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04 Jun 2022, 07:51
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My 2 cents on this:
Practically, I am always weary of using numbers with so many variables involved. So, like others have done, I also solved it through Algebra. Here's how:
From given, we know that x+y+z>0 --> x+y> -z or that z> -x -y
St 1:
x +y + 1 < z --> z> -x - y
OK. if we add our given equation? Let's see
z> - x -y
z> x + y + 1
------------------
2z> 1
z>1/2, Which means z COULD be greater than but not definitely. Hence insufficient.
St 2: x + y < -1 ---> -x - y > 1
OK. lets add the given equation again.
- x - y > 1
x + y + z > 0
------------------
z> 1
Sufficient! Answer is B
Practically, I am always weary of using numbers with so many variables involved. So, like others have done, I also solved it through Algebra. Here's how:
From given, we know that x+y+z>0 --> x+y> -z or that z> -x -y
St 1:
x +y + 1 < z --> z> -x - y
OK. if we add our given equation? Let's see
z> - x -y
z> x + y + 1
------------------
2z> 1
z>1/2, Which means z COULD be greater than but not definitely. Hence insufficient.
St 2: x + y < -1 ---> -x - y > 1
OK. lets add the given equation again.
- x - y > 1
x + y + z > 0
------------------
z> 1
Sufficient! Answer is B
03 Oct 2022, 09:35
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KarishmaB
Thank you for your helpful response!
To clarify on Bunuel's explanation at the start of this form, "You can only apply subtraction when their signs are in the opposite directions:
If a>ba>b and c<dc<d (signs in opposite direction: >> and <<) --> a−c>b−da−c>b−d (take the sign of the inequality you subtract from).
Example: 3<43<4 and 5>15>1 --> 3−5<4−13−5<4−1 ." I thought that you were not allowed to subtract nor divide inequalities? Why does Bunuel show how to subtract inequalities here?
Thank you
KarishmaB
05 Oct 2022, 02:54
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woohoo921
You can subtract/divide inequalities as long as you understand the constraints under which these operations are valid.
For Subtraction, the inequalities should have opposite signs and the result will take the sign of the first inequality.
a < b
c > d
-------
a - c < b - d
For Division, the inequalities should have opposite signs, both sides of both inequalities should be non negative and there should be no 0 in the denominator post division. Otherwise the result is inconclusive.
If a, b, c and d are positive numbers,
a < b
c > d
---------
a/c < b/d
