (1 - 3) = 0. Perfect! When we simplify, we get 0 = 0. In this case, the answer to the target question is ab = (2)(1) = 2
Case b: a = 2 and b = 2. In this case, the answer to the target question is ab = (2)(2) = 4
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: b = 2
Since we have no information about the value of a, there's no way to find the value of ab
Statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that (a - 2)(b - 3) = 0
Statement 2 tells us that b = 2

Take the equation (a - 2)(b - 3) = 0 and replace b with 2 to get: (a - 2)(2 - 3) = 0
Simplify: (a - 2)(-1) = 0
Expand: -a + 2 = 0
Solve: a = 2

Since we now know that a = 2 and b = 2, we can see that ab = (2)(2) = 4
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

Thanks for the kind words, sjuniv32!

Cheers,
Brent

What is the value of ab?

(1) (a - 2) (b - 3) = 0 --> insuff: (a - 2) (b - 3) = 0 => many solution for a & b i.e. ab

(2) b = 2 --> insuff: no known value for a

Combining (1) & (2)=>
(a-2)(2-3)=0, replacing b=2 in (1)
=> a-2=-1
=> a=1
ab=1*2=2

Answer: C

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