A 2 min read

Solution

Steps 1 & 2: Understand Question and Draw Inferences

In this question, we are asked to determine

• The value of the number, which is 6 more than x + y.

To find the number, we need to know either the individual values of x and y, or the sum of their values.

With this understanding, let us now analyse the individual statements.

Step 3: Analyse Statement 1

As per the information given in statement 1, y is 3 less than x.

• y = x – 3

Or, x – y = 3

From this statement, we can determine the value of x – y.

• However, we need to know the value of x + y, which cannot be determined only from the value of x – y

Hence, statement 1 is not sufficient to answer the question.

Step 4: Analyse Statement 2

As per the information given in statement 2, y is twice x.

• y = 2x

Or, 2x – y = 0

From this statement, we can determine the value of 2x – y.

• However, we need to know the value of x + y, which cannot be determined only from the value of 2x – y

Hence, statement 2 is not sufficient to answer the question.

Step 5: Combine Both Statements Together (If Needed)

Combining the information from both statements, we get

• x – y = 3 and 2x – y = 0

These are two simultaneous independent equations with two unknown variables. Solving them, we can get the individual values of x and y.

Hence, the correct answer choice is option C.

Takeaways:

1. One linear equation in two variables has infinite solutions.
   1. Example: y = x – 3 is one linear equation in two variables, x and y. This equation has infinite solutions.  
2. Two independent linear equations in two variables have a unique solution.
   1. Example: y = x – 3 and y – 2x = 0 has a unique solution of the form (x, y).