rishijhawar wrote:What is one possible solution of the quadratic equation (x + a)(x - b) = 0?
(1) a = 4, (2) b = 3
[spoiler]OA D
I chose E. Reason being:
Either (x + a)=0 or(x - b)=0 or both are zero. Taking statement 1 and assuming (x + a)=0, x=-4, but what if (x + a)#0 (not equal to 0). So, not sufficient.
Similar logic in 2, x=3 or not possible. So, not sufficient.
Taking together, I chose E as I due to time crunch I couldnt think beyond.[/spoiler]
It might be worth noting that if (x-2)(x-7)=0, then x=2 and x=7 are both possible solutions.
Does this mean that x
must equal 2? No. It could be the case that x=7.
In DS questions, this concept often plays out something like this:
What is the value of x?
1) (x-2)(x-7)=0
2) (x-1)(x-7)=0
Statement 1: Here x could equal 2 or 7. Since we cannot determine the value of x with certainty, statement 1 is insufficient
Going back to the original question:
What is one possible solution of the quadratic equation (x + a)(x - b) = 0?
(1) a = 4
(2) b = 3
This is an odd question (in fact, it couldn't be an official GMAT question) because DS questions are either Yes/No questions (e.g., "Is x > 4?"), or they are specific value questions (e.g., "What is the value of x+y?"), where there is only 1 answer. This question appears to have more than 1 answer.
That said, we can still answer the question.
Statement 1: a = 4
Our equation becomes (x+4)(x-b)=0
Since we
are able to identify one of the
possible solutions with certainty (x= -4), statement 1 is sufficient.
Aside: Does this mean that x definitely equals -4? No. So, if the question said "What is the value of x", statement 1 would be insufficient
Statement 2: b = 3
Our equation becomes (x+a)(x-3)=0
Since 3 becomes a
possible solution, we could say that statement 2 is sufficient.
So, the answer is
D
Cheers,
Brent
