BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Shortcut to this question???

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 25
Joined: Mon May 25, 2009 7:21 pm
Location: Ohio
Thanked: 1 times
GMAT Score:750

Shortcut to this question???

by irish200 » Thu Jul 09, 2009 3:52 pm
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
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2623
Joined: Mon Jun 02, 2008 3:17 am
Location: Montreal
Thanked: 1090 times
Followed by:355 members
GMAT Score:780

by Ian Stewart » Thu Jul 09, 2009 4:07 pm
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
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 472
Joined: Sun Mar 29, 2009 6:54 pm
Thanked: 56 times

by ssmiles08 » Thu Jul 09, 2009 4:35 pm
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.
Top
GMAT Instructor
Posts: 1223
Joined: Thu May 01, 2008 3:29 pm
Location: Los Angeles, CA
Thanked: 185 times
Followed by:15 members

by VP_Jim » Thu Jul 09, 2009 4:53 pm
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.
Jim S. | GMAT Instructor | Veritas Prep
Top
Junior | Next Rank: 30 Posts
Posts: 25
Joined: Mon May 25, 2009 7:21 pm
Location: Ohio
Thanked: 1 times
GMAT Score:750

by irish200 » Thu Jul 09, 2009 5:17 pm
awesome guys, thanks for the quick responses
Top
Post new topic Post Reply
• Page 1 of 1