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PQID = DS38502.01 | OG 2020: Question No. 316

If a and b are integers, is a⁵ < 4^b?

1. a³ = –27
2. b² = 16

Source	OG 2020
PQID	DS38502.01
Type	Data Sufficiency
Topic	Algebra
Sub-Topic	Exponents
Difficulty	Medium

Solution

Steps 1 & 2: Understand Question and Draw Inferences

In this question, we are given

• The numbers a and b are integers.

We need to determine

• Whether a⁵ < 4^b or not.

For this, we need more information about the integers a and b. Hence, let us analyse the individual statements.

Step 3: Analyse Statement 1

As per the information given in statement 1, a³ = -27

• If a³ = -27, then a = -3, which is a negative number
• Therefore, a⁵ will be equal to (-3)⁵, which is also a negative number.
• However, for any integer value of b, 4^b will be always positive.
  • Therefore, a⁵ < 4^b

Hence, statement 1 is sufficient to answer the question.

Step 4: Analyse Statement 2

As per the information given in statement 2, b² = 16

• From this statement, we can say that b can be either 4 or -4.
• However, we do not get any relevant information about the value of a.

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:

If x^2 = a^2, then the value of x can be either +a or –a.

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