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

If a and b are integers, is a^{5} < 4^{b}?

- a
^{3}= –27 - b
^{2}= 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__

__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 a
^{5}< 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__

__Step 3: Analyse Statement 1__

As per the information given in statement 1, a^{3} = -27

- If a
^{3}= -27, then a = -3, which is a negative number - Therefore, a
^{5}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, a
^{5}< 4^{b}

- Therefore, a

Hence, statement 1 is sufficient to answer the question.

__Step 4: Analyse Statement 2__

__Step 4: Analyse Statement 2__

As per the information given in statement 2, b^{2} = 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)__

__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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