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Jul 2, 2014
Inequalities: Tips and hints
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This post is a part of the Quant Tips and Hints by Topic Directory focusing on Quant topics and providing examples of how to approach them. Most of the questions are above average difficulty. |
Apr 5, 2018
adkikani wrote:Bunuel VeritasPrepKarishma chetan2u
2. You can only apply subtraction when their signs are in the opposite directions:If and (signs in opposite direction: and ) --> (take the sign of the inequality you subtract from).
Example: and --> .
Any alternative way to memorize highlighted text under time crunch other than picking numbers?
Dec 14, 2015
Aug 6, 2016
Apr 4, 2018
If and (signs in opposite direction: and ) --> (take the sign of the inequality you subtract from).
Example: and --> .
Apr 4, 2018
adkikani wrote:Bunuel VeritasPrepKarishma chetan2u
2. You can only apply subtraction when their signs are in the opposite directions:If and (signs in opposite direction: and ) --> (take the sign of the inequality you subtract from).
Example: and --> .
Any alternative way to memorize highlighted text under time crunch other than picking numbers?
Apr 13, 2018
Apr 14, 2018
adkikani wrote:Bunuel chetan2u VeritasPrepKarishma niks18
Let us say, I am given a SINGLE inequality:
a - b > a + b
Given: a and b are integers.
Can I add / subtract an integer with unknown sign (ie positive or negative)
to both sides of inequality WITHOUT knowing existing sign of another variable?
Eg. Here, can I subtract a from both sides, without knowing sign of b?
Apr 14, 2018
adkikani wrote:Bunuel chetan2u VeritasPrepKarishma niks18
Let us say, I am given a SINGLE inequality:
a - b > a + b
Given: a and b are integers.
Can I add / subtract an integer with unknown sign (ie positive or negative)
to both sides of inequality WITHOUT knowing existing sign of another variable?
Eg. Here, can I subtract a from both sides, without knowing sign of b?
Can I add / subtract an integer with unknown sign (ie positive or negative) to both sides of inequality WITHOUT knowing existing sign of another variable?
Mar 10, 2020
Mar 10, 2020
Debo1988 wrote:Bunuel chetan2u Gladiator59 VeritasKarishma
The post says "We can raise both parts of an inequality to an even power if we know that both parts of an inequality are non-negative (the same for taking an even root of both sides of an inequality)."
To me, the bold part means : "We can take even root of both parts of an inequality if we know that both parts of the inequality are non-negative"
However, this does not seem to hold true for the below example, can you please clarify?
Let's say : x^2 > y^4 (given)
So according to the above rule (see bold part of the excerpt), since both sides of the inequality are non-negative(as anything raised to even power is non negative), we can say:
x > y^2 (taking square root on both sides of the inequality)
But that's not necessarily true.
Consider the example :
Case 1 : X = 300, Y = 2
Case 2 : X = -300 , Y = 2
In both cases x^2 > y^4, but for case 1 : x > y^2, whereas for case 2 : x < y^2
Jul 25, 2020
chetan2u wrote:adkikani wrote:Bunuel VeritasPrepKarishma chetan2u
2. You can only apply subtraction when their signs are in the opposite directions:If and (signs in opposite direction: and ) --> (take the sign of the inequality you subtract from).
Example: and --> .
Any alternative way to memorize highlighted text under time crunch other than picking numbers?
Just remember that you can add INEQUALITIES by adding the terms on same side of INEQUALITY..
So if a>b and c<d...c<d is same as d>c..
So we have a>b and d>c...
Add the same sides of INEQUALITY..
a+d>b+c.......a>b+c-d.....a-c>b-d...
Same as what you are trying to remember about SUBTRACTION
Aug 1, 2020
sheldoncooper wrote:chetan2u wrote:adkikani wrote:Bunuel VeritasPrepKarishma chetan2u
2. You can only apply subtraction when their signs are in the opposite directions:If and (signs in opposite direction: and ) --> (take the sign of the inequality you subtract from).
Example: and --> .
Any alternative way to memorize highlighted text under time crunch other than picking numbers?
Just remember that you can add INEQUALITIES by adding the terms on same side of INEQUALITY..
So if a>b and c<d...c<d is same as d>c..
So we have a>b and d>c...
Add the same sides of INEQUALITY..
a+d>b+c.......a>b+c-d.....a-c>b-d...
Same as what you are trying to remember about SUBTRACTION
Hi chetan2u / Bunuel
Does this concept also work in multiplication.
Like highlighted above, we can multiple inequalities only when both sides of both inequalities are positive and the inequalities have the same sign.
Say if the signs are not the same ; can we multiply the inequality with -1 to make the sign same & then multiply ?
Like
if x<a and y>b ; then (-1)y<-b
hence on multiplying : x*(-y) < a(-b) ? will the signs cancel ; nullifying the approach or multiplication of 2 inequalities with opposite signs just can't happen ?
Sep 6, 2021
Sep 6, 2021
irene727008 wrote:the hints and notes about inequalities are really helpful, thanks!
I have a question.
MULTIPLYING/DIVIDING AN INEQUALITY BY A NUMBER
3. Never multiply (or reduce) an inequality by a variable (or the expression with a variable) if you don't know the sign of it or are not certain that variable (or the expression with a variable) doesn't equal to zero.
⬆️
does "reduce" here mean divide or subtract? I am a little bit confuse.
as I understand, we could not multiply or divide a variable whose sign is unknown.
but we could add or subtract a variable whose sign is unknown without changing the sign of INEQUALITY.
Sep 17, 2022
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