Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 13 Oct 2015, 16:06

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A function V(a, b) is defined for positive integers a, b and

Author Message
TAGS:
Intern
Joined: 03 Oct 2012
Posts: 10
GMAT 1: 620 Q39 V38
GMAT 2: 700 Q49 V38
Followers: 0

Kudos [?]: 3 [0], given: 23

A function V(a, b) is defined for positive integers a, b and [#permalink]  10 Dec 2012, 12:25
3
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

60% (03:33) correct 40% (02:36) wrong based on 100 sessions
A function V(a, b) is defined for positive integers a, b and satisfies V(a, a) = a, V(a, b) = V(b, a), V(a, a+b) = (1 + a/b) V(a, b). The value represented by V(66, 14) is ?

(A) 364
(B) 231
(C) 455
(D) 472
(E) None of the foregoing

Bunuel,
I know it shouldn't be here but could you explain the solution of this one?
[Reveal] Spoiler: OA

Last edited by Bunuel on 11 Dec 2012, 01:14, edited 1 time in total.
Edited the question and added the OA.
Math Expert
Joined: 02 Sep 2009
Posts: 29856
Followers: 4925

Kudos [?]: 53970 [3] , given: 8260

Re: A function V(a, b) is defined for positive integers a, b and [#permalink]  11 Dec 2012, 01:57
3
KUDOS
Expert's post
felixjkz wrote:
A function V(a, b) is defined for positive integers a, b and satisfies V(a, a) = a, V(a, b) = V(b, a), V(a, a+b) = (1 + a/b) V(a, b). The value represented by V(66, 14) is ?

(A) 364
(B) 231
(C) 455
(D) 472
(E) None of the foregoing

Bunuel,
I know it shouldn't be here but could you explain the solution of this one?

Given that:
$$V(a, a) = a$$;
$$V(a, b) = V(b, a)$$;
$$V(a, a+b) = (1 + \frac{a}{b}) V(a, b)$$.

Question asks to find the value of $$V(66, 14)$$.

Notice that only the first function gives answer as a simple value rather than another function, thus we should manipulate with $$V(66, 14)$$ so that to get $$V(a, a) = a$$ in the end.

$$V(66,14 ) = V(14,66) = V(14, 14+52)$$;

$$V(14, 14+52)=(1+\frac{14}{52})V(14,52)=\frac{33}{26}*V(14,14+38)$$;

$$\frac{33}{26}*V(14,14+38)=\frac{33}{26}*(1+\frac{14}{38})V(14,38)=\frac{33}{19}*V(14, 14+24)$$;

$$\frac{33}{19}*V(14,14+24)=\frac{33}{19}*(1+\frac{14}{24})V(14,24)=\frac{33}{12}*V(14,14+10)$$;

$$\frac{33}{12}V(14,14+10)=\frac{33}{12}*(1+\frac{14}{10})V(14,10)=\frac{33}{5}*V(10,14)=\frac{33}{5}*V(10, 10+4)$$;

$$\frac{33}{5}V(10,10+4)=\frac{33}{5}*(1+\frac{10}{4})V(10,4)=\frac{33*7}{5*2}*V(4,10)=\frac{33*7}{5*2}*V(4, 4+6)$$;

$$\frac{33*7}{5*2}*V(4, 4+6)=\frac{33*7}{5*2}*(1+\frac{4}{6})V(4,6)=\frac{33*7}{2*3}*V(4,4+2)$$;

$$\frac{33*7}{2*3}*V(4,4+2)=\frac{33*7}{2*3}*(1+\frac{4}{2})V(4,2)=\frac{33*7}{2}*V(2,4)=\frac{33*7}{2}*V(2, 2+2)$$;

$$\frac{33*7}{2}*V(2, 2+2)=\frac{33*7}{2}*(1+\frac{2}{2})V(2,2)=\frac{33*7}{2}*2*2=462$$.

_________________
Manager
Joined: 28 Feb 2012
Posts: 115
GPA: 3.9
WE: Marketing (Other)
Followers: 0

Kudos [?]: 29 [0], given: 17

Re: A function V(a, b) is defined for positive integers a, b and [#permalink]  13 Dec 2012, 02:12
Bunuel wrote:
felixjkz wrote:
A function V(a, b) is defined for positive integers a, b and satisfies V(a, a) = a, V(a, b) = V(b, a), V(a, a+b) = (1 + a/b) V(a, b). The value represented by V(66, 14) is ?

(A) 364
(B) 231
(C) 455
(D) 472
(E) None of the foregoing

Bunuel,
I know it shouldn't be here but could you explain the solution of this one?

Given that:
$$V(a, a) = a$$;
$$V(a, b) = V(b, a)$$;
$$V(a, a+b) = (1 + \frac{a}{b}) V(a, b)$$.

Question asks to find the value of $$V(66, 14)$$.

Notice that only the first function gives answer as a simple value rather than another function, thus we should manipulate with $$V(66, 14)$$ so that to get $$V(a, a) = a$$ in the end.

$$V(66,14 ) = V(14,66) = V(14, 14+52)$$;

$$V(14, 14+52)=(1+\frac{14}{52})V(14,52)=\frac{33}{26}*V(14,14+38)$$;

$$\frac{33}{26}*V(14,14+38)=\frac{33}{26}*(1+\frac{14}{38})V(14,38)=\frac{33}{19}*V(14, 14+24)$$;

$$\frac{33}{19}*V(14,14+24)=\frac{33}{19}*(1+\frac{14}{24})V(14,24)=\frac{33}{12}*V(14,14+10)$$;

$$\frac{33}{12}V(14,14+10)=\frac{33}{12}*(1+\frac{14}{10})V(14,10)=\frac{33}{5}*V(10,14)=\frac{33}{5}*V(10, 10+4)$$;

$$\frac{33}{5}V(10,10+4)=\frac{33}{5}*(1+\frac{10}{4})V(10,4)=\frac{33*7}{5*2}*V(4,10)=\frac{33*7}{5*2}*V(4, 4+6)$$;

$$\frac{33*7}{5*2}*V(4, 4+6)=\frac{33*7}{5*2}*(1+\frac{4}{6})V(4,6)=\frac{33*7}{2*3}*V(4,4+2)$$;

$$\frac{33*7}{2*3}*V(4,4+2)=\frac{33*7}{2*3}*(1+\frac{4}{2})V(4,2)=\frac{33*7}{2}*V(2,4)=\frac{33*7}{2}*V(2, 2+2)$$;

$$\frac{33*7}{2}*V(2, 2+2)=\frac{33*7}{2}*(1+\frac{2}{2})V(2,2)=\frac{33*7}{2}*2*2=462$$.

Dear Bunuel,

Your explanation is brilliant. But do you think this is a kind of question that i will face in GMAT because i think the sollution is quite time consuming or there is quiker way?
_________________

If you found my post useful and/or interesting - you are welcome to give kudos!

Math Expert
Joined: 02 Sep 2009
Posts: 29856
Followers: 4925

Kudos [?]: 53970 [0], given: 8260

Re: A function V(a, b) is defined for positive integers a, b and [#permalink]  13 Dec 2012, 02:15
Expert's post
ziko wrote:
Bunuel wrote:
felixjkz wrote:
A function V(a, b) is defined for positive integers a, b and satisfies V(a, a) = a, V(a, b) = V(b, a), V(a, a+b) = (1 + a/b) V(a, b). The value represented by V(66, 14) is ?

(A) 364
(B) 231
(C) 455
(D) 472
(E) None of the foregoing

Bunuel,
I know it shouldn't be here but could you explain the solution of this one?

Given that:
$$V(a, a) = a$$;
$$V(a, b) = V(b, a)$$;
$$V(a, a+b) = (1 + \frac{a}{b}) V(a, b)$$.

Question asks to find the value of $$V(66, 14)$$.

Notice that only the first function gives answer as a simple value rather than another function, thus we should manipulate with $$V(66, 14)$$ so that to get $$V(a, a) = a$$ in the end.

$$V(66,14 ) = V(14,66) = V(14, 14+52)$$;

$$V(14, 14+52)=(1+\frac{14}{52})V(14,52)=\frac{33}{26}*V(14,14+38)$$;

$$\frac{33}{26}*V(14,14+38)=\frac{33}{26}*(1+\frac{14}{38})V(14,38)=\frac{33}{19}*V(14, 14+24)$$;

$$\frac{33}{19}*V(14,14+24)=\frac{33}{19}*(1+\frac{14}{24})V(14,24)=\frac{33}{12}*V(14,14+10)$$;

$$\frac{33}{12}V(14,14+10)=\frac{33}{12}*(1+\frac{14}{10})V(14,10)=\frac{33}{5}*V(10,14)=\frac{33}{5}*V(10, 10+4)$$;

$$\frac{33}{5}V(10,10+4)=\frac{33}{5}*(1+\frac{10}{4})V(10,4)=\frac{33*7}{5*2}*V(4,10)=\frac{33*7}{5*2}*V(4, 4+6)$$;

$$\frac{33*7}{5*2}*V(4, 4+6)=\frac{33*7}{5*2}*(1+\frac{4}{6})V(4,6)=\frac{33*7}{2*3}*V(4,4+2)$$;

$$\frac{33*7}{2*3}*V(4,4+2)=\frac{33*7}{2*3}*(1+\frac{4}{2})V(4,2)=\frac{33*7}{2}*V(2,4)=\frac{33*7}{2}*V(2, 2+2)$$;

$$\frac{33*7}{2}*V(2, 2+2)=\frac{33*7}{2}*(1+\frac{2}{2})V(2,2)=\frac{33*7}{2}*2*2=462$$.

Dear Bunuel,

Your explanation is brilliant. But do you think this is a kind of question that i will face in GMAT because i think the sollution is quite time consuming or there is quiker way?

I doubt that this is a GMAT question. So, I wouldn't worry about it at all.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 6784
Followers: 369

Kudos [?]: 83 [0], given: 0

Re: A function V(a, b) is defined for positive integers a, b and [#permalink]  31 Jan 2014, 13:43
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.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 6784
Followers: 369

Kudos [?]: 83 [0], given: 0

Re: A function V(a, b) is defined for positive integers a, b and [#permalink]  20 Sep 2015, 08:40
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.
_________________
Intern
Joined: 19 Jul 2013
Posts: 25
Followers: 0

Kudos [?]: 11 [0], given: 14

Re: A function V(a, b) is defined for positive integers a, b and [#permalink]  21 Sep 2015, 19:15
felixjkz wrote:
A function V(a, b) is defined for positive integers a, b and satisfies V(a, a) = a, V(a, b) = V(b, a), V(a, a+b) = (1 + a/b) V(a, b). The value represented by V(66, 14) is ?

(A) 364
(B) 231
(C) 455
(D) 472
(E) None of the foregoing

Bunuel,
I know it shouldn't be here but could you explain the solution of this one?

Once you have figured out the way to solve this (see Bunnel's explanation above), it becomes clear that the expansion of the function continues till you arrive at the greatest common factor between a and b. As the multiplication to arrive at the solution starts with 66, the solution itself should be divisible by 66. Without any further calculations it becomes clear that none of the options here satisfy that condition.
Re: A function V(a, b) is defined for positive integers a, b and   [#permalink] 21 Sep 2015, 19:15
Similar topics Replies Last post
Similar
Topics:
Two functions A(x) and B(x) are defined such that 1 11 Nov 2012, 10:14
16 The function f is defined for all positive integers n by the 12 29 Jan 2012, 15:53
5 A function V(a, b) is defined for positive integers a, b and satisfies 4 20 May 2011, 03:13
8 The function f is defined for all the positive integers n by 4 28 Oct 2010, 07:27
5 The function F is defined for all positive integers n by the 5 24 Jan 2010, 18:38
Display posts from previous: Sort by