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

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

functions

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 20
Joined: Fri Nov 18, 2011 11:28 pm
Location: Ludhiana ,Punjab, India
Thanked: 1 times
by vishal chugh » Sat Nov 19, 2011 12:11 am
The function f is defined for each positive three-digit integer n by f(n) = 2^x3^y5^z , where x, y and z are the hundreds, tens, and units digits of n, respectively. If m and v are three-digit positive integers such that f(m)=9f(v), them m-v=?
(A) 8
(B) 9
(C) 18
(D) 20
(E) 8
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Legendary Member
Posts: 1084
Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members
Thanked: 158 times

by pemdas » Sat Nov 19, 2011 12:21 am
2^x3^y5^z=9*(2^X3^Y5^Z)=2^X3^(Y+2)5^Z,
it's clear that the difference between two numbers is in the ten's unit by 2
since unit's digits are the same and we have difference only in ten's digit, the difference in unit's digit=0 and we look for difference in ten's digit, which is d=20
vishal chugh wrote:The function f is defined for each positive three-digit integer n by f(n) = 2^x3^y5^z , where x, y and z are the hundreds, tens, and units digits of n, respectively. If m and v are three-digit positive integers such that f(m)=9f(v), them m-v=?
(A) 8
(B) 9
(C) 18
(D) 20
(E) 8
Success doesn't come overnight!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members
Location: New York, NY
Thanked: 13060 times
GMAT Score:790

by GMATGuruNY » Sat Nov 19, 2011 5:42 am
vishal chugh wrote:The function f is defined for each positive three-digit integer n by f(n) = 2^x3^y5^z , where x, y and z are the hundreds, tens, and units digits of n, respectively. If m and v are three-digit positive integers such that f(m)=9f(v), them m-v=?
(A) 8
(B) 9
(C) 18
(D) 20
(E) 8
Let m = 120.
f(120) = (2^1)(3^2)(5^0) = 18.

Since f(m) = 9f(v):
18 = 9f(v).
f(v) = 2.

If f(v) = 2, then v=100:
f(100) = (2^1)(3^0)(5^0) = 2.

Thus, m-v = 120-100 = 20.

The correct answer is D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 37
Joined: Thu Oct 06, 2011 2:49 pm
Thanked: 4 times

by ollapodrida » Sun Nov 20, 2011 6:54 pm
GMATGuruNY wrote:
vishal chugh wrote:The function f is defined for each positive three-digit integer n by f(n) = 2^x3^y5^z , where x, y and z are the hundreds, tens, and units digits of n, respectively. If m and v are three-digit positive integers such that f(m)=9f(v), them m-v=?
(A) 8
(B) 9
(C) 18
(D) 20
(E) 8
Let m = 120.
f(120) = (2^1)(3^2)(5^0) = 18.

Since f(m) = 9f(v):
18 = 9f(v).
f(v) = 2.

If f(v) = 2, then v=100:
f(100) = (2^1)(3^0)(5^0) = 2.

Thus, m-v = 120-100 = 20.

The correct answer is D.
What motivated your choice of m=120 in this problem?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 37
Joined: Thu Oct 06, 2011 2:49 pm
Thanked: 4 times

by ollapodrida » Sun Nov 20, 2011 7:01 pm
pemdas wrote:2^x3^y5^z=9*(2^X3^Y5^Z)=2^X3^(Y+2)5^Z,
it's clear that the difference between two numbers is in the ten's unit by 2
since unit's digits are the same and we have difference only in ten's digit, the difference in unit's digit=0 and we look for difference in ten's digit, which is d=20
I don't quite follow your logic. Can you add a little more detail or break things down to make your logic more clear here?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Senior | Next Rank: 100 Posts
Posts: 48
Joined: Sun Jul 17, 2011 12:04 am

by shikh » Sun Nov 20, 2011 11:08 pm
can u plz explain it more clearly
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 966
Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members
Thanked: 230 times

by shankar.ashwin » Sun Nov 20, 2011 11:43 pm
You are given f(m) = 9f(v)

Assume minimum value of 'v' = 1 (001)

Therefore f(v) = 2^0 * 3^0 * 5^1 = 5

Since, f(m) = 9* f(v) = 9*5 = 2^0 * 3^2 * 5^1.

THe powers here correspond to x,y,z respectively (or) m = 021

m-v = 21-1 = 20 D
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members
Location: New York, NY
Thanked: 13060 times
GMAT Score:790

by GMATGuruNY » Mon Nov 21, 2011 4:22 am
ollapodrida wrote:
GMATGuruNY wrote:
vishal chugh wrote:The function f is defined for each positive three-digit integer n by f(n) = 2^x3^y5^z , where x, y and z are the hundreds, tens, and units digits of n, respectively. If m and v are three-digit positive integers such that f(m)=9f(v), them m-v=?
(A) 8
(B) 9
(C) 18
(D) 20
(E) 8
Let m = 120.
f(120) = (2^1)(3^2)(5^0) = 18.

Since f(m) = 9f(v):
18 = 9f(v).
f(v) = 2.

If f(v) = 2, then v=100:
f(100) = (2^1)(3^0)(5^0) = 2.

Thus, m-v = 120-100 = 20.

The correct answer is D.
What motivated your choice of m=120 in this problem?
Since f(m) = 9f(v), f(m) is a multiple of 9.
If three-digit m = 120, then f(120) = (2^1)(3^2)(5^0) = 18, which is a multiple of 9.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 36
Joined: Fri Mar 27, 2009 6:53 pm

by adamsmith2009 » Tue Nov 22, 2011 10:53 am
Isn't the question asking (2^x)(3^y)(5^z)?

The way you wrote it: f(n) = 2^x3^y5^z it looks like everything is two is being raised with all of the powers or is it just me?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 296
Joined: Sun May 29, 2011 5:10 amFollowed by: 5 members
Location: Vietnam
Thanked: 10 times

by tuanquang269 » Tue Nov 22, 2011 8:32 pm
Thank guru for explanation :D
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 15
Joined: Mon Oct 10, 2011 3:06 am
Location: UK
Thanked: 1 times

by nskandan » Wed Nov 23, 2011 8:52 am
I went through a more linear route
m = xyz, v = abc

(2^x)(3^y)(4^z) = 9. (2^a)(3^b)(4^c)
(2^(x-a))(3^(y-b))(4^(z-c)) = 9

so y-b = 2 and x-a & z-c has to be 0

hence m-v = xyz-abc = 20
NSK
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1