**Que :**When the equation \(x^2+ax+b=0\) has roots p and q, what is the value of p + q?

(1) a = 4

(2) b = 9

- [email protected] Revolution
- Elite Legendary Member
**Posts:**3834**Joined:**24 Jul 2015**Location:**Las Vegas, USA**Thanked**: 19 times**Followed by:**36 members

00:00

**A**

**B**

**C**

**D**

**E**

(1) a = 4

(2) b = 9

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

Email to : [email protected]

- [email protected] Revolution
- Elite Legendary Member
**Posts:**3834**Joined:**24 Jul 2015**Location:**Las Vegas, USA**Thanked**: 19 times**Followed by:**36 members

00:00

**A**

**B**

**C**

**D**

**E**

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.

Visit https://www.mathrevolution.com/gmat/lesson for details.

Now we will solve this DS question using the Variable Approach.

Let’s apply the 3 steps suggested previously.

Follow the first step of the Variable Approach by modifying and rechecking the original condition and the question.

We have to find the value of p + q.

=> Given: \(x^2+ax+b=0\) has ‘p’ and ‘q’ as its roots.

=> (x – p) (x – q)=0 => \(x^2-\left(p+q\right)x+pq=0\)

=> a=-(p+q) and b=pq

=> We have to find the value of a

=> a = 4 = -(p + q)

=> -( p + q) = 4

=> p + q = -4

The answer is unique, so condition (1) alone is sufficient, according to CMT 2 - there must be only one answer

=> b = pq = 9

=> If p = q = 3, then pq = 3 * 3 = 9 => p + q = 3 + 3 = 6

=> But if p =1; q = 9, then pq = 1 * 9 = 9 => p + q = 1 + 9 = 10

The answer is not unique, so condition (1) alone is not sufficient, according to CMT 2 - there must be only one answer.

Therefore, A is the correct answer.

Answer: A

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

Email to : [email protected]