If x is a positive integer

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NandishSS: Master | Next Rank: 500 Posts; Posts: 366; Joined: Fri Jun 05, 2015 3:35 am; Thanked: 3 times; Followed by:2 members

If x is a positive integer

by NandishSS » Fri Jan 19, 2018 4:12 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 a common factor with x other than 1. If x is prime, then f(x)=?

A. xâˆ’2
B. xâˆ’1
C. (x+1)/2
D. (xâˆ’1)/2
E. 2

OA:B

HI Experts,

Can you pls explain the question. Didn't get the question at all

Thanks
Nandish

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Source: Beat The GMAT — Problem Solving | Fri Jan 19, 2018 4:12 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Fri Jan 19, 2018 4:48 am

NandishSS wrote: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 a common factor with x other than 1. If x is prime, then f(x)=?

A. xâˆ’2
B. xâˆ’1
C. (x+1)/2
D. (xâˆ’1)/2
E. 2

Let x = 2.
f(2) = the number of positive integers that are less than 2 and that do not share a factor with 2 other than 1.
Only one positive integer satisfies the conditions in red: 1.
Thus:
f(2) = 1.

Now plug x=2 into the answers to see which yields the target value in blue.
Only B works:
x-1 = 2-1 = 1.

The correct answer is B.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Fri Jul 26, 2019 11:14 am

NandishSS wrote: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 a common factor with x other than 1. If x is prime, then f(x)=?

A. xâˆ’2
B. xâˆ’1
C. (x+1)/2
D. (xâˆ’1)/2
E. 2

We are given that f(x) is defined as the number of positive integers that are less than x and do not have a common factor with x other than 1. We also are given that x is a prime number and we must determine the value of f(x).

Since x can be any prime number, let's let x = 5. The positive integers less than 5 are 1, 2, 3, and 4. Note that those integers do not have a common factor with 5, other than 1. Thus, f(x) = 4.

Substituting 5 for x in our answer choices, we see that the only answer choice that equals 4 is B, x - 1.

Answer: B

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