If s and t are the roots of x^2 + bx + c = 0, then |s − t| = ?

Question

(1) c = −10
(2) b = 3

Kurtosis · Answer

Std form of quadratic equation: ax^2 + bx + c

Assume, s = (-b + sqrt(b^2 - 4ac))/2a and t = (-b - sqrt(b^2 - 4ac))/2a
a = 1

|s - t| = 2(sqrt(b^2 - 4c))/2 = sqrt(b^2 - 4c)

St1: c=−10 --> Insufficient as we do not know the value of b
St2: b = 3 --> Insufficient as we do not know the value of c

Combining statement 1 and 2, we have the values of b and c --> Sufficient --> |s - t| = 7

Answer: C

FightToSurvive · Answer

If s and t are the roots of x2+bx+c=0, then |s−t|=?

(1) c=−10
(2) b=3

From the definition of quadratic equation, we know:
1. Product of the roots of the equation is c/a = (s*t)/a
Here a = 1 so, Product of the equation = s*t

2. Sum of the roots of the equation = - b/a = -(s+t)/a = -s-t (as a=1)
Combining both statements we get two roots as -5 and 2 and with all combinations we get |s-t|= 7. Hence C is the answer.

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution

If s and t are the roots of x^2 +bx+c=0 , then |s−t|=?

(1) c=−10
(2) b=3

There are 2 variables (s and t) in the original condition. In order to match the number of variables and the number of equations, we need 2 equations. Since the condition 1) and 2) each has 1 equation, there is high chance C is the answer.

Using both the condition 1) and 2), we get x^2+3x-10=0. Then, (x-2)(x+5)=0. So, x=2 and -5. Then, |s-t|=|2-(-5)|=7. The answer is unique and the condition is sufficient. Therefore, the correct answer is C.

For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.

If s and t are the roots of x^2 + bx + c = 0, then |s − t| = ?

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GMAT Data Sufficiency (DS) Questions

If s and t are the roots of x^2 + bx + c = 0, then |s − t| = ?

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