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