I posted a solution here:
https://www.beatthegmat.com/official-gma ... 85301.html
Inequalities problem
This topic has expert replies
Source: Beat The GMAT — Problem Solving |
-
GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
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
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
-
goalevan
- Master | Next Rank: 500 Posts
- Posts: 111
- Joined: Tue Dec 30, 2008 1:25 pm
- Location: USA
- Thanked: 28 times
- GMAT Score:770
d > 0 and 0 < 1 - c/d < 1, so:
0 < (d - c)/d < 1
0 < d - c < d (we can multiply and preserve the direction of inequality since d > 0)
c < d < c + d
If c + d > d, then c + d - d > d - d, or c > 0.
Which of the following must be true?
I. c > 0. check, this must be true as shown above.
II. c/d < 1. c < d and d is positive as shown above, so c/d < d/d = 1. check
III. c^2 + d^2 > 1. (c,d) could be (0.000000001, 0.0001), which is less than 1, or could be (100000, 10000000000000), which is greater than 1. This does not have to be true.
0 < (d - c)/d < 1
0 < d - c < d (we can multiply and preserve the direction of inequality since d > 0)
c < d < c + d
If c + d > d, then c + d - d > d - d, or c > 0.
Which of the following must be true?
I. c > 0. check, this must be true as shown above.
II. c/d < 1. c < d and d is positive as shown above, so c/d < d/d = 1. check
III. c^2 + d^2 > 1. (c,d) could be (0.000000001, 0.0001), which is less than 1, or could be (100000, 10000000000000), which is greater than 1. This does not have to be true.
