Events & Promotions
|
|
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.
Apr 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
16 Jan 2020, 00:56
Kudos
Bookmarks
Here is a list of some important properties of inequalities:
1. ADDITION/SUBTRACTION
As long as you are adding/subtracting quantities in an inequality, its sign remains the same.
Eg: 2x + 5 < 3: When you take the 5 to the RHS and subtract, the sign will stay the same. You will get: 2x < -2.
2. MULTIPLICATION/DIVISION
If you multiply/divide by a positive number, the sign of the inequality does not change.
If you multiply/divide by a negative number, the sign of the inequality flips.
Eg: 2x < -2 => x < -1
while, -2x < -2 => x > (-2/-2) = 1
3. RECIPROCAL
If x < y, then 1/x > 1/y if and only if x and y have the same sign (both positive or both negative).
While if x and y have different signs, then even taking the reciprocal would not change the sign of the inequality.
(A substitute of taking the reciprocal is cross-multiplication, where you have to be careful of the sign of the number you are transporting.)
4. MINIMUM/MAXIMUM VALUES
Consider this example:
If -1<x<5 and -10<y<-2,
then to find range of expressions made of x and y, eg, x+y, xy, x-y, 2x+y, etc.,
we should evaluate these expressions using all four extreme cases.
So, for xy, we should find this product 4 times: (-1 x -10), (-1 x -2), (5 x -10), (5 x -2)= 10, 2, -50, -10.
Hence, range of xy is : -50 < xy < 10.
5. If \(x^{2}\) < \(y^{2}\), then |x| < |y|.
6. If |x - a| < b, then (a-b) < x < (a+b)
7. If |x - a| > b, then: x <(a-b) or x> (a+b)
1. ADDITION/SUBTRACTION
As long as you are adding/subtracting quantities in an inequality, its sign remains the same.
Eg: 2x + 5 < 3: When you take the 5 to the RHS and subtract, the sign will stay the same. You will get: 2x < -2.
2. MULTIPLICATION/DIVISION
If you multiply/divide by a positive number, the sign of the inequality does not change.
If you multiply/divide by a negative number, the sign of the inequality flips.
Eg: 2x < -2 => x < -1
while, -2x < -2 => x > (-2/-2) = 1
3. RECIPROCAL
If x < y, then 1/x > 1/y if and only if x and y have the same sign (both positive or both negative).
While if x and y have different signs, then even taking the reciprocal would not change the sign of the inequality.
(A substitute of taking the reciprocal is cross-multiplication, where you have to be careful of the sign of the number you are transporting.)
4. MINIMUM/MAXIMUM VALUES
Consider this example:
If -1<x<5 and -10<y<-2,
then to find range of expressions made of x and y, eg, x+y, xy, x-y, 2x+y, etc.,
we should evaluate these expressions using all four extreme cases.
So, for xy, we should find this product 4 times: (-1 x -10), (-1 x -2), (5 x -10), (5 x -2)= 10, 2, -50, -10.
Hence, range of xy is : -50 < xy < 10.
5. If \(x^{2}\) < \(y^{2}\), then |x| < |y|.
6. If |x - a| < b, then (a-b) < x < (a+b)
7. If |x - a| > b, then: x <(a-b) or x> (a+b)
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
