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27 Sep 2018, 03:10
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Hi all! Thanks for your help in advance. This basic question is driving me crazy! Imagine that I have two inequalities,let's call them A and B.
A is (2 < x)
B is (y + 3< x).
My understanding is that if I merge these two inequalities, I am going to get a new inequality C that will yield valid solutions for itself and also the previous two inequalities. My understanding is that to merge A and B, I can only add them up when the signs face the same direction. I did that and got a new inequality C which is
C is (y + 5 < 2x).
Now, if x is 2.5 (which is greater than 2 hence meets inequality A), then substituting 2.5 for x on C gives me y<0 HOWEVER substituting in B gives me y<-0.5. Why? Shouldn't both give me the same?
Thanks a lot.
A is (2 < x)
B is (y + 3< x).
My understanding is that if I merge these two inequalities, I am going to get a new inequality C that will yield valid solutions for itself and also the previous two inequalities. My understanding is that to merge A and B, I can only add them up when the signs face the same direction. I did that and got a new inequality C which is
C is (y + 5 < 2x).
Now, if x is 2.5 (which is greater than 2 hence meets inequality A), then substituting 2.5 for x on C gives me y<0 HOWEVER substituting in B gives me y<-0.5. Why? Shouldn't both give me the same?
Thanks a lot.
27 Sep 2018, 09:56
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Hi gmat800live,
this is an interesting problem. I might be wrong, but common sense tells me that y should be less than -1 (solved it graphically). Maybe Bunuel could shed some light on this problem?
this is an interesting problem. I might be wrong, but common sense tells me that y should be less than -1 (solved it graphically). Maybe Bunuel could shed some light on this problem?
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27 Sep 2018, 10:24
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Hi gmat800live,
In simple terms, the reason why the 'solution' to the two inequalities changes is because you are NOT adding the same value to each side of larger inequality.
Here's a simple example:
0 < X
IF we add 1 to BOTH sides, we have...
(0+1) < (X+1)
1 < X + 1
The solution set for the two inequalities is the SAME because those 2 inequalities are the SAME (once you simplify them).
In your example, you are NOT adding the same value to both sides. You're adding '2' to the 'left side' and 'X' to the 'right side', so you are fundamentally changing the inequality (it's DIFFERENT from the one you started with) - thus, the solution sets will be different.
GMAT assassins aren't born, they're made,
Rich
In simple terms, the reason why the 'solution' to the two inequalities changes is because you are NOT adding the same value to each side of larger inequality.
Here's a simple example:
0 < X
IF we add 1 to BOTH sides, we have...
(0+1) < (X+1)
1 < X + 1
The solution set for the two inequalities is the SAME because those 2 inequalities are the SAME (once you simplify them).
In your example, you are NOT adding the same value to both sides. You're adding '2' to the 'left side' and 'X' to the 'right side', so you are fundamentally changing the inequality (it's DIFFERENT from the one you started with) - thus, the solution sets will be different.
GMAT assassins aren't born, they're made,
Rich
