Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

If x is an integer and |1-x|<2 then which of the following [#permalink]
03 Sep 2012, 22:59

3

This post received KUDOS

6

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

37% (02:40) correct
63% (01:27) wrong based on 794 sessions

If x is an integer and |1-x|<2 then which of the following must be true?

A. x is not a prime number B. x^2+x is not a prime number C. x is positive D. Number of distinct positive factors of x+2 is a prime number E. x is not a multiple of an odd prime number

Re: If x is an integer and |1−x|<2 [#permalink]
04 Sep 2012, 01:11

5

This post received KUDOS

1

This post was BOOKMARKED

sanjoo wrote:

If x is an integer and |1−x|<2 then which of the following must be true?

A) x is not a prime number B) x^2+x is not a prime number C) x is positive D) Number of distinct positive factors of x+2 is a prime number E) x is not a multiple of an odd prime number

|1−x|<2 = -2<(1-x)<2 = -3<-x<1 = 3>x>-1 So x can hold values of 0,1 & 2 to satisfy the condition. Now we can evaluate the choices. A) 1 & 2 primes, so incorrect B) 1^2+1=2 is a prime, so incorrect C) 0 is not +ve, So incorrect D) x+2= 2,3,or 4, here 2 has 2 factor(prime), 3 has 2 factor (prime) & 4 has 3factors (prime). Hence correct choice. E) 2 is multiple of 1. So incorrect.

Re: If x is an integer and |1−x|<2 [#permalink]
04 Sep 2012, 02:02

4

This post received KUDOS

Expert's post

1

This post was BOOKMARKED

sanjoo wrote:

If x is an integer and |1−x|<2 then which of the following must be true?

A) x is not a prime number B) x^2+x is not a prime number C) x is positive D) Number of distinct positive factors of x+2 is a prime number E) x is not a multiple of an odd prime number

If x is an integer and |1-x|<2 then which of the following must be true?

|1-x| is just the distance between 1 and x on the number line. We are told that this distance is less than 2: --(-1)----1----3-- so, -1<x<3. Since given that x is an integer then x can be 0, 1 or 2.

A. x is not a prime number. Not true if x=2. B. x^2+x is not a prime number. Not true if x=1. C. x is positive. Not true if x=0. D. Number of distinct positive factors of x+2 is a prime number. True for all three values of x. E. x is not a multiple of an odd prime number. Not true if x=0, since zeo is a multiple of every integer except zero itself.

If x is an integer and |1-x|<2 then which of the following m [#permalink]
09 Jul 2013, 10:21

If x is an integer and |1-x|<2 then which of the following must be true?

A. x is not a prime number B. x^2+x is not a prime number C. x is positive D. Number of distinct positive factors of x+2 is a prime number E. x is not a multiple of an odd prime number

I am confused between D & E. D seems perfectly correct.

My analysis: -1<x<3 Possible values of x -> 0, 1 & 2 " E. x is not a multiple of an odd prime number"

x=0 - False as 0 is a multiple of any odd prime number x=1 - False as 1 is a multiple of any odd prime number x=2 - True as 2 is not a multiple of any odd prime number.

smallest odd prime number is "3". So, when x=2 the statement is true.

Re: If x is an integer and |1-x|<2 then which of the following m [#permalink]
09 Jul 2013, 11:17

1

This post received KUDOS

Expert's post

mohitvarshney wrote:

My analysis: -1<x<3 Possible values of x -> 0, 1 & 2 " E. x is not a multiple of an odd prime number"

x=0 - False as 0 is a multiple of any odd prime number x=1 - True as 1 is NOT a multiple of any odd prime number x=2 - True as 2 is not a multiple of any odd prime number. smallest odd prime number is "3". So, when x=2 the statement is true.

Is there any flaw in my reasoning?

Apart from the highlighted part, everything is correct. For the reason that you could demonstrate that option E is not valid for x=0, we can not have E as a correct answer for a Must be True type question.

1 is a factor of every integer, not a multiple of every integer. _________________

Re: If x is an integer and |1-x|<2 then which of the following m [#permalink]
09 Jul 2013, 12:38

mau5 wrote:

mohitvarshney wrote:

My analysis: -1<x<3 Possible values of x -> 0, 1 & 2 " E. x is not a multiple of an odd prime number"

x=0 - False as 0 is a multiple of any odd prime number x=1 - True as 1 is NOT a multiple of any odd prime number x=2 - True as 2 is not a multiple of any odd prime number. smallest odd prime number is "3". So, when x=2 the statement is true.

Is there any flaw in my reasoning?

Apart from the highlighted part, everything is correct. For the reason that you could demonstrate that option E is not valid for x=0, we can not have E as a correct answer for a Must be True type question.

1 is a factor of every integer, not a multiple of every integer.

Yup I got my mistake. It is a "Must be true" question. Thanks a lot.

Re: If x is an integer and |1-x|<2 then which of the following [#permalink]
21 Aug 2013, 02:57

Expert's post

PiyushK wrote:

Hi Bunuel,

I have a doubt, as per this thread D is the correct answer. I calculated the range of x as -1<x<3, further option D says : D. Number of distinct positive factors of x+2 is a prime number for x=0 x+2 = 2 => distinct positive factors are 1 and 2 for x=1 x+2 = 3 => distinct positive factors are 1 and 3 for x=2 x+2 = 4 => distinct positive factors are 1 and 2

2,3 are prime numbers but 1 is not a prime number as per rule/definition.

Therefor I think D is also not a well articulated option.

If x is an integer and |1−x|<2 then which of the following must be true?

A) x is not a prime number B) x^2+x is not a prime number C) x is positive D) Number of distinct positive factors of x+2 is a prime number E) x is not a multiple of an odd prime number

If x is an integer and |1-x|<2 then which of the following must be true?

|1-x| is just the distance between 1 and x on the number line. We are told that this distance is less than 2: --(-1)----1----3-- so, -1<x<3. Since given that x is an integer then x can be 0, 1 or 2.

A. x is not a prime number. Not true if x=2. B. x^2+x is not a prime number. Not true if x=1. C. x is positive. Not true if x=0. D. Number of distinct positive factors of x+2 is a prime number. True for all three values of x. E. x is not a multiple of an odd prime number. Not true if x=0, since zeo is a multiple of every integer except zero itself.

Answer: D.

Responding to pm.

D. Number of distinct positive factors of x+2 is a prime number. x+2 is 2, 3, or 4.

2 has 2 factors 1 and 2. 3 has 2 factors 1 and 3. 4 has 3 factors 1, 2 and 4.

The number of factors of each number is a prime number.

Re: If x is an integer and |1-x|<2 then which of the following [#permalink]
22 May 2014, 02:58

Expert's post

dansa wrote:

E ist also correct1 The question is flawed!!

number 1 is not considered prime, as it has only one factor (itself).

Yes, 1 is NOT prime but it has nothing to do with option E.

E says: x is not a multiple of an odd prime number. IF x=0, then this option is not always true because 0 is a multiple of every integer except 0 itself, hence it's a multiple of all odd primes: 3, 5, 7, .... _________________

Re: If x is an integer and |1−x|<2 [#permalink]
09 Jun 2014, 13:10

This might be a naive question and also highlights a gap in my understand but can you please explain how |1−x|<2 translates into "-2<(1-x)<2". Thank you.

SOURH7WK wrote:

sanjoo wrote:

If x is an integer and |1−x|<2 then which of the following must be true?

A) x is not a prime number B) x^2+x is not a prime number C) x is positive D) Number of distinct positive factors of x+2 is a prime number E) x is not a multiple of an odd prime number

|1−x|<2 = -2<(1-x)<2 = -3<-x<1 = 3>x>-1 So x can hold values of 0,1 & 2 to satisfy the condition. Now we can evaluate the choices. A) 1 & 2 primes, so incorrect B) 1^2+1=2 is a prime, so incorrect C) 0 is not +ve, So incorrect D) x+2= 2,3,or 4, here 2 has 2 factor(prime), 3 has 2 factor (prime) & 4 has 3factors (prime). Hence correct choice. E) 2 is multiple of 1. So incorrect.

Re: If x is an integer and |1−x|<2 [#permalink]
10 Jun 2014, 05:56

1

This post received KUDOS

Expert's post

farhanabad wrote:

This might be a naive question and also highlights a gap in my understand but can you please explain how |1−x|<2 translates into "-2<(1-x)<2". Thank you.

SOURH7WK wrote:

sanjoo wrote:

If x is an integer and |1−x|<2 then which of the following must be true?

A) x is not a prime number B) x^2+x is not a prime number C) x is positive D) Number of distinct positive factors of x+2 is a prime number E) x is not a multiple of an odd prime number

|1−x|<2 = -2<(1-x)<2 = -3<-x<1 = 3>x>-1 So x can hold values of 0,1 & 2 to satisfy the condition. Now we can evaluate the choices. A) 1 & 2 primes, so incorrect B) 1^2+1=2 is a prime, so incorrect C) 0 is not +ve, So incorrect D) x+2= 2,3,or 4, here 2 has 2 factor(prime), 3 has 2 factor (prime) & 4 has 3factors (prime). Hence correct choice. E) 2 is multiple of 1. So incorrect.

Re: If x is an integer and |1−x|<2 [#permalink]
10 Jun 2014, 06:07

Bunuel - Thank you very much. It absolutely helps (no pun intended); and like I said there is a gap in my understanding since I believed that the absolute value of anything is always positive, hence I was viewing |x-1| as simply (x-1) and did not consider -(x-1). Thanks again.

Re: If x is an integer and |1−x|<2 [#permalink]
10 Jun 2014, 06:10

1

This post received KUDOS

Expert's post

farhanabad wrote:

Bunuel - Thank you very much. It absolutely helps (no pun intended); and like I said there is a gap in my understanding since I believed that the absolute value of anything is always positive, hence I was viewing |x-1| as simply (x-1) and did not consider -(x-1). Thanks again.

Absolute value of any number, expression, is more than or equal to zero but the expression in the modulus can be negative as well as positive. So, \(|x-1|\geq{0}\) but x-1 can be positive negative or 0. _________________

Re: If x is an integer and |1-x|<2 then which of the following [#permalink]
11 Jun 2014, 02:16

Bunuel wrote:

dansa wrote:

E ist also correct1 The question is flawed!!

number 1 is not considered prime, as it has only one factor (itself).

Yes, 1 is NOT prime but it has nothing to do with option E.

E says: x is not a multiple of an odd prime number. IF x=0, then this option is not always true because 0 is a multiple of every integer except 0 itself, hence it's a multiple of all odd primes: 3, 5, 7, ....

Bunnel, where do the multiples start for an integer? Say for 3 Do they start at 0 or should the negative multiples be considered too? 0 being the multilple of every integer is certainly a revelation to me. Thanks for that! Btw, zero has no multiples then?

Re: If x is an integer and |1-x|<2 then which of the following [#permalink]
11 Jun 2014, 02:29

Expert's post

Kconfused wrote:

Bunuel wrote:

dansa wrote:

E ist also correct1 The question is flawed!!

number 1 is not considered prime, as it has only one factor (itself).

Yes, 1 is NOT prime but it has nothing to do with option E.

E says: x is not a multiple of an odd prime number. IF x=0, then this option is not always true because 0 is a multiple of every integer except 0 itself, hence it's a multiple of all odd primes: 3, 5, 7, ....

Bunnel, where do the multiples start for an integer? Say for 3 Do they start at 0 or should the negative multiples be considered too? 0 being the multilple of every integer is certainly a revelation to me. Thanks for that! Btw, zero has no multiples then?

Yes, no number is a multiple of 0.

As for negative multiples: multiples of 3 are: ..., -6, -3, 0, 3, 6, ... But you should not worry about it since every GMAT divisibility question will tell you in advance that any unknowns represent positive integers, which means that ALL GMAT divisibility questions are limited to positive integers only. _________________

Type of Visa: You will be applying for a Non-Immigrant F-1 (Student) US Visa. Applying for a Visa: Create an account on: https://cgifederal.secure.force.com/?language=Englishcountry=India Complete...