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.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.
Re: For a three-digit number xyz, where x, y, and z are the
[#permalink]
Show Tags
29 Jan 2008, 18:08
5
4
JCLEONES wrote:
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
Re: For a three-digit number xyz, where x, y, and z are the
[#permalink]
Show Tags
29 Jan 2008, 12:49
JCLEONES wrote:
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.
Re: For a three-digit number xyz, where x, y, and z are the
[#permalink]
Show Tags
29 Jan 2008, 12:53
Incognito,
Could you please detail your work?
Thanks
incognito1 wrote:
JCLEONES wrote:
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.
Re: For a three-digit number xyz, where x, y, and z are the
[#permalink]
Show Tags
29 Jan 2008, 12:57
JCLEONES wrote:
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
Re: For a three-digit number xyz, where x, y, and z are the
[#permalink]
Show Tags
29 Jan 2008, 13:03
testgmat wrote:
Incognito,
Could you please detail your work?
Thanks
incognito1 wrote:
JCLEONES wrote:
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!
_________________
Re: For a three-digit number xyz, where x, y, and z are the
[#permalink]
Show Tags
29 Jan 2008, 20:32
JCLEONES wrote:
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.
Re: For a three-digit number xyz, where x, y, and z are the
[#permalink]
Show Tags
19 May 2018, 12:38
testgmat wrote:
Incognito,
Could you please detail your work?
Thanks
incognito1 wrote:
JCLEONES wrote:
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.
close
63% (02:19) correct 
