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If a and b are integers, is a5 < 4b? - OG 2020 Question #316 with Solution

OG 2020: Question No. 316

If a and b are integers, is a5 < 4b?

  1. a3 = –27
  2. b2 = 16
SourceOG 2020
TypeData Sufficiency
TopicAlgebra
Sub-TopicExponents
DifficultyMedium

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 < 4b 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, 4b will be always positive.
    • Therefore, a5 < 4b

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.

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