Last Updated on May 10, 2023
GMAT OFFICIAL GUIDE DS
Solution:
We are given that n is a positive integer and need to determine whether (1/10)^n < 0.01. We can convert 0.01 to a fraction and display the question as:
Is (1/10)^n < 1/100 ?
Is (1/10)^n < (1/10)^2 ?
Using the negative exponent rule, we can take the reciprocal of our bases and switch the signs of the exponents.
Is 10^-n < 10^-2 ?
Because the bases are now the same, we equate the exponents.
Is -n < -2 ?
Is n > 2 ?
Statement One Alone:
n > 2
We see that statement one directly answers the question. Statement one is sufficient to answer the question. We can eliminate answer choices B, C, and E.
Statement Two Alone:
(1/10)^(n-1) < 0.1
We can simplify the inequality in statement two.
(1/10)^(n-1) < 0.1
(1/10)^(n-1) < (1/10)^1
Using the negative exponent rule, we can take the reciprocal of our bases and switch the signs of the exponents.
10^-(n-1) < 10^-1
The bases are now equal, so we can equate the exponents.
-(n – 1) < -1
n – 1 > 1
n > 2
We see that n is greater than 2. Statement two alone is sufficient to answer the question.
Answer: D
