Last visit was: 12 Jul 2025, 07:06 It is currently 12 Jul 2025, 07:06
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
User avatar
JCLEONES
Joined: 01 Nov 2007
Last visit: 13 Jan 2017
Posts: 93
Own Kudos:
2,428
 [98]
Posts: 93
Kudos: 2,428
 [98]
10
Kudos
Add Kudos
88
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
rgajare14
Joined: 02 Aug 2007
Last visit: 19 Nov 2013
Posts: 296
Own Kudos:
213
 [29]
Location: Greater New York City area
Concentration: Consulting, Marketing
Schools:Tuck, Ross (R1), Duke, Tepper, ISB (R2), Kenan Flagler (R2)
 Q49  V38
Posts: 296
Kudos: 213
 [29]
17
Kudos
Add Kudos
12
Bookmarks
Bookmark this Post
General Discussion
User avatar
incognito1
Joined: 26 Jan 2008
Last visit: 11 Dec 2016
Posts: 160
Own Kudos:
266
 [2]
Given Kudos: 16
Posts: 160
Kudos: 266
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
testgmat
Joined: 15 Jan 2008
Last visit: 07 Mar 2008
Posts: 5
Own Kudos:
Posts: 5
Kudos: 2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Incognito,

Could you please detail your work?

Thanks

incognito1
JCLEONES
For a three-digit number xyz, where x, y, and z are the digits of the number,
f(xyz)=5^x 2^y 3^z . If f(abc)=3*f(def), what is the value of abc-def ?
(A) 1
(B) 2
(C) 3
(D) 9
(E) 27

Since f(abc) = 3*f(def), I would assume that f = c - 1 from the function above.

The answer should be (A).
User avatar
maratikus
Joined: 01 Jan 2008
Last visit: 22 Jul 2010
Posts: 257
Own Kudos:
Given Kudos: 1
Posts: 257
Kudos: 340
Kudos
Add Kudos
Bookmarks
Bookmark this Post
JCLEONES
For a three-digit number xyz, where x, y, and z are the digits of the number,
f(xyz)=5^x 2^y 3^z . If f(abc)=3*f(def), what is the value of abc-def ?
(A) 1
(B) 2
(C) 3
(D) 9
(E) 27

f(abc)/f(def)=5^(a-d) 2^(b-e) 3^(c-f) = 3^1 -> a = d, b = e, c = f+1 -> A is the answer
User avatar
incognito1
Joined: 26 Jan 2008
Last visit: 11 Dec 2016
Posts: 160
Own Kudos:
266
 [3]
Given Kudos: 16
Posts: 160
Kudos: 266
 [3]
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
testgmat
Incognito,

Could you please detail your work?

Thanks

incognito1
JCLEONES
For a three-digit number xyz, where x, y, and z are the digits of the number,
f(xyz)=5^x 2^y 3^z . If f(abc)=3*f(def), what is the value of abc-def ?
(A) 1
(B) 2
(C) 3
(D) 9
(E) 27

Since f(abc) = 3*f(def), I would assume that f = c - 1 from the function above.

The answer should be (A).

Sure. The function consists purely of powers of 5, 2 and 3. None of which are multiples of each other.

Since f(abc) = 3*f(def), and since the function is entirely made up of multiples of 5, 2 and 3, it would imply that the only difference is a power of 3. This would mean that a = d (since there is no multiple of 5 from the functions output), b = e (no multiple of 2 in the functions output) and c = f + 1 (since there is a multiple of 3 in the two functions output). Since abc and def are 3-digit numbers, and c = f + 1, the difference between abc and def would be 1. Hope that helps!
User avatar
eschn3am
Joined: 12 Jul 2007
Last visit: 03 Apr 2017
Posts: 396
Own Kudos:
 Q50  V45
Posts: 396
Kudos: 573
Kudos
Add Kudos
Bookmarks
Bookmark this Post
JCLEONES
For a three-digit number xyz, where x, y, and z are the digits of the number,
f(xyz)=5^x 2^y 3^z . If f(abc)=3*f(def), what is the value of abc-def ?
(A) 1
(B) 2
(C) 3
(D) 9
(E) 27

f(abc)=3*f(def) so the only difference is one more multiple of 3 in f(abc). The only way for this to happens is if z is one more. z is the units digit so it's total value is 1 more.

Answer A
User avatar
kyatin
Joined: 29 Jan 2007
Last visit: 16 Oct 2016
Posts: 250
Own Kudos:
158
 [2]
Location: Earth
 Q50  V40
Posts: 250
Kudos: 158
 [2]
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
I went totally tangent on this one.

thought abc is a*b*c and not a number abc

and wasnt sure why every one was thinking its too obvious.

lesson learnt! :shock:
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 11 Jul 2025
Posts: 102,636
Own Kudos:
740,669
 [4]
Given Kudos: 98,172
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,636
Kudos: 740,669
 [4]
1
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
JCLEONES
For a three-digit number xyz, where x, y, and z are the digits of the number, f(xyz)=5^x 2^y 3^z . If f(abc)=3*f(def), what is the value of abc-def ?

(A) 1
(B) 2
(C) 3
(D) 9
(E) 27

Similar questions to practice:
the-function-f-is-defined-for-each-positive-three-digit-100847.html
k-and-l-are-each-four-digit-positive-integers-with-thousands-91004.html
the-three-digit-positive-integer-x-has-the-hundreds-163241.html
for-any-four-digit-number-abcd-abcd-3-a-5-b-7-c-11-d-126522.html
k-and-l-are-each-four-digit-positive-integers-with-thousands-126646.html

Hope it helps.
User avatar
mvictor
User avatar
Board of Directors
Joined: 17 Jul 2014
Last visit: 14 Jul 2021
Posts: 2,126
Own Kudos:
1,249
 [1]
Given Kudos: 236
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE:General Management (Transportation)
Products:
GMAT 1: 650 Q49 V30
Posts: 2,126
Kudos: 1,249
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
oh yeah..tricky one
f(def) = 5^d*2*e*3^f
a is the same multiplied by 3
we have same prime factorization
abc = def+1
abc-def = 1
User avatar
Nunuboy1994
Joined: 12 Nov 2016
Last visit: 24 Apr 2019
Posts: 559
Own Kudos:
Given Kudos: 167
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
Posts: 559
Kudos: 122
Kudos
Add Kudos
Bookmarks
Bookmark this Post
https://gmatclub.com/forum/the-function ... 00847.html

The answer is "A" - VeritasPrepKarishma gives an incredibly clear explanation in a similar problem linked above.
avatar
nightvision
Joined: 04 Mar 2018
Last visit: 11 Sep 2020
Posts: 20
Own Kudos:
9
 [1]
Given Kudos: 34
GPA: 3.5
Products:
Posts: 20
Kudos: 9
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
testgmat
Incognito,

Could you please detail your work?

Thanks

incognito1
JCLEONES
For a three-digit number xyz, where x, y, and z are the digits of the number,
f(xyz)=5^x 2^y 3^z . If f(abc)=3*f(def), what is the value of abc-def ?
(A) 1
(B) 2
(C) 3
(D) 9
(E) 27

Since f(abc) = 3*f(def), I would assume that f = c - 1 from the function above.

The answer should be (A).



f(abc) = 5^a * 2^b *3^c
f(def) = 5^d * 2^e * 3^f

since, f(abc) = 3*f(def)
5^a * 2^b *3^c = 5^d * 2^e * 3^(f+1)

so, a=d
b=e
c=f+1

so, for example, if abcis 123, then def is 124,

hence difference is 1.
User avatar
CEdward
Joined: 11 Aug 2020
Last visit: 14 Apr 2022
Posts: 1,212
Own Kudos:
Given Kudos: 332
Posts: 1,212
Kudos: 247
Kudos
Add Kudos
Bookmarks
Bookmark this Post
rgajare14
JCLEONES
For a three-digit number xyz, where x, y, and z are the digits of the number,
f(xyz)=5^x 2^y 3^z . If f(abc)=3*f(def), what is the value of abc-def ?
(A) 1
(B) 2
(C) 3
(D) 9
(E) 27
This is how I solved.
f(abc) = 3 * f(def)
So, 5^a*2^b*3^c = 3*[5^d*2^e*3^f]
So, (5^a*2^b*3^c)/(5^d*2^e*3^f) = 3
So, 5^(a-d)*2^(b-e)*3^(c-f) = 3^1
So,5^(a-d)*2^(b-e)*3^(c-f) = 3^1*5^0*2^0
S0, a-d =0, b-e =0 and c -f =1.
So, a =d, b = e and c = f +1
So abc - def is equal to abc - abf
And since c = f + 1, differrence is 1
Answer is A

My issue was even getting to this step:
So, 5^a*2^b*3^c = 3*[5^d*2^e*3^f]

How are we to conclude that abc = def = xyz?

I never even got off the ground on this one.
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,078
Own Kudos:
18,736
 [2]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,078
Kudos: 18,736
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
f(xyz) = \(5^x 2^y 3^z\)

=> f(abc)=\(5^a 2^b 3^c\)

=> f(def)=\(5^d 2^e 3^f\)

=> f(abc)=\(5^a 2^b 3^c\) = 3 * f(def)=\(5^d 2^e 3^f\)

=> \(\frac{[5^a 2^b 3^c]}{ [5^d 2^e 3^f]}\) = 3

=> \(5^{a - d} 2^{b - e} 3^{e - f}\) = 3

=> \(5^{a - d} 2^{b - e} 3^{e - f} = 5^0 2^0 3^1\)

Comparing the bases:

=> a - d = 0
=> b - e = 0
=> c - f = 1

Adding all:

=> (a + b + c) - (d + e + f) = 0 + 0 + 1

Answer A
User avatar
Kinshook
User avatar
Major Poster
Joined: 03 Jun 2019
Last visit: 12 Jul 2025
Posts: 5,698
Own Kudos:
5,212
 [1]
Given Kudos: 161
Location: India
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
GMAT 1: 690 Q50 V34
Posts: 5,698
Kudos: 5,212
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Given: For a three-digit number xyz, where x, y, and z are the digits of the number, f(xyz)=5^x 2^y 3^z .
Asked: If f(abc)=3*f(def), what is the value of abc-def ?

f(abc)=3*f(def)
5^a 2^b 3^c = 3* 5^d 2^e 3^f = 5^d 2^e 3^(f+1)
b = e;
a = d;
c = f+1;
f = c -1
abc-def = abc - ab(c-1) = 1

IMO A
User avatar
RastogiSarthak99
Joined: 20 Mar 2019
Last visit: 10 Aug 2024
Posts: 142
Own Kudos:
21
 [1]
Given Kudos: 282
Location: India
Posts: 142
Kudos: 21
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I think there is an easier way to look at this:

5^a 2^b 3^c = 3 * 5^d 2^e 3^f

--> 5^a 2^b 3^c = 5^d 2^e 3^f+1

a = d
b = e

c = f+ 1
c-f = 1


abc
(-)def
---------
001

A
User avatar
gmatmonster805
Joined: 14 Aug 2023
Last visit: 21 Jun 2024
Posts: 2
Own Kudos:
1
 [1]
Given Kudos: 22
Posts: 2
Kudos: 1
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Answer

\[ f(abc) = 3 \cdot f(def) \]

So, 

\[ 5^a \cdot 2^b \cdot 3^c = 3 \cdot (5^d \cdot 2^e \cdot 3^f) \]

Dividing both sides by \( 5^d \cdot 2^e \cdot 3^f \), we get:

\[ \frac{5^a \cdot 2^b \cdot 3^c}{5^d \cdot 2^e \cdot 3^f} = 3 \]

Which simplifies to:

\[ 5^{a-d} \cdot 2^{b-e} \cdot 3^{c-f} = 3^1 \]

Equating the exponents on both sides, we have:

\[ 5^{a-d} \cdot 2^{b-e} \cdot 3^{c-f} = 3^1 \cdot 5^0 \cdot 2^0 \]

Therefore,

\[ a - d = 0 \]
\[ b - e = 0 \]
\[ c - f = 1 \]

Thus,

\[ a = d \]
\[ b = e \]
\[ c = f + 1 \]

So, \( abc - def \) is equal to \( abc - abf \). 

Since \( c = f + 1 \), the difference is 1.

Answer: \( \boxed{A} \)­
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,376
Own Kudos:
Posts: 37,376
Kudos: 1,010
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderators:
Math Expert
102636 posts
PS Forum Moderator
688 posts