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In the equation x^2 - bx + c = 0, b and c are constants. What is the

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In the equation x^2 - bx + c = 0, b and c are constants. What is the  [#permalink]

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New post 10 Dec 2017, 01:04
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In the equation \(x^2 - bx + c = 0\), b and c are constants. What is the value of b ?


(1) -3 is a root of the equation \(x^2 - bx + c = 0\).

(2) x + 3 is a factor of \(x^2 - bx + c = 0\).

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In the equation x^2 - bx + c = 0, b and c are constants. What is the  [#permalink]

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New post 10 Dec 2017, 06:49
Bunuel wrote:
In the equation \(x^2 - bx + c = 0\), b and c are constants. What is the value of b ?


(1) -3 is a root of the equation \(x^2 - bx + c = 0\).

(2) x + 3 is a factor of \(x^2 - bx + c = 0\).


To know the value of \(b\) we need to know either both the roots of the equation of the value of \(c\)

Statement 1: only one of the root is given. Substituting the value of x in the equation will lead to \(9+3b+c=0\). two unknowns and only one equation. Hence insufficient

Statement 2: as \(x+3\) is factor so one of the root of the equation will be \(x+3=0=>x=-3\). This is the same information as Statement 1. Insufficient

Combining 1 & 2 we get the same information which is Insufficient to solve the equation.

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Re: In the equation x^2 - bx + c = 0, b and c are constants. What is the  [#permalink]

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New post 10 Dec 2017, 23:52
Bunuel wrote:
In the equation \(x^2 - bx + c = 0\), b and c are constants. What is the value of b ?


(1) -3 is a root of the equation \(x^2 - bx + c = 0\).

(2) x + 3 is a factor of \(x^2 - bx + c = 0\).



Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 2 variables which are b and c, C is most likely to be the answer.
Then we need to consider both conditions 1) & 2) together.


Since -3 is a root of the equation, \(9 + 3b + c = 0\).
Since \(x+3\) is a factor of the equation, it has a root \(-3\) and we have \(9 + 3b + c = 0\).

There are a lot of possible values of \(b\).

Therefore, the answer is E.

Normally, in problems which require 2 or more additional equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
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Re: In the equation x^2 - bx + c = 0, b and c are constants. What is the  [#permalink]

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New post 10 Dec 2017, 23:57
It should be E
both statements tell that x =-3 and by knowing value of x we cant find out value of b
putting value of x in equation we get 9 + 3b + c = 0
now b can be 1, 3 or any value
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Re: In the equation x^2 - bx + c = 0, b and c are constants. What is the &nbs [#permalink] 10 Dec 2017, 23:57
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