largest possible values

Oldest

Best Reply

Author

Message

TAGS:

Intern

Joined: 21 Feb 2010

Posts: 33

Location: Ukraine

Followers: 1

Kudos [?]: 1 [1] , given: 9

largest possible values [#permalink]

14 May 2010, 04:56

This post received
KUDOS

00:00

Question Stats:

100% (01:38) correct

0% (00:00) wrong

based on 5 sessions

If m is a positive integer and 75^3 is a multiple of 5^m , what is the largest possible values for m?

3
4
5
6
7

Can somebody explain how to solve it?

Intern

Joined: 11 Jan 2007

Posts: 44

Location: United States

Concentration: Marketing, Healthcare

Schools: Kellogg PT '14, Booth '14, Stern PT '14

GMAT 1: 600 Q49 V25
GMAT 2: 650 Q49 V32

GPA: 3.5

WE: Pharmaceuticals (Consulting)

Followers: 0

Kudos [?]: 11 [0], given: 4

Re: largest possible values [#permalink]

14 May 2010, 07:17

IMO m=6. here is why

75^3=(25X3)^3=(5^2 X 3)^3 = 5^6 x3^3

which means that largest factor would be 5^6

What is the OA ?

Intern

Affiliations: Scrum Alliance

Joined: 09 Feb 2010

Posts: 20

Location: United States (MI)

Concentration: Strategy, Technology

Schools: Kellogg PT '16, Booth PT '16, Ross PT '16

Followers: 1

Kudos [?]: 10 [2] , given: 8

Re: largest possible values [#permalink]

14 May 2010, 07:54

This post received
KUDOS

75^3 = 75*75*75=(15*5)*(15*5)*(15*5)=(3*5*5)*(3*5*5)*(3*5*5)=3^3*5^6=27*5^6

if 27*5^6 is a multiple of 5^m, then \frac{27*5^6}{5^m} should result in an integer. Also, remember that m is an integer.

Let us look at the answer options.

A. if m = 3, then the expression becomes \frac{27*5^6}{5^3}, which leaves 27*5^3, an integer.
B. if m = 4, then the expression becomes \frac{27*5^6}{5^4}, which leaves 27*5^2, an integer.
C. if m = 5, then the expression becomes \frac{27*5^6}{5^5}, which leaves 27*5^1, an integer.
D. if m = 6, then the expression becomes \frac{27*5^6}{5^6}, which leaves 27*5^0, an integer.
E. if m = 7, then the expression becomes \frac{27*5^6}{5^7}, which leaves \frac{27}{5}, NOT an integer.

So, out of all the 4 choices that leave us with an integer result, the largest value of m is 6. Hence correct answer is D.

Manager

Joined: 16 Feb 2010

Posts: 175

Followers: 2

Kudos [?]: 4 [0], given: 10

Re: largest possible values [#permalink]

14 May 2010, 09:30

great explanation agreed wid hideyoshi oa shud be d

Manager

Joined: 17 Mar 2010

Posts: 193

Followers: 2

Kudos [?]: 23 [0], given: 9

Re: largest possible values [#permalink]

16 May 2010, 09:22

Hi,
I think the simplest method is...

Find out the highest factor of 5s in 75^3. i.e., 5^6 so, m=6. Because that will be the HCF.

Re: largest possible values [#permalink] 16 May 2010, 09:22

	Similar topics	Author	Replies	Last post
Similar Topics:	Largest value	hardworker_indian	2	13 Sep 2004, 05:08
	What is the largest possible value of x if (x^2 + 16)(x +	rdg	2	09 Mar 2007, 11:03
	Largest value	beatgmat	2	19 Sep 2007, 19:38
	Possible value	sondenso	4	31 May 2009, 02:40
	largest possible value of actual area of rectangle ?	MichelleSavina	1	23 Jan 2011, 03:16

largest possible values

Main navigation

GMAT Resources

Partners

MBA Resources

GMAT ® is a registered trademark of the Graduate Management Admission Council ® (GMAC ®). GMAT Club's website has not been reviewed or endorsed by GMAC.

GMAT Courses

Admissions Consulting

largest possible values

largest possible values

Main navigation

GMAT Resources

Partners

MBA Resources