sandy wrote:
If \(0 < a < \frac{1}{b}< 1\), then which of the following must be true?
(A) \(a^2 > a > b > b^2\)
(B) \(b > a > a^2 > b^2\)
(C) \(b^2 > a > a^2 > b\)
(D) \(b^2 > a^2 > b > a\)
(E) \(b^2 > b > a > a^2\)
Let's solve this by
testing valuesGIVEN: 0 < a < 1/b < 1
Since a is POSITIVE, we can safely multiply all parts of the inequality by a to get: 0 <
a² < a/b <
aSo, one thing that is definitely true is that
a² < aCheck the answer choices
(A)
a² > a > b > b² NO GOOD. ELIMINATE
(B) b >
a > a² > b² WORKS. KEEP
(C) b² >
a > a² > b WORKS. KEEP
(D) b² >
a² > b >
a NO GOOD. ELIMINATE
(E) b² > b >
a > a² WORKS. KEEP
GIVEN: 0 < a < 1/b < 1
Since b is POSITIVE, we can safely multiply all parts of the inequality by b to get: 0 < ab < 1 < b
Hmmm, this new inequality doesn't have b and b² (which is needed to check the answer choices)
So, let's take 0 < ab < 1 < b and multiply all parts by b to get: 0 < ab² <
b < b²Let's check the answer choices to see which ones adhere to the inequality
b < b²(B)
b > a > a² >
b² NO GOOD. ELIMINATE
(C)
b² > a > a² >
b WORKS. KEEP
(E)
b² > b > a > a² WORKS. KEEP
We're left with 2 answer choices:
(C) b² > a > a² > b
(E) b² > b > a > a²
Answer choice C says a > b and answer choice E says b > a
So, which is it?
Well, we know that a < 1/b
So, it COULD be the case that a = 1/3 and b = 2, which means b > a
So, the correct answer must be E
Cheers,
Brent
_________________
Brent Hanneson – Creator of greenlighttestprep.comSign up for GRE Question of the Day emails