OG 2020: Question No. 314
What number is 6 more than x + y?
- y is 3 less than x.
- y is twice x.
Source | OG 2020 |
Type | Data Sufficiency |
Topic | Algebra |
Sub-Topic | Linear Equations |
Difficulty | Medium |
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:
- One linear equation in two variables has infinite solutions.
- Example: y = x – 3 is one linear equation in two variables, x and y. This equation has infinite solutions.
- Two independent linear equations in two variables have a unique solution.
- Example: y = x – 3 and y – 2x = 0 has a unique solution of the form (x, y).