jjjinapinch wrote:If n is an integer, is (0.1)^n greater than (10)^n?
(1) n > -10
(2) n < 10
Official Guide question
Answer: E
Target question: Is (0.1)^n > (10)^n?
This is a good candidate for
rephrasing the target question.
Since (0.1)^n is always POSITIVE, we can safely divide both sides of the inequality by (0.1)^n to get:
1 > [(10)^n]/[(0.1)^n]
There's a nice rule that says (a^n)/(b^n) = (a/b)^n
When we apply this rule to the right side of the inequality, we get:
1 > (10/0.1)^n
Simplify to get:
Is 1 > 100^n?
Notice that, when n = 0, then 100^n = 100^0 = 1
So, when n > 0, then 100^n > 1, and when
n < 0, then 100^n < 1
So, we can REPHRASE the target question as....
REPHRASED target question: Is n < 0?
Aside: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
Statement 1: n > -10
There are several values of n that satisfy statement 1. Here are two:
Case a: n = -9, in which case
n < 0
Case b: n = 2, in which case
n > 0
Since we cannot answer the
REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: n < 10
There are several values of n that satisfy statement 1. Here are two:
Case a: n = -9, in which case
n < 0
Case b: n = 2, in which case
n > 0
Since we cannot answer the
REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
IMPORTANT: Notice that I was able to use the
same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED.
Since we cannot answer the
REPHRASED target question with certainty, the combined statements are NOT SUFFICIENT
Answer:
E
Cheers,
Brent
