[GMAT math practice question]
$$When\ \ a\ne0,\ how\ many\ solutions\ does\ the\ equation\ a\left(x+b\right)^2+c=0\ have?$$
$$\left(1\right)\ bc=0$$
$$\left(2\right)\ |b|+|c|=0$$
) When a≠0, how many solutions does the equation
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- Max@Math Revolution
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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.
The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.
There are three cases to consider:
Case 1: a > 0, c > 0 or a < 0, c < 0
The equation has no roots.
Case 2: c = 0.
The equation has only one root.
Case 3: a > 0, c < 0 or a < 0, c > 0
The equation has two roots.
Condition 1):
If bc = 0, then when
a = 1, b = 0, c = -1, the equation has two roots, and when
a = 1, b = 0, c = 0, the equation has one root.
As the question does not have a unique answer, condition 1) is not sufficient.
Condition 2)
|b| + |c| = 0 ⇔ b = c = 0.
Since c = 0, the equation has only one root.
Condition 2) is sufficient.
Therefore, the answer is B.
Answer: B
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.
The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.
There are three cases to consider:
Case 1: a > 0, c > 0 or a < 0, c < 0
The equation has no roots.
Case 2: c = 0.
The equation has only one root.
Case 3: a > 0, c < 0 or a < 0, c > 0
The equation has two roots.
Condition 1):
If bc = 0, then when
a = 1, b = 0, c = -1, the equation has two roots, and when
a = 1, b = 0, c = 0, the equation has one root.
As the question does not have a unique answer, condition 1) is not sufficient.
Condition 2)
|b| + |c| = 0 ⇔ b = c = 0.
Since c = 0, the equation has only one root.
Condition 2) is sufficient.
Therefore, the answer is B.
Answer: B
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]