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

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10 Dec 2012, 12:25

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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? Thanks in advance!

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? Thanks in advance!

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.

Re: A function V(a, b) is defined for positive integers a, b and [#permalink]

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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? Thanks in advance!

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.

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!

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? Thanks in advance!

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.

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.
_________________

Re: A function V(a, b) is defined for positive integers a, b and [#permalink]

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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).

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Re: A function V(a, b) is defined for positive integers a, b and [#permalink]

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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.
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Re: A function V(a, b) is defined for positive integers a, b and [#permalink]

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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? Thanks in advance!

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]

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17 Jun 2016, 03:21

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? Thanks in advance!

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.

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? Thanks in advance!

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.

IMP STEP -In the NEXT step b = a+c.. so V(a,c) will become \(\frac{(a+c)}{c} V(a,c)\)..... and \(\frac{(a+b)}{b}* V(a,b)=\frac{(a+b)}{b}*\frac{(a+c)}{c} V(a,c) = \frac{(a+b)}{c} V(a,c)\).. and will continue till the right portion , b or c, becomes lesser than a, and at that POINT the right portion will become the REMAINDER when b is divided by a...

so \(V(14, 14+52)=(1+\frac{14}{52})V(14,52)=\frac{66}{38}*V(14,14+38) = \frac{66}{38}*\frac{38}{38-14}*V(14,14+24) = \frac{66}{10}V(14,10)\).... 10 since 66 div by 14 gives 10 as remainder.... Reverse a and b and continue.... \(\frac{66}{10}V(14,10)=\frac{66}{10}V(10,14) = \frac{66}{10}*\frac{14}{4}V(10,4)\) reverse a and b and same steps \(\frac{66}{10}*\frac{14}{4}V(10,14)=\frac{66}{10}*\frac{14}{4}V(4,10)=\frac{66}{10}*\frac{14}{4}*\frac{10}{2}V(4,2)=\frac{66}{10}*\frac{14}{4}*\frac{10}{2}V(2,4)=\frac{66}{10}*\frac{14}{4}*\frac{10}{2}*\frac{4}{2}V(2,2)= \frac{66}{10}*\frac{14}{4}*\frac{10}{2}*\frac{4}{2}*2 = 66*7 = 462\)
_________________

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