|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
18 Jun 2018, 01:25
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
72% (01:57) correct
28%
(02:28)
wrong
based on 46
sessions
History
Date
Time
Result
Not Attempted Yet
If \(0 < 2x + 3y < 10\) and \(-10 < 3x+2y < 0\), then which of the following must be true?
I. \(x < 0\)
II. \(y < 0\)
III. \(x < y\)
A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III
I. \(x < 0\)
II. \(y < 0\)
III. \(x < y\)
A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III
Updated on: 05 Aug 2018, 23:05
Originally posted by MathRevolution on 18 Jun 2018, 01:26.
Last edited by MathRevolution on 05 Aug 2018, 23:05, edited 1 time in total.
Last edited by MathRevolution on 05 Aug 2018, 23:05, edited 1 time in total.
Kudos
Bookmarks
Official Solution:
If \(0 < 2x + 3y < 10\) and \(-10 < 3x+2y < 0\), then which of the following must be true?
I. \(x < 0\)
II. \(y < 0\)
III. \(x < y\)
A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III
Label the inequalities as follows:
\(0 < 2x+3y < 10\) --- (1)
\(-10 < 3x+2y < 0\) --- (2)
We consider each statement individually.
Statement I:
Multiplying (1) by -2 yields \(-20 < -4x – 6y < 0\), and multiplying (2) by 3 yields \(-30 < 9x + 6y < 0\). Adding these inequalities gives \(-50 < 5x < 0\) or \(-10 < x < 0\).
This statement is true.
Statement II:
Multiplying (1) by 3 yields \(0 < 6x + 9y < 30\), and multiplying (2) by -2 yields \(0 < -6x – 4y < 20\). Adding these inequalities gives \(0 < 5y < 50\) or \(0 < y < 10\).
This statement is false.
Statement III:
Multiplying (1) by – 1 yields \(-10 < -2x – 3y < 0\). Adding this to inequality (2) yields \(-20 < x – y < 0\).
This implies that \(x < y\), and statement III is true.
Answer: D
If \(0 < 2x + 3y < 10\) and \(-10 < 3x+2y < 0\), then which of the following must be true?
I. \(x < 0\)
II. \(y < 0\)
III. \(x < y\)
A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III
Label the inequalities as follows:
\(0 < 2x+3y < 10\) --- (1)
\(-10 < 3x+2y < 0\) --- (2)
We consider each statement individually.
Statement I:
Multiplying (1) by -2 yields \(-20 < -4x – 6y < 0\), and multiplying (2) by 3 yields \(-30 < 9x + 6y < 0\). Adding these inequalities gives \(-50 < 5x < 0\) or \(-10 < x < 0\).
This statement is true.
Statement II:
Multiplying (1) by 3 yields \(0 < 6x + 9y < 30\), and multiplying (2) by -2 yields \(0 < -6x – 4y < 20\). Adding these inequalities gives \(0 < 5y < 50\) or \(0 < y < 10\).
This statement is false.
Statement III:
Multiplying (1) by – 1 yields \(-10 < -2x – 3y < 0\). Adding this to inequality (2) yields \(-20 < x – y < 0\).
This implies that \(x < y\), and statement III is true.
Answer: D
01 Aug 2018, 04:16
Kudos
Bookmarks
Must do before exam. It teaches a lot of concepts. This is an easy question. If someone has command over inequalities can surely do it correctly.
