PQID = DS24571.01 | OG 2020 Question No. 353
If a and b are constants, is the expression (x + b)/√(x + a) defined for x = –2?
- a = 5
- b = 6
| Source | OG 2020 |
| PQID | DS24571.01 |
| Type | Data Sufficiency |
| Topic | Algebra |
| Sub-topic | Simplifying Algebraic Expressions |
| Difficulty | Medium |
Solution
Steps 1 & 2: Understand the Question and Draw Inferences
In this question, we are given
- An expression (x + b)/√(x + a), where a and b are constants.
We need to determine
- Whether the expression is defined for x = -2.
Now, the given expression is defined if √(x + a) is a nonzero real number.
- This is true when (x + a) must be a positive number.
Or, x > -a.
As in this question, it is mentioned that x = -2, we need to check whether -2 > -a or, a > 2 or not.
With this understanding, let us now analyze the individual statements.
Step 3: Analyse Statement 1
As per the information given in statement 1, a = 5.
- Since a = 5, a > 2.
Hence, statement 1 is sufficient to answer the question.
Step 4: Analyse Statement 2
As per the information given in statement 2, b = 6.
- However, from this statement, we cannot determine whether a > 2 or not.
Hence, statement 2 is not sufficient to answer the question.
Step 5: Combine Both Statements Together (If Needed)
Since we can determine the answer from statement 1 individually, this step is not required.
Hence, the correct answer choice is option A.
Takeaways:
- √x is defined when x is positive.
- 1/x is defined when x is non-zero.
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