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 500,000 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]

Show Tags

03 Sep 2012, 23:59

2

This post received KUDOS

39

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

38% (01:42) correct
62% (01:29) wrong based on 1637 sessions

HideShow timer Statistics

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?

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.

Hence Answer D.
_________________

Regards SD ----------------------------- Press Kudos if you like my post. Debrief 610-540-580-710(Long Journey): http://gmatclub.com/forum/from-600-540-580-710-finally-achieved-in-4th-attempt-142456.html

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]

Show Tags

09 Jul 2013, 11:21

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]

Show Tags

09 Jul 2013, 12:17

1

This post received KUDOS

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]

Show Tags

09 Jul 2013, 13:38

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.

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.

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, ....
_________________

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.

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.

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.

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]

Show Tags

11 Jun 2014, 03:16

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?

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.
_________________

Re: If x is an integer and |1-x|<2 then which of the following [#permalink]

Show Tags

15 May 2015, 09:52

Bunuel 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

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.

Just one question. I know by trial and error that the below process is wrong. But why does the algebra not match the intuitive way of solving??? Could you pls point out where you think I am making an error? TIA.

Given |1-x| < 2

(a) If x>0: 1-x < 2 -> x > -1

But this is true only for x>=0 which is a more limiting condition than x > -1. So shouldn't the result of opening the modulus be x>=0?

(b) If x<0: -1+x < 2 -> x<3

But this is true only for x<0 which is a more limiting condition that x<3. So shouldn't the result of opening the modulus be x<0?

By the above logic x = 0. But I can clearly see that x = 1 and x =2 will also work - why the discrepancy

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.

Just one question. I know by trial and error that the below process is wrong. But why does the algebra not match the intuitive way of solving??? Could you pls point out where you think I am making an error? TIA.

Given |1-x| < 2

(a) If x>0: 1-x < 2 -> x > -1

But this is true only for x>=0 which is a more limiting condition than x > -1. So shouldn't the result of opening the modulus be x>=0?

(b) If x<0: -1+x < 2 -> x<3

But this is true only for x<0 which is a more limiting condition that x<3. So shouldn't the result of opening the modulus be x<0?

By the above logic x = 0. But I can clearly see that x = 1 and x =2 will also work - why the discrepancy

You are not getting the right result because you are considering the zero points of x when deciding the sign of the expression when it comes out of the modulus. We consider the zero points of the expression inside the modulus to decide the sign of the expression when it comes out of the modulus i.e. in this case zero points of (1-x). So we can solve this modulus as

1. When 1- x > 0 1 - x < 2 i.e. x > -1

2. When 1 - x < 0 -(1-x) < 2 i.e. x < 3

Combining the above we get the range as -1 < x < 3. Since x is an integer it can take values of only 0,1 and 2.

Just to add on to the concept, we write |x| = x if x > 0 and -x if x < 0. On the same line, we would write |x -1| = x-1 if x-1 > 0 and -(x-1) if x-1 < 0

Version 8.1 of the WordPress for Android app is now available, with some great enhancements to publishing: background media uploading. Adding images to a post or page? Now...

Post today is short and sweet for my MBA batchmates! We survived Foundations term, and tomorrow's the start of our Term 1! I'm sharing my pre-MBA notes...

“Keep your head down, and work hard. Don’t attract any attention. You should be grateful to be here.” Why do we keep quiet? Being an immigrant is a constant...