What is the value of ab + bc ? (1) b = 5 (2) a + c = 8

The solutions above are great, so I won't re-solve the question.

This is a great question, because it tests a common misconception that many students have about the solve-ability of certain systems of equations.
Many students will see that the target question has 3 variables, so they will incorrectly assume that 3 equations are required to evaluate the expression. If they make this assumption, they will conclude that the answer is E, when it is actually C.
While the 2 given equations will NOT help us determine the INDIVIDUAL values of a, b and c, they will allow us to EVALUATE ab + bc.

We have two free videos on common GMAT Data Sufficiency myths.
- https://www.gmatprepnow.com/module/gmat- ... video/1106
- https://www.gmatprepnow.com/module/gmat- ... video/1107

Cheers,
Brent

ab+bc = b( a+c)?

1) b= 5.. a=?, c=? (NS)

2) a+c=8 ..b =? (NS)

1+2

S..

C

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

What is the value of ab + bc ?

(1) b = 5

(2) a + c = 8

There are 3 variables (a,b,c) but only 2 equations are given by the conditions, so there is high chance (E) will become the answer.
Looking at the conditions together, from ab+bc=(a+c)b=8*5=40, we can obtain an unique answer, making the conditions sufficient.
The answer therefore becomes (C).

For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.

Statement 1- b=5
5a+5c=?
5c=-5a
c=-5a/5
c=-a
Now substituting the value of 'c' in
ab+bc
5a+5(-a)=0
Why is statement 1 not sufficient?

You assumed 5a + 5b = 0

That’s not mentioned anywhere


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The red part is not correct. The question becomes: what is the value of 5a + 5c? It does not say that 5a + 5c = 0, ,from which you could get that 5a = -5c.

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