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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If x is an integer and |1-x|<2 then which of the following

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Intern  Joined: 03 Mar 2016
Posts: 2
Location: United States
GMAT 1: 740 Q47 V45
GPA: 3.17
Re: If x is an integer and |1-x|<2 then which of the following  [#permalink]

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I agree with this, except the explanation for answer E. 1 is actually not a prime number (2 is the smallest prime, and 3 is the first odd prime number). However, 0 is a multiple of any number, so we could say that the odd prime is 3, and that 0 x 3 = 0 (a multiple of a prime number).

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.

Intern  Joined: 30 Sep 2016
Posts: 7
Re: If x is an integer and |1-x|<2 then which of the following  [#permalink]

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Hi,

Would you mind having a look? This is what I did.

I 1-x I<2
-2<1-x<2
Subtracted -1 ie -3<-x<1
Multiplied by - 3>x>-1 Now I understand option D, zero is an integer correct? It is just not a positive integer?

Can you explain option D three distinct positive values ie in my case 2,1,0? Just a little confused or do I have it all wrong?
Math Expert V
Joined: 02 Sep 2009
Posts: 60645
Re: If x is an integer and |1-x|<2 then which of the following  [#permalink]

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Nasahtahir wrote:
Hi,

Would you mind having a look? This is what I did.

I 1-x I<2
-2<1-x<2
Subtracted -1 ie -3<-x<1
Multiplied by - 3>x>-1 Now I understand option D, zero is an integer correct? It is just not a positive integer?

Can you explain option D three distinct positive values ie in my case 2,1,0? Just a little confused or do I have it all wrong?

|1-x|<2 means -1<x<3. Since given that x is an integer then x can be 0, 1 or 2.

D says: 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.
_________________
Intern  B
Joined: 07 May 2019
Posts: 11
Re: If x is an integer and |1-x|<2 then which of the following  [#permalink]

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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.

Hi Bunuel,

Thank you for the explanation. May you please elaborate why zero cannot be a multiple of itself?

Thank you. Re: If x is an integer and |1-x|<2 then which of the following   [#permalink] 30 Sep 2019, 07:06

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