Jeff Miller

GMAT OFFICIAL GUIDE DS – If n is a positive integer, is the value of b…

If n is a positive integer, is the value of b…

Solution:

We are given that n is a positive integer, and we must determine whether the value of b – a is at least twice the value of 3^n – 2^n. We can rewrite this question as:

Is b – a ≥ 2(3^n – 2^n) ?

Statement One Alone: 

a= 2^(n+1) and b= 3^(n+1)

Using the information in statement one we can substitute 2^(n+1) for a and 3^(n+1) for b in the inequality b – a ≥ 2(3^n – 2^n). The question is now expressed as:

Is 3^(n+1) – 2^(n+1) ≥ 2(3^n – 2^n) ?

Is 3(3^n) – 2(2^n) ≥ 2(3^n) – 2(2^n) ?

Adding 2(2^n) to both sides of the inequality, we have:

Is 3(3^n) ≥ 2(3^n) ?

Dividing both sides of the equation by 3^n gives us:

Is 3 ≥ 2 ?

We can answer the question: yes, 3 is greater than or equal to 2.

Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone: 

n = 3

Without knowing the value of b or of a, we cannot answer the question. Statement two is not sufficient to answer the question.

Answer: A

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