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23 Apr 2021, 05:28
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Dear all:
I have a question about the text noted in Bunuel's Signature Collection. As I understand, we can multiply two inequalities that have the same sign and divide two inequalities that have opposite signs, keeping in mind that we take the sign of the dividend. Stated in one of the documents titled EVEN-ODD, the author notes that we need to flip the sign of the inequality when two negative inequalities are multiplied. This point makes sense. I would assume that the sign remains the same when one negative inequality is multiplied with a positive one. However, it further notes that we can divide two negative inequalities of the same sign and states the variables in an order that is not typical. I am not sure if this is typo or if it is correct. I request clarification.
"Deal with negative numbers:
-a<-b<0, -c<-d<0
Then
-a-c<-b-d<0
-a-(-d)<-b-(-c)
However the sign needs to be flipped one more time if you are doing multiplication or division
(because you are multiplying/dividing a negative number):
(-a)*(-c)>(-b)*(-d)
(-a)/(-d)>(-b)/(-c)
For example:
If x<-4, y<-2, we know that xy>8, but we don't know how x/y compare to (-4)/(-2)=2 since
you can only do division when their signs are in different directions
If x>-4 and y<-2 then x/y<2 but we don't know how xy is compared to 8 since we can only do
multiplication when their signs are the same direction."
I have a question about the text noted in Bunuel's Signature Collection. As I understand, we can multiply two inequalities that have the same sign and divide two inequalities that have opposite signs, keeping in mind that we take the sign of the dividend. Stated in one of the documents titled EVEN-ODD, the author notes that we need to flip the sign of the inequality when two negative inequalities are multiplied. This point makes sense. I would assume that the sign remains the same when one negative inequality is multiplied with a positive one. However, it further notes that we can divide two negative inequalities of the same sign and states the variables in an order that is not typical. I am not sure if this is typo or if it is correct. I request clarification.
"Deal with negative numbers:
-a<-b<0, -c<-d<0
Then
-a-c<-b-d<0
-a-(-d)<-b-(-c)
However the sign needs to be flipped one more time if you are doing multiplication or division
(because you are multiplying/dividing a negative number):
(-a)*(-c)>(-b)*(-d)
(-a)/(-d)>(-b)/(-c)
For example:
If x<-4, y<-2, we know that xy>8, but we don't know how x/y compare to (-4)/(-2)=2 since
you can only do division when their signs are in different directions
If x>-4 and y<-2 then x/y<2 but we don't know how xy is compared to 8 since we can only do
multiplication when their signs are the same direction."
24 Apr 2021, 09:31
Kudos
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Hello, imslogic. Why not ask Bunuel directly in the appropriate "theory" thread? (Did you find this somewhere from section 9 of the Ultimate GMAT Quantitative Megathread?
- Andrew
- Andrew
28 Apr 2021, 10:19
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Hi Andrew:
I found the document in a zip file titled Bunuel Signature Collection that I located in a google search. I tried to DM Bunuel but was not able to do so. I figured out the dilemma:The inequalities simply show the same inequality under two adjustments versus two different inequalities highlighting order of operation rules. The thread you posted is an interesting summary. Is there a similar thread on GMATCLUB for verbal areas as critical reasoning and sentence correction? Thanks.
Posted from my mobile device
I found the document in a zip file titled Bunuel Signature Collection that I located in a google search. I tried to DM Bunuel but was not able to do so. I figured out the dilemma:The inequalities simply show the same inequality under two adjustments versus two different inequalities highlighting order of operation rules. The thread you posted is an interesting summary. Is there a similar thread on GMATCLUB for verbal areas as critical reasoning and sentence correction? Thanks.
Posted from my mobile device
