Shortcut to this question???

[irish200]

I can solve this with a calculator (not allowed) or by hand but it takes WAY too long (over 2 min) to be sufficient at solving problems quickly. Does anyone have any shortcuts/ hints to approximating...

(1001^2)-(999^2) / (101^2)-(99^2)
(the first part divided by the second)

a) 10
b) 20
c) 40
d) 80
e) 100

Again I know how to get the answer (A)...I just need to get it faster




on another note...
Also is there some kind of shortcut for multiplying numbers like 43x89 or 432x23 without doing it the grade school way?

Or a general shortcut for knowing squares?

Any tips will help...
Thanks

[Ian Stewart]

Recall that x^2 - y^2 = (x+y)(x-y). So:

[1001^2 - 999^2]/[101^2 - 99^2]
= [(1001 + 999)(1001 - 999)]/[(101+99)(101-99)]
= [2000*2]/[200*2]
= 10

[ssmiles08]

I learnt a lot from this website on how to multiply fast, so maybe it could help you too.

https://www.vedicmaths.org/Introduction/ ... torial.asp

as for squares, you are better off memorizing the first 20 squares.

you might also want to memorize powers of 2 up the 10th power.

-also know that if you see a question like the one you asked on any GMAT exam, you are not expected to solve it manually, there is ALWAYS some sort of technique behind it. GMAT tests you on your thinking ability, not how much you can solve manually. Obviously, they would never put a question like that up if it wasn't easily solvable within the 2 minute mark.

-hope this helps.

[VP_Jim]

Regarding your question about multiplying things like 42 x 89 faster...

A great way to do this, particularly if you're multiplying by something ends in 1 or 9, is to round up or down and then add or subtract. For example, for 42 x 89, we can round that to 42 x 90, which is easy because that's just 42 x 9 with a zero added on (or, 42x10 - 42).

Then, we can take that result and subtract 42 from it, since we want 42x89, not 42x90.

I should say, however, that the vast majority of GMAT problems don't require such calculations and if you find yourself working out lots of math you're likely approaching the problem the wrong way. There's usually some other way to do it, be it number properties, rounding, backsolving, or whatever.

[irish200]

awesome guys, thanks for the quick responses