a - b = 10 a(a - b) + b(b - a) = ? Anyone know what the best

Question

a - b = 10
a(a - b) + b(b - a) = ?

Anyone know what the best way to do this problem is?

Vithal · Answer

what's the trick here?

isn't it (a-b)^2 = 100?

ian7777 · Answer

it is, but there's a better way that's great for dealing with tough gmat algebra questions.

check out the OG10, DS 245, and DS 260. 

These questions use the same trick, but in a more difficult way.

If you get it, you'll have an easy, non-algebra, time with all of these questions...

boksana · Answer

Agree with Vithal. it's no trick here. Pretty simple :wink:

ian7777 · Answer

This is a great insider trick I teach my students. Think about this: 5-3 is 2, and 3-5 is -2. Another example: 10-7=3, 7-10=-3. The difference between any two numbers will always be the same, although it could be negative or positive.

The GMAT loves this - take two variables and stick them around a minus sign, but reverse them for part of the problem, and it looks like an algebra problem, when it's really a positive/negative problem.

The problem above says,

a-b = 10, 

so what is a(a-b)+b(b-a)?

If you understand that b-a must be -10, then you've got:

a(10) + b(-10)
or 10a-10b
or 10(a-b)
or 10(10) = 100

Now I agree that either way, this isn't a tough problem, and perhaps you want to use the algebraic way more. But in a more difficult problem, like the OG10 data sufficiency questions I referenced in my last post, knowing this little trick will save you full minutes of time as you ignore the algebra temptation and just look at the problem as a positive/negative one in disguise.

Try it out...

Paul · Answer

Great, thank you ian :good

a - b = 10 a(a - b) + b(b - a) = ? Anyone know what the best

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