If sqrt x = 25, then x^3 â€“ x^2 = ?

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bhumika.k.shah: Legendary Member; Posts: 941; Joined: Sun Dec 27, 2009 12:28 amFollowed by: 1 member; Thanked: 20 times

by bhumika.k.shah » Wed Jan 20, 2010 9:40 am

If sqrt x = 25, then x^3 - x^2 = ?

A. 5^12
B. 5^20
C. 6(5^5)
D. 5^4(5^2 + 1)
E. 5^8(5^4 minus 1)

OA E

I got the answer but after literally multiplying 625^3-625^ and then solving each of the answer options

it was toooo time consuming

I would like to know a quicker approach.

Thanks

Last edited by bhumika.k.shah on Wed Jan 20, 2010 10:09 am, edited 2 times in total.

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Source: Beat The GMAT — Problem Solving | Wed Jan 20, 2010 9:40 am

apuso: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Mon Jan 18, 2010 8:27 pm; Thanked: 1 times

by apuso » Wed Jan 20, 2010 10:03 am

Below way of solving is an option:

x^3 - x^2
= (625)^3 - (625)^2
= (625)^2 ((625) - 1 )
= (5^4)^2 ((5^4)-1)
= (5^8) ((5^4) - 1)

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amittilak: Senior | Next Rank: 100 Posts; Posts: 34; Joined: Wed Nov 11, 2009 11:23 amFollowed by: 1 member; Thanked: 8 times

by amittilak » Wed Jan 20, 2010 10:42 am

Given: sqrt x = 25,
which equals to, sqrt (x) = 5^2 (you have to realize after looking at the answer choices that you need to find the value in terms of 5)
hence, x = 5 ^4
and x^2 = 5^8
Now, lets look at what was asked:
x^3 - x^2 = ??
Simplifying,
x^3 - x^2 = x^2 (x - 1)
= 5^8 (5^4 - 1), which happens to be answer choice E.

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Fri Nov 18, 2016 8:32 pm

bhumika.k.shah wrote:If sqrt x = 25, then x^3 - x^2 = ?

A. 5^12
B. 5^20
C. 6(5^5)
D. 5^4(5^2 + 1)
E. 5^8(5^4 minus 1)

OA E

I got the answer but after literally multiplying 625^3-625^ and then solving each of the answer options
it was toooo time consuming

I would like to know a quicker approach.

Thanks

Answer: Option D

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melguy: Master | Next Rank: 500 Posts; Posts: 335; Joined: Mon Mar 21, 2011 11:31 pmFollowed by: 2 members; Location: Australia / India; Thanked: 37 times

by melguy » Sat Nov 19, 2016 7:23 pm

âˆšx = 25
x = 25 x 25 (i.e. 5â�´)

Rephrase
What is 5â�´ x 5â�´ x 5â�´ - 5â�´ x 5â�´

Take 5â�´ x 5â�´ common
5â�´ x 5â�´ (5â�´ - 1)
5^8 (5â�´ - 1)

Answer is E

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Nov 20, 2016 6:36 am

bhumika.k.shah wrote:If âˆšx = 25, then xÂ³ - xÂ² = ?

A. 5Â¹Â²
B. 5Â²â�°
C. 6(5â�µ)
D. 5â�´(5Â² + 1)
E. 5â�¸(5â�´ - 1)

If âˆšx = 25, then x = 625
Or we can say that x = 25Â²
Since 25 = 5Â², we can say that x = 25Â² = (5Â²)Â² = 5â�´

So, xÂ³ - xÂ² = (5â�´)Â³ - (5â�´)Â²
= 5Â¹Â² - 5â�¸
= 5â�¸(5â�´ - 1) [we factored out the greatest common factor]
= E

RELATED VIDEOS
- Laws of exponents - part I: https://www.gmatprepnow.com/module/gmat ... video/1025
- Greatest common factor factoring: https://www.gmatprepnow.com/module/gmat ... /video/954

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Fri Nov 25, 2016 3:06 pm

I'd start with factoring:

xÂ³ - xÂ² =

xÂ² * (x - 1)

Then plug in x = 625:

625Â² * 624

or

5â�¸ * (5â�´ - 1)

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Sun Nov 27, 2016 5:56 pm

bhumika.k.shah wrote:If âˆšx = 25, then x^3 - x^2 = ?

A. 5^12
B. 5^20
C. 6(5^5)
D. 5^4(5^2 + 1)
E. 5^8(5^4 - 1)

OA E

We start by squaring both sides of the equation âˆšx = 25 to get:

x = 25^2 = (5^2)^2 = 5^4

We need to determine the value of x^3 - x^2, thus:

x^3 = (5^4)^3 = 5^12

x^2 = (5^4)^2 = 5^8

Thus:

x^3 - x^2 = 5^12 - 5^8 = 5^8(5^4 - 1)

Answer:E

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