EgmatQuantExpert wrote:
reto wrote:
Im having troubles with absolute value, im never sure if I considered all the options. Let me try:
Statement 1:
\(2^{a-b} > 16\) can be rewritten as \(2^{a-b} > 2^4\). This means a-b must be > 4 in order to be true. Therefore a > 4 + b. However if B is negative, e.g. -10 and a is 3, the statement 1 is still true but it changes the answer to the question. Statement 1 = Insufficient.
Statement 2
Shows us that a-b<b and a+b<b because of the absolute values. Change the latter and you arrive at a<0. All this on it's own doesn't help. Insufficient.
Combined:
a > 4 + b
a<0
Plug in: a = -10 and b -15 > Is \(a > |b|?\) > NO
Sufficient if you combine it.
Dear
retoThe key to getting comfortable with Absolute Value questions is:
1. Understanding what Absolute Value means in the first place. We should not try to solve questions just by applying formulae without understanding why we are doing what we are doing. For example, in an expression |something| < c, why do we FLIP the sign of inequality and put a - sign before c when the 'something' is negative? You should feel confident about the logic behind this.
2. When you practice Absolute Value questions, do them step-by-step. DO NOT try to skip steps or do calculations in the air. This leads to mistakes that could have been easily avoided if we were writing each step down. Keeping this in mind, would you want to give the red part in your solution another try?
Hope you found this discussion useful!
Best Regards
Japinder
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