reto wrote:
Hello Japinder
Thanks for your comments. It's always nice to experience this spirit here on gmatclub.com (people helping each other). Im honest, yesterday I had to reread some theory about absolut value before I could start to solve your questions. Im still in the early stages of my preperation.
Okay, the red part:
a-b<b This is correct, rewrite as a<2b
a+b<b Wow that's ugly, for the negative scenario the term needs to look like this with flipped sign: a-b > -b, which then translates into a>0
All in all Statement 2 tells us:
b > |a-b| this means, that b is 0 or positive right? That's what I should have discovered at first!
a<2b
a>0
Is it that what you were missing in my remarks? If I now combine everything:
From Statement 1
a>4+b
From Statement 2
a>0 this is useless in combination with St. 1
a<2b this is useless in combination with St. 1
The most important is to see that b is 0 or positive. Combined with statement 1 then it will be sufficient.
Any Remarks? Thx
Dear
reto2 remarks, both pertaining to Statement 2 analysis:
1. Please look at the highlighted part. The correct statement would be:
|a-b| can be positive or 0.
Since b > |a-b|, this means b will be strictly greater than 0.
2. When you are considering different cases, always remember to also consider the defining conditions of those cases.Let me explain what I mean:
Look at the
pink line in the quote above. This is your case 1. What is the defining condition of Case 1? That a - b ≥ 0 (this is why you wrote |a-b| = a - b)
So, a ≥ b
So, you should combine the inequality you obtained from the pink line with this inequality to get:
b ≤ a < 2bThis can also be written as |b| ≤ a < 2b (|b| = b since b is positive)
Looking at this inequality, you can say that the answer to 'Is a > |b|' is YES (if a ≠ b) or NO (if a = b)
Now, look at the
orange line in the quote above.
You are absolutely right in the way you processed the negative scenario, but remember to also consider that the defining condition of this case is that a - b < 0, that is, a < b
Therefore, the overall inequality that will result in this case will be:
0 < a < b.This can also be written as 0 < a < |b| (|b| = b since b is positive)
Looking at this inequality, you can say that the answer to 'Is a > |b|' is NO
Since we do not get a unique YES/NO answer from St. 2, it is not sufficient.
Look at the
blue part in the quote above. I hope that you are now able to see that the 2 cases of St. 2 felt useless in combination with St. 1 only because you did not take the defining conditions of the 2 cases into consideration.
Best Regards
Japinder
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