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10 Dec 2017, 01:04
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
80% (01:10) correct
20%
(01:20)
wrong
based on 146
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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 \(x^2 - bx + c = 0\).
(1) -3 is a root of the equation \(x^2 - bx + c = 0\).
(2) x + 3 is a factor of \(x^2 - bx + c = 0\).
10 Dec 2017, 06:49
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Bunuel
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.
Option E
10 Dec 2017, 23:52
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Bunuel
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.
