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GmatPrep?? (function)

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Re: GmatPrep?? (function)

by parallel_chase » Wed Sep 03, 2008 4:20 pm
dferm wrote:Help Please!!!
f(n) = number of positive integers less than n, no factor with n except 1

f(6) = 1,5 i.e. 1 number
f(8) = 1,3,5,7 i.e. 3 numbers

p is a prime number

f(p)

f(7) = 1,2,3,4,5,6 i.e. 6 numbers 7-1 = 6 (p-1)
f(13) = 1,2,3,4,5,6,7,8,9,10,11,12. i.e 12 numbers 13-1 = 12 (p-1)

Hence answer is p-1.

Hope this helps.
Last edited by parallel_chase on Wed Sep 03, 2008 7:25 pm, edited 1 time in total.
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by dferm » Wed Sep 03, 2008 7:11 pm
I don't quite the logic
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by parallel_chase » Wed Sep 03, 2008 7:17 pm
dferm wrote:I don't quite the logic
f(p)
p=7
f(7) = 1,2,3,4,5,6 , total numbers = 6
p-1
7-1=6

p=13
f(13) = 1,2,3,4,5,6,7,8,9,10,11,12, total numbers = 12
p-1
13-1=12

Let me know which part you are not able to understand.
Last edited by parallel_chase on Wed Sep 03, 2008 7:26 pm, edited 1 time in total.
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by dferm » Wed Sep 03, 2008 7:23 pm
f(n) = number of positive integers less than n, no factor with n except 1


This is the part i don't understand............
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by Fab » Wed Sep 03, 2008 7:26 pm
Why are you not considering 1 ??

F(7): 6, 5, 4, 3, 2 , 1... ???

THANKS
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by parallel_chase » Wed Sep 03, 2008 7:27 pm
Fab wrote:Why are you not considering 1 ??

F(7): 6, 5, 4, 3, 2 , 1... ???

THANKS
You are right 1 should be considered, answer should be p-1.
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by Fab » Wed Sep 03, 2008 7:30 pm
Now is clear.

THANKS.
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by Ian Stewart » Wed Sep 03, 2008 7:31 pm
The key to the problem is decoding the language here:

f(n) is the number of positive integers each of which is less than n and has no positive factor in common with n other than 1.

and understanding what a prime number is. Start with an example- what is f(2)? f(2) is the number of positive integers less than 2 (there's only one of those- 1) which have no divisor in common with 2 besides 1. Does 1 have no divisor in common with 2 besides 1? Yes, of course. So f(2) = 1. You could now just plug p=2 into each answer choice to find that p-1 must be correct.

In general, if p is prime, then p has no positive divisors besides 1 and p. So p cannot share a divisor besides 1 with any number less than p. That is, all p-1 positive integers (1, 2, 3, ..., p-2, p-1) less than p cannot share a divisor larger than 1 with p, and will all be counted by f(p). So the answer is p-1.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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