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Quadratic Equations-Manhattan-CAT

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Quadratic Equations-Manhattan-CAT

by rishijhawar » Tue Jul 19, 2011 4:56 am
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]
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by rishimaharaj » Tue Jul 19, 2011 6:20 am
Hello Rishi,

The stem is asking for one *possible* solution for the quadratic. It is not asking for only one solution. So any solution you can give would be sufficient.

1. a=4, so x=-4 is one possible solution. Sufficient.
2. b=3, so x=-3 is one possible solution. Sufficient.

Thus the answer is D.

The reasoning you posted regarding ( x+a ) != 0 was actually thinking too deep into the problem!
Any quadratic equation can have 0, 1, or 2 possible solutions. These solutions are gathered by setting each factor to zero. Hence, the two possible solutions are going to be either:
( x + a ) = 0
or
( x + b ) = 0

Each of them gives one possible solution, so each of the statements can answer the question stem, giving us D as the answer.

Hope this helps,
--Rishi
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by Brent@GMATPrepNow » Tue Jul 19, 2011 6:34 am
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
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by rishijhawar » Tue Jul 19, 2011 11:45 am
Brent, if the question asks Whats the value of X, would the answer be E.
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[/quote]
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by Brent@GMATPrepNow » Tue Jul 19, 2011 11:50 am
rishijhawar wrote:So, if the question said "What is the value of x", statement 1 would be insufficient
Yes. Since we would be unable to determine the value of x with certainty, the statement is insufficient

Cheers,
Brent
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