GRE Prep 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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
The function f is defined for each positive three-digit integer n by
[#permalink]
05 Nov 2021, 07:52
05 Nov 2021, 07:52
Expert Reply
00:00
Question Stats:
57% (01:54) correct
42% (02:19) wrong based on 7 sessions
Hide Show timer Statistics
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 \(f(m)=9*f(v)\) , then \(m-v=\) ?
(A) 8
(B) 9
(C) 18
(D) 20
(E) 80
(A) 8
(B) 9
(C) 18
(D) 20
(E) 80
Re: The function f is defined for each positive three-digit integer n by
[#permalink]
08 Nov 2021, 14:01
08 Nov 2021, 14:01
Expert Reply
Let the 3-digit positive integer \({m}\) be \({abc}\) and positive integer \(v\) be \(rst\). Question: \((100a+10b+c)-(100r+10s+t)=?\).
Then \(f(m)=2^a*3^b*5^c\) and \(f(v)=2^r*3^s*5^t\).
Given: \(f(m)=9*f(v)\) --> \(2^a*3^b*5^c=9*2^r*3^s*5^t\) --> \(2^{a-r}*3^{b-s}*5^{c-t}=3^2\) (or \(2^a*3^b*5^c=2^r*3^{s+2}*5^t\)).
So, \(a-r=0\), \(b-s=2\) and \(c-t=0\) (or \(a=r\), \(b=s+2\) and \(c=t\)) --> \(m-v=(100a+10b+c)-(100r+10s+t)=10b-10(b-2)=20\). For example if \(m\) and \(v\) are 143 and 123 respectively (hundreds and units digit are equal and tens digit of \(m\) is 2 more than tens digit of \(v\)) then \(143-123=20\).
Answer: D.
Then \(f(m)=2^a*3^b*5^c\) and \(f(v)=2^r*3^s*5^t\).
Given: \(f(m)=9*f(v)\) --> \(2^a*3^b*5^c=9*2^r*3^s*5^t\) --> \(2^{a-r}*3^{b-s}*5^{c-t}=3^2\) (or \(2^a*3^b*5^c=2^r*3^{s+2}*5^t\)).
So, \(a-r=0\), \(b-s=2\) and \(c-t=0\) (or \(a=r\), \(b=s+2\) and \(c=t\)) --> \(m-v=(100a+10b+c)-(100r+10s+t)=10b-10(b-2)=20\). For example if \(m\) and \(v\) are 143 and 123 respectively (hundreds and units digit are equal and tens digit of \(m\) is 2 more than tens digit of \(v\)) then \(143-123=20\).
Answer: D.
gmatclubot
Re: The function f is defined for each positive three-digit integer n by [#permalink]
08 Nov 2021, 14:01
Moderators:
