Troika wrote:If d > 0 and 0 < 1 - c/d < 1, which of the following must be true?
I. c > 0
II. c/d < 1
III. c^2 + d^2 > 1
A. I only
B. II only
C. I and II only
D. II and III only
E. I, II and III
[spoiler]OA: C[/spoiler]
0 < 1 - c/d < 1
[Subtract 1 from each part]
-1 < -c/d < 0
[Multiply through by -1, remembering to switch the direction of the inequality signs]
1 > c/d > 0
[Multiply by d -- since d>0, no need to worry about switching the direction of the inequality signs]
d >
c > 0.
The portions in red show that both II and I must be true.
Eliminate A, B and D.
If c and d are fractions between 0 and 1, then III does not have to be true.
To illustrate:
If d = 1/2 and c = 1/4, then c² + d² = (1/4)² + (1/2)² = 1/16 + 1/4 = 5/16, which is not greater than 1.
Eliminate E.
The correct answer is
C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
