Question 4 (nov.17th)

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bacali: Master | Next Rank: 500 Posts; Posts: 245; Joined: Thu Aug 16, 2007 12:41 pm

by bacali » Mon Nov 17, 2008 11:23 am

99,999^2 - 1^2 =

A. 10^10 - 2
B. (10^5 – 2)^2
C. 10^4(10^5 – 2)
D. 10^5(10^4 – 2)
E. 10^5(10^5 – 2)

OA: [spoiler] E

This is a tough one. Can someone please explain?[/spoiler]

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Source: Beat The GMAT — Problem Solving | Mon Nov 17, 2008 11:23 am

dmateer25: Community Manager; Posts: 1049; Joined: Sun Apr 06, 2008 5:15 pmFollowed by: 27 members; Location: Pittsburgh, PA; Thanked: 113 times; GMAT Score:710

by dmateer25 » Mon Nov 17, 2008 11:39 am

99999 = 10^5-1

(10^5-1)^2 - 1

10^10 - 10^5 - 10^5 + 1 - 1

10^10 - 10^5 - 10^5

10^5(10^5-1-1)

10^5(10^5 - 2)

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vittalgmat: Legendary Member; Posts: 621; Joined: Wed Apr 09, 2008 7:13 pmFollowed by: 4 members; Thanked: 33 times

by vittalgmat » Mon Nov 17, 2008 3:00 pm

Here is another way.

99,999^2 - 1^2 is of the form a^2 -b^2 ==> (a+b) (a -b)

= (99999 +1) (99999 -1)
= 100000 * 99998
= 10^5 (10^5 -2)

HT Helps
-Vittal

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vishubn: Legendary Member; Posts: 574; Joined: Sun Jun 01, 2008 8:48 am; Location: Bangalore; Thanked: 28 times

by vishubn » Mon Nov 17, 2008 5:48 pm

Here is another way.

99,999^2 - 1^2 is of the form a^2 -b^2 ==> (a+b) (a -b)

on the same line

(99998)(100000)

(100000-2)(100000)
= 10^5 (10^5 -2)
vishu

KILL !! DIE !! or BEAT my FEAR !!! de@D END!!

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jnellaz: Master | Next Rank: 500 Posts; Posts: 114; Joined: Mon Oct 20, 2008 7:03 pmFollowed by: 5 members; Thanked: 4 times

by jnellaz » Tue Nov 18, 2008 6:44 am

dmateer25, How did you get from (10^5-1)^2 - 1 to

10^10 - 10^5 - 10^5 + 1 - 1 ?

From (10^5-1)^2 - 1 , I get 10^10-1^2 - 1 or 10^10 +1 -1. Where did I go wrong?

Thanks!

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mals24: Legendary Member; Posts: 683; Joined: Tue Jul 22, 2008 1:58 pmFollowed by: 2 members; Location: Dubai; Thanked: 73 times

by mals24 » Tue Nov 18, 2008 7:15 am

Hope dmateer25 wouldn't mind me replying to your question.

(10^5-1)^2 is in the form (a+b)^2 = a^2+2ab+b^2

(10^5-1)^2 = 10^10-2*10^5+1

10^10-10^5-10^5+1

jnellaz You haven't applied the (a+b)^2 rule while squaring the bracket.

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dmateer25: Community Manager; Posts: 1049; Joined: Sun Apr 06, 2008 5:15 pmFollowed by: 27 members; Location: Pittsburgh, PA; Thanked: 113 times; GMAT Score:710

by dmateer25 » Tue Nov 18, 2008 7:16 am

(10^5-1)^2 -1

Set it up like this and then FOIL: (10^5 – 1)(10^5 – 1) - 1

10^10 – 10^5 – 10^5 + 1 - 1

“From (10^5-1)^2 - 1 , I get 10^10-1^2 - 1 or 10^10 +1 -1. Where did I go wrong?”

You canceled out -10^5 -10^5.

Think of it like this, what is the value of -10 - 10? It is -20 not 0

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jnellaz: Master | Next Rank: 500 Posts; Posts: 114; Joined: Mon Oct 20, 2008 7:03 pmFollowed by: 5 members; Thanked: 4 times

by jnellaz » Tue Nov 18, 2008 10:42 am

Thanks to you both for the explanations

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