M23 #35

sset009 · **Posted:** Fri Aug 29, 2008 9:59 am

If x is a positive integer, f(x) is defined as the number of positive integers which are less than x and do not have common factor with x other than 1. If x is prime then f(x) = ?

(A) x - 2
(B) x - 1
(C) \frac{x + 1}{2}
(D) \frac{x - 1}{2}
(E) 2

[Reveal] Spoiler: OA

B

Source: GMAT Club Tests - hardest GMAT questions

sset009 · **Posted:** Fri Aug 29, 2008 9:59 am

i disagree with teh OA. just want to get an opinion

stallone · **Posted:** Fri Aug 29, 2008 11:13 am

x-2 for me !

x2suresh · **Posted:** Fri Aug 29, 2008 11:19 am

sset009 wrote:

i disagree with teh OA. just want to get an opinion

I will go with B.
X is prime number..

value <x are
1.2... x-1

there are x-1 integers that are less than x

x2suresh · **Posted:** Fri Aug 29, 2008 11:20 am

stallone wrote:

x-2 for me !

Show me your work.. how did you get x-2

sset009 · **Posted:** Fri Aug 29, 2008 3:48 pm

i was thinking of x = 3

the number of numbers below three that do not have a any factor apart from 1 is 2
since 1 has a factor of 1 itself, it doenst count.
therefore, f(x3) = 1

similarily, f(2) = 0

bipolarbear · **Posted:** Tue Aug 04, 2009 7:47 pm

The answer is wrong. OA should be (A).

f(2) = 0 = 0 numbers
f(3) = 2 = 1 number
f(5) = 2,3,4 = 3 numbers
f(7) = 2,3,4,5,6 = 5 numbers
f(x) = x-2 numbers

viperm5 · **Posted:** Wed Aug 05, 2009 5:48 pm

bipolarbear wrote:

The answer is wrong. OA should be (A).

f(2) = 0 = 0 numbers
f(3) = 2 = 1 number
f(5) = 2,3,4 = 3 numbers
f(7) = 2,3,4,5,6 = 5 numbers
f(x) = x-2 numbers

bipolar u're forgetting 1.
u need to count 1 as well.
hence f(2) = 1
f(3) = 1,2 -> 2
f(4) = 1,2,3 -> 3

i got this exact question on the gmatprep and answer is x-1.

bipolarbear · **Posted:** Wed Aug 05, 2009 5:54 pm

viperm5 wrote:

bipolarbear wrote:

The answer is wrong. OA should be (A).

f(2) = 0 = 0 numbers
f(3) = 2 = 1 number
f(5) = 2,3,4 = 3 numbers
f(7) = 2,3,4,5,6 = 5 numbers
f(x) = x-2 numbers

bipolar u're forgetting 1.
u need to count 1 as well.
hence f(2) = 1
f(3) = 1,2 -> 2
f(4) = 1,2,3 -> 3

i got this exact question on the gmatprep and answer is x-1.

but the question states f(x) = number of factors OTHER than 1, so you can't count one... but i guess if gmatprep says so

am i just interpreting the question wrong?

viperm5 · **Posted:** Wed Aug 05, 2009 6:04 pm

bipolarbear wrote:

viperm5 wrote:

bipolarbear wrote:

The answer is wrong. OA should be (A).

f(2) = 0 = 0 numbers
f(3) = 2 = 1 number
f(5) = 2,3,4 = 3 numbers
f(7) = 2,3,4,5,6 = 5 numbers
f(x) = x-2 numbers

bipolar u're forgetting 1.
u need to count 1 as well.
hence f(2) = 1
f(3) = 1,2 -> 2
f(4) = 1,2,3 -> 3

i got this exact question on the gmatprep and answer is x-1.

but the question states f(x) = number of factors OTHER than 1, so you can't count one... but i guess if gmatprep says so

am i just interpreting the question wrong?

i fell for the wording too

f(x) defined as all numbers positive less than x AND do not have same factor with x other than 1....meaning that you DO include x.....

do NOT have ...OTHER THAN 1 - means you include 1.

bipolarbear · **Posted:** Wed Aug 05, 2009 6:39 pm

ah i see it now... this is a tricky gmat problem and even if its part of gmatprep, i think its more of a verbal question than math 8-)

dmetla · **Posted:** Wed Mar 10, 2010 12:48 pm

Ans should be x-1

prabir2001 · **Posted:** Wed Mar 10, 2010 5:58 pm

Answer should be B.... Need to include '1'.

varun2410 · **Posted:** Wed Mar 10, 2010 8:19 pm

Ans:A

f(2) = 0 = 0 numbers
f(3) = 2 = 1 number
f(5) = 2,3,4 = 3 numbers
f(7) = 2,3,4,5,6 = 5 numbers
f(x) = x-2 numbers
if Ans is b then
f(2) = 1 = 1 numbers
f(3) = 2 = 2 number
f(5) = 4 = 4 numbers
f(7) = 6 = 6 numbers
f(x) = x-1 numbers all numbers other then 1 is having comman factor 2 with x and it is given that x is do not have common factor with f(x)

ExecMBA2010 · **Posted:** Fri Mar 12, 2010 8:25 pm

Plug in 23 for x, f(x) = 22
Plug in another prime 37, f(x) = 36

Ans B

xyztroy · **Posted:** Fri Mar 12, 2010 9:54 pm

I also fell for the wording and chose x-2 (A), but now I also agree that the ans should be x-1 or B.

sidhu4u · **Posted:** Sat Mar 13, 2010 4:05 am

yup, (x-2) was confusing until I read the question again and figured out that I could use 1.
(x-1) it is.

M23 #35

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