What is the value of x^2 + 6x + 9 ? (1) x^2 + 6x = 40 (2) x + 3 = 7

Always remember one thing. In data sufficiency questions, don't try to find the solution of the problem. Instead check whether solution can be found based on the information provided or not. In first statement, x can be found with 2 values. So the equation in question is solvable using the values to x. Hence either statement is sufficient to. Solve the question.

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I beg to differ here. DS type question is based on whether we are able to arrive on a particular answer or not. If a particular statement leads to two different answers, then that statement should be considered insufficient.

In this particular question, if we solve statement 1, it is giving two different values for x, ie, 4 and -10. So putting the values in the original equation, we will get two different values. Hence we cannot conclude a single solution for that equation.

Whereas, statement 2 gives us a single value of x, ie, 4. Putting the value in the original equation gives us an undisputed solution.

So IMO answer should be B.

Requesting experts to point out where i went wrong since OA is provided as D.

Sorry, I made a mistake in the question. I will delete this and post the right one.
Question should have been x^2 + 6x + 9 ? (1) x^2 + 6x = 40 (2) x + 3 = 7

Statement 1:

\(x^2 + 6x = 40\)

\(x^2 + 6x - 40 = 0\)

\((x + 10) (x - 4)\)

X can be -10 or 4. Plugging in the numbers into the equation (\(x^2+6x+9\)) gives us the same answer: 49

Statement 2:

X+3=7
X=4

Plugging in 4 into the equation (\(x^2+6x+9\)) gives us 49

Answer is D

Statement 1: x= 4 or -10

When the values are substituted in the equation, the answer obtained in 49.

A is sufficient to answer the question.

Statement 2: x=4; value = 49.

B is sufficient to answer the question.

D is the correct answer choice.

Forget the conventional way to solve DS questions.

We will solve this DS question using the variable approach.

DS question with 1 variable: Let the original condition in a DS question contain 1 variable. Now, 1 variable would generally require 1 equation for us to be able to solve for the value of the variable.

We know that each condition would usually give us an equation, and Since we need 1 equation to match the numbers of variables and equations in the original condition, the logical answer is D.

To master the Variable Approach, visit https://www.mathrevolution.com and check our lessons and proven techniques to score high in DS questions.

Let’s apply the 3 steps suggested previously. [Watch lessons on our website to master these 3 steps]

Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question.

We have to find the value of \(x^2 + 6x + 9\).

Second and the third step of Variable Approach: From the original condition, we have 1 variable (x).To match the number of variables with the number of equations, we need 1 equation. Since conditions (1) and (2) will provide 1 equation each, D would most likely be the answer.

Let’s take look at each condition separately.

Condition(1) tells us that \(x^2 + 6x = 40\).

=> \(x^2 + 6x = 40\) :

=> \(x^2 + 6x + 9 \) = 40 + 9 = 49

Since the answer is unique , Condition(1) is alone sufficient by CMT 2.

Condition(2) tells us that x + 3 = 7.

=> Squaring both the sides of x + 3 = 7: \(x^2 + 6x + 9 = 49\)

Since the answer is unique , Condition(2) is alone sufficient by CMT 2.


Each condition alone is sufficient.

So, D is the correct answer.

Answer: D


SAVE TIME: By Variable Approach, when you know that value of Con(1) = Con(2), then 'D' is the correct answer.

Asked: What is the value of \(x^2 + 6x + 9\) ?
\(x^2 + 6x + 9 = (x+3)^2\)

(1) \(x^2 + 6x = 40\)
\(x^2 + 6x +9 = 49\)
SUFFICIENT

(2) \(x + 3 = 7\)
\(x^2 + 6x + 9 = (x+3)^2 = 7^2 = 49\)
SUFFICIENT

IMO D

We have to find the value of x^2 + 6x + 9.

Statement (1) gives the value of x^2 + 6x = 40. Putting this value in the equation x^2 + 6x + 9 gives us 40 + 9= 49.
We have a unique answer, hence sufficient.

You are trying to find the value of x, whereas we have to find the value of the whole equation.

Hope it helps!