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99,999^2 - 1^2 = ?

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mitzwillrockgmat: Master | Next Rank: 500 Posts; Posts: 124; Joined: Wed May 19, 2010 10:20 pm; Thanked: 3 times; GMAT Score:1100

by mitzwillrockgmat » Mon Jun 07, 2010 4:17 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)

Hi can someone help me out with this problem??

This is what I did:

99,999^2 - 1^2

=> (99,999 + 1)(99,999 - 1) step 1
=> 100,000 (99,999 - 1) step 2
=> 10^5 (99,999 - 1) step 3

now after this im unsure what to do to get one of the answers above.

in another post, (https://www.beatthegmat.com/99-999-2-1-2-t55211.html) i saw that the 99,999 was rounded off to
100,000 & the 1 was increased to 2. hence, the sol is:

=> 100,000 (100,000 - 2) step 4
= 10^5(10^5 -2)

can someone pls explain the logic behind step 3 to step 4? can one increase the value of 2 numbers like this?? thanks!
this question doesn't even ask for an approximation otherwise i would've bought the answer but im not convinced. thanks in advance!

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Source: Beat The GMAT — Problem Solving | Mon Jun 07, 2010 4:17 am

liferocks: Legendary Member; Posts: 576; Joined: Sat Mar 13, 2010 8:31 pmFollowed by: 1 member; Thanked: 97 times

by liferocks » Mon Jun 07, 2010 4:19 am

mitzwillrockgmat wrote: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)

10^5 (99,999 - 1) step 3
=10^5((99999+1)-2)step 4
=10^5(10000-2)step5
=10^5(10^5-2)

"If you don't know where you are going, any road will get you there."
Lewis Carroll

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liferocks: Legendary Member; Posts: 576; Joined: Sat Mar 13, 2010 8:31 pmFollowed by: 1 member; Thanked: 97 times

by liferocks » Mon Jun 07, 2010 4:20 am

liferocks wrote:
mitzwillrockgmat wrote: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)

10^5 (99,999 - 1) step 3
=10^5((99999+1)-2)step 4
=10^5(10000-2)step5
=10^5(10^5-2)

let me know if this clarifies.

"If you don't know where you are going, any road will get you there."
Lewis Carroll

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mitzwillrockgmat: Master | Next Rank: 500 Posts; Posts: 124; Joined: Wed May 19, 2010 10:20 pm; Thanked: 3 times; GMAT Score:1100

by mitzwillrockgmat » Mon Jun 07, 2010 4:28 am

liferocks wrote:
liferocks wrote:
mitzwillrockgmat wrote: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)

10^5 (99,999 - 1) step 3
=10^5((99999+1)-2)step 4
=10^5(10000-2)step5
=10^5(10^5-2)

let me know if this clarifies.

i see that you increased both 99,999 and 1 by 1 to 100,000 & 2. but my question is how can one do that?? can we increase the value of two constants on one side of an equation?

or did you do this as an attempt to match the answer choice e?

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Rich@VeritasPrep: GMAT Instructor; Posts: 147; Joined: Tue Aug 25, 2009 7:57 pmFollowed by: 17 members; Location: New York City; Thanked: 76 times; GMAT Score:770

by Rich@VeritasPrep » Mon Jun 07, 2010 5:08 am

Hey there,

It may look as if the two constants were each increased by 1, but in actuality, one was increased by 1, while the other was decreased by 1.

Again, going from 99999 - 1 to 100000 - 2 makes it seem as if I increased each constant by 1. But don't forget about the NEGATIVE in front of the second constant. So in actuality, 1 was added to 99999 and -1 was added to -1.

You could also recognize that 99999-1 is the same quantity as 100000-2 (namely, 99998). That's really all you need to know.

If you need confirmation, here's another way you could get it:

99999 - 1

= (100000 - 1) - 1

= 100000 - 1 - 1

= 100000 - 2

In the future, you can always make number properties clearer by using simpler examples. For instance, it's very easy to see that 3 - 1 gives you the exact same quantity as 4 - 2.

Rich Zwelling
GMAT Instructor, Veritas Prep

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mitzwillrockgmat: Master | Next Rank: 500 Posts; Posts: 124; Joined: Wed May 19, 2010 10:20 pm; Thanked: 3 times; GMAT Score:1100

by mitzwillrockgmat » Mon Jun 07, 2010 5:25 am

raz1024 wrote:Hey there,

It may look as if the two constants were each increased by 1, but in actuality, one was increased by 1, while the other was decreased by 1.

Again, going from 99999 - 1 to 100000 - 2 makes it seem as if I increased each constant by 1. But don't forget about the NEGATIVE in front of the second constant. So in actuality, 1 was added to 99999 and -1 was added to -1.

You could also recognize that 99999-1 is the same quantity as 100000-2 (namely, 99998). That's really all you need to know.

If you need confirmation, here's another way you could get it:

99999 - 1

= (100000 - 1) - 1

= 100000 - 1 - 1

= 100000 - 2

In the future, you can always make number properties clearer by using simpler examples. For instance, it's very easy to see that 3 - 1 gives you the exact same quantity as 4 - 2.

fantastic explaination, thanks!

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