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GMAT Quant OG 2020 Question No. 353 with Solution- “If a and b are constants, is the expression…”

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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?

  1. a = 5
  2. b = 6
SourceOG 2020
PQID DS24571.01
TypeData Sufficiency
TopicAlgebra
Sub-topicSimplifying Algebraic Expressions
DifficultyMedium

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:

  1. √x is defined when x is positive.
  2. 1/x is defined when x is non-zero.

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