Forum Home > GMAT > Quantitative > Problem Solving (PS)
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.
Dec 1511:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease.
Dec 1410:00 AM EST
-12:00 PM EST
Think a 100% GMAT Verbal score is out of your reach? Target Test Prep will make you think again! Our course uses techniques such as topical study and spaced repetition to maximize knowledge retention and make studying simple and fun.- Dec 14
11:00 AM IST
-01:00 PM IST
Attend this session to learn how to Deconstruct arguments, Pre-Think Author’s Assumptions, and apply Negation Test. 
Dec 1608:00 AM PST
-11:59 PM PST
GMAT Club 12 Days of Christmas is a 4th Annual GMAT Club Winter Competition based on solving questions. This is the Winter GMAT competition on GMAT Club with an amazing opportunity to win over $40,000 worth of prizes!- Dec 17
09:00 AM PST
-10:00 AM PST
Join Manhattan Prep instructor Whitney Garner for a fun—and thorough—review of logic-based (non-math) problems, with a particular emphasis on Data Sufficiency and Two-Parts. - Dec 18
10:00 AM PST
-11:00 AM PST
Here is the essential guide to securing scholarships as an MBA student! In this video, we explore the various types of scholarships available, including need-based and merit-based options.
sv9154
Joined: 12 Jan 2020
Last visit: 24 Dec 2021
Posts: 11
Own Kudos:
Given Kudos: 14
Location: India
Concentration: Leadership, General Management
Schools: Anderson '22 Harvard '23 Ross '22 Yale '22
GPA: 4
WE:Business Development (Computer Software)
12 Jan 2020, 07:56
Kudos
Bookmarks
Here are the some properties of the Inequalities.
1) If both the sides of an inequality as L.H.S and R.H.S are Positive, then you can square it.
2) If two inequalities are in same direction such as x>0,y>0 you can add them. If both are in different direction such as x>0,y<0 you can subtract one from another.
3) If two inequalities are in different direction such as x+y>0,y-x<0 then you can multiply one of them with -1 to change the sign. (example,y-x<0, if you multiply with -1 then x-y>0)
Kindly add if you know other properties of Inequalities below.
Kudos if you like my post!
1) If both the sides of an inequality as L.H.S and R.H.S are Positive, then you can square it.
2) If two inequalities are in same direction such as x>0,y>0 you can add them. If both are in different direction such as x>0,y<0 you can subtract one from another.
3) If two inequalities are in different direction such as x+y>0,y-x<0 then you can multiply one of them with -1 to change the sign. (example,y-x<0, if you multiply with -1 then x-y>0)
Kindly add if you know other properties of Inequalities below.
Kudos if you like my post!
13 Jan 2020, 08:57
Kudos
Bookmarks
Important property: Do not cross multiply the variables in the inequality equation unless one knows the +ve and -ve sign of the variables.
Posted from my mobile device
Posted from my mobile device
16 Jan 2020, 00:44
Kudos
Bookmarks
Here is a list of more properties:
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).
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|.
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).
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|.
