If it is well known that 1.0001^100 is approx… | GMAT Sprint

Free Practice Question

PS · Problem Solving

705-805

Divisibility/Multiples/Factors

If it is well known that $1.0001^{100}$ is approximately 1.01 and $1.01^{100}$ is approximately 2.7, what is the value of $(1.0001^{200})^{200}$ approximately?

Correct answer marked below

Correct

You can see the correct answer above. Sign in for free to unlock the complete worked solution.

Get detailed analytics, unlock full explanations, and move up difficulty tiers as you practice.

Explanation

Preview

Official Explanation

Official

Given:

1.0001^{100} \approx 1.01

1.01^{100} \approx 2.7

We need to find

(1.0001^{200})^{200}

.

Step 1: Rewrite the expression:

(1.0001^{200})^{200} = (1.0001^{100})^{2 \times 200}

Step 2: Substitute the given approximation:

(1.0001^{100})^{400} \approx (1.01)^{400}

Step 3: Rewrite using the second given approximation:

(1.01)^{400} = ((1.01)^{100})^{4} \approx (2.7)^4

Step 4: Compute

(2.7)^4

(2.7)^4 = (2.7)^2 \times (2.7)^2 = 7.29 \times 7.29

…

Comments

Be the first to share your thoughts and help others understand it better.

What this question tests

Your understanding of divisibility rules, least common multiples, and greatest common factors.

Forgetting that 1 is not prime and that every integer divides 0.