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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

00:00

A

B

C

D

E

Difficulty:

65% (medium)

Question Stats:

37% (02:32) correct
62% (01:18) wrong based on 406 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

3

This post received KUDOS

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

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 m [#permalink]
09 Jul 2013, 13:23

Expert's post

mohitvarshney 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

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.

Is there any flaw in my reasoning?

Merging similar topics. Please refer to the solutions above.
_________________

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.