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

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

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Last edited by Bunuel on 04 Sep 2012, 02:03, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If x is an integer and |1−x|<2 [#permalink] New post 04 Sep 2012, 01:11
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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.

Hence Answer D.
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Re: If x is an integer and |1−x|<2 [#permalink] New post 04 Sep 2012, 02:02
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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.

Answer: D.
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If x is an integer and |1−x|<2 [#permalink] New post 11 May 2013, 02:25
If x is an integer and |1−x|<2 what are values of x ?

I understood that through number plugging we can find x value ranges from 0,1,2 through number plugging

But I tried to find this in this way

case 1:
If x>0 1-x<2 ---> x>-1
Since considering x>0 taking positive values alone so x>0
Case 2:
If x<0
-1+X<2 so X<3

Considering -ve sign only so took -ve part so took X<0

Through this method i am not able to find the x values as 0,1,2...please help me in understanding...
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Re: If x is an integer and |1−x|<2 [#permalink] New post 11 May 2013, 02:30
Expert's post
skamal7 wrote:
If x is an integer and |1−x|<2 what are values of x ?

I understood that through number plugging we can find x value ranges from 0,1,2 through number plugging

But I tried to find this in this way

case 1:
If x>0 1-x<2 ---> x>-1
Since considering x>0 taking positive values alone so x>0
Case 2:
If x<0
-1+X<2 so X<3

Considering -ve sign only so took -ve part so took X<0

Through this method i am not able to find the x values as 0,1,2...please help me in understanding...


Merging similar topics.

Please post the whole questions with answer choices and OA!
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If x is an integer and |1-x|<2 then which of the following m [#permalink] New post 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.

Is there any flaw in my reasoning?
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Re: If x is an integer and |1-x|<2 then which of the following m [#permalink] New post 09 Jul 2013, 11:17
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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.
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Re: If x is an integer and |1-x|<2 then which of the following m [#permalink] New post 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.
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Re: If x is an integer and |1-x|<2 then which of the following m [#permalink] New post 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.
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Re: If x is an integer and |1-x|<2 then which of the following [#permalink] New post 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.

Could you please share your opinion on this.

Regards,
PiyushK

Subject: If x is an integer and |1-x|<2 then which of the following

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.

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.

Hope it's clear.
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COLLECTION OF QUESTIONS:
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Re: If x is an integer and |1-x|<2 then which of the following [#permalink] New post 14 Apr 2014, 03:06
Bunuel,

Why does 2 have 2 factors? I thought the smallest factor of any number was 2.. Is there a definition difference that I am missing?

Thanks for the reply!
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Re: If x is an integer and |1-x|<2 then which of the following [#permalink] New post 14 Apr 2014, 03:31
Expert's post
demandi wrote:
Bunuel,

Why does 2 have 2 factors? I thought the smallest factor of any number was 2.. Is there a definition difference that I am missing?

Thanks for the reply!


A factor is a positive integer which divides some integer without a remainder. Thus the smallest factor of any integer is 1.

The factors of 2 are 1 and 2.
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PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
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Re: If x is an integer and |1-x|<2 then which of the following   [#permalink] 14 Apr 2014, 03:31
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