Absolute Negatives

[svyessayan]

I literally am going crazy with this question!

CAT #4, Q2

D is the correct answer, but all the numbers I test ARE negative (i.e., a=1 and b= -2 is (1+4 - 2|-2*-1|) = 5 - 2(3) which is -1. What am I doing wrong?

Which of the following expressions CANNOT have a negative value?

A. |a + b| - |a - b|

B. |a + b| - |a|

C. |2a + b| - |a + b|

D. a2 + b2 - 2|ab|

E. |a3 + b3| - a - b

[magoood_2020]

Double check your work with 1+4 - 2|-2*-1|

It should be 5-2|-2*1|=5-4=1 (+ve)
P.S. also in the abs. value, you typed -1 for a while you picked a=1 in the first place so take care from wrong pluggings (in this particular scenario the mistake didn't make any difference!)

[tim]

I can't tell what you're doing wrong until you share a little more about what calculations you've made. The only thing I can say for sure is that you made one or more calculation errors.

[abdullahmatt]

D. a2 + b2 - 2|ab|

how about a=1 and b=2
1 squared plus 2 squared = 5- 2(absulute value of 1*2)=5-2(3)=-1

[tim]

1*2 = 2, not 3.

[RonPurewal]

There's also a theory approach here, if you recognize factoring patterns readily enough.

Remember that |stuff| is always equal to either (stuff) or (-stuff). Therefore, the expression in choice (d) equals either
a^2 + b^2 + 2ab
or
a^2 + b^2 - 2ab

The former of these factors to (a + b)^2.
The latter factors to (a - b)^2.
These are squares, so neither of them can be negative. So (d) can't be negative.

[abdullahmatt]

stupid mistake
a2 + b2 - 2|ab|
is the correct anwser any tips on how to recognize this as the correct anwser quicky and by intuition?
my intuition guess was b
|a + b| - |a|

if you are adding 2 numbers and since you are taking absulute value, how can subtracting 1 of those numbers as an absolute value give you a negative?

could someone please provide numbers to plug in here to show a negative? i dont think it can be done since 2>1

d makes sense as an anwser especially with the factoring but i still see no problem with b

[abdullahmatt]

this would be a factoring question and should be obvious since the more you look at it the anwser sticks out like a sore thumb

a2 + b2 - 2|ab|

(a+b)^2= (a+b)(a+b)= a^2 +ab +ab +b^2= a^2 +2ab+b^2= a2+b2+2ab

any number squared minused by itself with absolute values has to be positive


still could someone give me numbers to show |a + b| - |a| negative

[RonPurewal]

could someone give me numbers to show |a + b| - |a| negative

Try -1 and 1.

[RonPurewal]

By the way, two more things:

this would be a factoring question and should be obvious since the more you look at it the anwser sticks out like a sore thumb

The boldface things here are not only completely pointless, but also insulting to readers of the forum. If someone is reading this thread, it's because the solution is NOT "obvious", and does NOT "stick out like a sore thumb".

Please don't post things like this. From now on, we'll just delete them.

is the correct anwser any tips on how to recognize this as the correct anwser quicky and by intuition?

If you're counting on seeing answers "quickly and by intuition", then you can say goodbye to the possibility of a high score on the GMAT quant section. Especially in data sufficiency, but, overall.

The entire point of the quant section is to give you problems that are NOT necessarily "intuitive".
(In fact, once you're past a certain level, the one thing you can consistently count on is that the "intuitive" answers to DS problems are just about always wrong.)

[prajwalk346]

There's also a theory approach here, if you recognize factoring patterns readily enough.

Remember that |stuff| is always equal to either (stuff) or (-stuff). Therefore, the expression in choice (d) equals either
a^2 + b^2 + 2ab
or
a^2 + b^2 - 2ab

The former of these factors to (a + b)^2.
The latter factors to (a - b)^2.
These are squares, so neither of them can be negative. So (d) can't be negative.

Hi Ron,
I agree with the logic..
But then if u plug in numbers, say a=0.1 and b=0.2 even option " d " will turn negative!
help please..
Thanks,
Prajwal

[tim]

Okay here's something to think about, not because I want to give you a hard time here, but because it is CRUCIAL to your success on the GMAT:

When Ron gives an iron clad proof that something ALWAYS works (no part of which you've taken issue with BTW), and then you plug in some numbers and appear to get a different result, who do you think is wrong?

This happens a lot on the forums, and I can usually tell which students are the ones who are going to be successful at their GMAT studying: It's the ones who, when they disagree with the official answer, ask themselves what THEY did wrong rather than coming onto the forums to announce that they have found a "mistake" in the GMAT. You want to be in that successful category, right?

If so, take another look at the problem, this time with the perspective that you MUST have done something wrong because you didn't arrive at what you know is the correct answer. See if you can find your mistake. If you try over and over and still can't figure out your mistake, feel free to post a followup here with DETAILED calculations so we can follow along and help you find your mistake.

[RonPurewal]

^^ that.

you probably just made some kind of arithmetic error. (in particular, i see a lot of errors with decimal places-- e.g., multiplying 0.1 by 0.2 and mistakenly getting 0.2.)

if you walk away from the problem for a couple of days and then return to it, you'll be much more likely to find whatever you did wrong. (this is pretty common with puzzles in general. if you keep staring at something, it will keep confusing you-- but if you shrug your shoulders, walk away, and then return later, you'll often have a new perspective as if by magic.)