IMO p-1.
n is prime . number of integers less than n is (n-1)
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Source: Beat The GMAT — Problem Solving |
Let us take a prime number for p.
If p = 5, then positive integers less than 5 are 1, 2, 3, and 4.
1, 5; 2, 5; 3, 5; and 4, 5 have only 1 as a common factor. Here integers less than 5 are 4 in number.
If p = 7, then positive integers less than 7 are 1, 2, 3, 4, 5, and 6.
Again we see that 1, 7; 2, 7; 3, 7; 4, 7; 5, 7; and 6, 7 have only 1 as a common factor. Here integers less than 7 are 6 in number.
SO, generalizing we have f(p) = p - 1
[spoiler]The correct answer is (A).[/spoiler]
If p = 5, then positive integers less than 5 are 1, 2, 3, and 4.
1, 5; 2, 5; 3, 5; and 4, 5 have only 1 as a common factor. Here integers less than 5 are 4 in number.
If p = 7, then positive integers less than 7 are 1, 2, 3, 4, 5, and 6.
Again we see that 1, 7; 2, 7; 3, 7; 4, 7; 5, 7; and 6, 7 have only 1 as a common factor. Here integers less than 7 are 6 in number.
SO, generalizing we have f(p) = p - 1
[spoiler]The correct answer is (A).[/spoiler]
Rahul Lakhani
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Gurome, Inc.
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Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
