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# How many integers x are there so that |x-3.5 | < 2

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Joined: 13 Oct 2013
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How many integers x are there so that |x-3.5 | < 2  [#permalink]

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11 Nov 2014, 09:12
1
5
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Difficulty:

15% (low)

Question Stats:

70% (00:46) correct 30% (00:53) wrong based on 616 sessions

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How many integers $$x$$ are there so that $$|x - 3.5| \lt 2$$?

A. 2
B. 3
C. 4
D. 5
E. 6

M10-01

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Posts: 52231
Re: How many integers x are there so that |x-3.5 | < 2  [#permalink]

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11 Nov 2014, 09:21
2
1
sunita123 wrote:
How many integers $$x$$ are there so that $$|x - 3.5| \lt 2$$?

A. 2
B. 3
C. 4
D. 5
E. 6

M10-01

$$|x-3.5| \lt 2$$ means that $$-2 \lt x-3.5 \lt 2$$. Now, add 3.5 to all three parts: $$1.5 \lt x \lt 5.5$$. Since given that $$x$$ is an integer, then it can take the following four values: 2, 3, 4, and 5.

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Re: How many integers x are there so that |x-3.5 | < 2  [#permalink]

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11 Nov 2014, 09:28
Thanks Bunuel,
But I did not understand this part

|x-3.5| < 2 means that -2 <| x-3.5 |< 2

Bunuel wrote:
sunita123 wrote:
How many integers $$x$$ are there so that $$|x - 3.5| \lt 2$$?

A. 2
B. 3
C. 4
D. 5
E. 6

M10-01

$$|x-3.5| \lt 2$$ means that $$-2 \lt x-3.5 \lt 2$$. Now, add 3.5 to all three parts: $$1.5 \lt x \lt 5.5$$. Since given that $$x$$ is an integer, then it can take the following four values: 2, 3, 4, and 5.

_________________

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Kindly press +1 Kudos if my post helped you in any way

Math Expert
Joined: 02 Sep 2009
Posts: 52231
How many integers x are there so that |x-3.5 | < 2  [#permalink]

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11 Nov 2014, 09:35
sunita123 wrote:
Thanks Bunuel,
But I did not understand this part

|x-3.5| < 2 means that -2 <| x-3.5 |< 2

Bunuel wrote:
sunita123 wrote:
How many integers $$x$$ are there so that $$|x - 3.5| \lt 2$$?

A. 2
B. 3
C. 4
D. 5
E. 6

M10-01

$$|x-3.5| \lt 2$$ means that $$-2 \lt x-3.5 \lt 2$$. Now, add 3.5 to all three parts: $$1.5 \lt x \lt 5.5$$. Since given that $$x$$ is an integer, then it can take the following four values: 2, 3, 4, and 5.

Let me ask you a question how does |x| < 1 translate?
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Re: How many integers x are there so that |x-3.5 | < 2  [#permalink]

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11 Nov 2014, 10:11
-1<x<1

ok now i got it:).thank you

sunita123 wrote:
Thanks Bunuel,
But I did not understand this part

|x-3.5| < 2 means that -2 <| x-3.5 |< 2

Bunuel wrote:
sunita123 wrote:
How many integers $$x$$ are there so that $$|x - 3.5| \lt 2$$?

A. 2
B. 3
C. 4
D. 5
E. 6

M10-01

$$|x-3.5| \lt 2$$ means that $$-2 \lt x-3.5 \lt 2$$. Now, add 3.5 to all three parts: $$1.5 \lt x \lt 5.5$$. Since given that $$x$$ is an integer, then it can take the following four values: 2, 3, 4, and 5.

_________________

---------------------------------------------------------------------------------------------
Kindly press +1 Kudos if my post helped you in any way

Senior Manager
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 416
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
How many integers x are there so that |x-3.5 | < 2  [#permalink]

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Updated on: 14 Jan 2015, 02:40
I guess this is the same as doing this?

|x-3.5|<2
x-3.5<2
x<5.5 and,

-x+3.5<2
-x<2-3.5
-x<-1.5
x>1.5

Both together:
1.5<x<5.5

So, x can be 1.5, 2.5, 3.5 or 4.5 (0r in fact 2,3,4,5 since it is an integer). Is this the solution?

Originally posted by pacifist85 on 14 Jan 2015, 02:36.
Last edited by pacifist85 on 14 Jan 2015, 02:40, edited 2 times in total.
Math Expert
Joined: 02 Sep 2009
Posts: 52231
Re: How many integers x are there so that |x-3.5 | < 2  [#permalink]

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14 Jan 2015, 02:40
pacifist85 wrote:
I guess this is the same as doing this?

|x-3.5|<2
x-3.5<2
x<5.5 and,

-x+3.5<2
-x<2-3.5
-x<-0.5
x>0.5

Both together:
0.5<x<5.5

So, x can be: 1.5, 2.5, 3.5 or 4.5 (0r 1,2,3,4 since it is an integer). Is this the solution?

-x < 2 - 3.5
x > 1.5.

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Re: How many integers x are there so that |x-3.5 | < 2  [#permalink]

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14 Jan 2015, 02:42
Yes thank you Bunuel,

I copied it wrong from my notebook..
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Re: How many integers x are there so that |x-3.5 | < 2  [#permalink]

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14 Jan 2015, 22:39
Hi All,

Sometimes the easiest/fastest way to get to the correct answer is to use "brute force" - you can literally just jam numbers into this question until you physically find all of the answers. Children can do it, so you can do it.

The prompt asks for all of the INTEGER values of X that fit |X - 3.5| < 2. From the answer choices, we know that there are at least 2, but no more than 6, possibilities.

The first answer you will find is probably the easiest: X = 4

|4 - 3.5| = .5 which IS < 2

Now, let's go "bigger"
X = 5
|5 - 3.5| = 1.5 which IS < 2

X = 6 gives us...
|6 - 3.5| = 2.5 which is TOO BIG. So X CANNOT be 6 and it CANNOT be > 6

Let's go "smaller" (from X = 4)

X = 3
|3 - 3.5| = |-.5| = .5 which IS < 2

X = 2
|2 - 3.5| = |-1.5| = 1.5 which IS < 2

X = 1
|1 - 3.5| = |-2.5| = 2.5 which is TOO BIG. So X CANNOT be 1 and it CANNOT be < 1.

The values of X that "fit" are 2, 3, 4, and 5 --> 4 integers.

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Re: How many integers x are there so that |x-3.5 | < 2  [#permalink]

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14 Apr 2015, 21:23
sunita123 wrote:
Thanks Bunuel,
But I did not understand this part

|x-3.5| < 2 means that -2 <| x-3.5 |< 2

Bunuel wrote:
sunita123 wrote:
How many integers $$x$$ are there so that $$|x - 3.5| \lt 2$$?

A. 2
B. 3
C. 4
D. 5
E. 6

M10-01

$$|x-3.5| \lt 2$$ means that $$-2 \lt x-3.5 \lt 2$$. Now, add 3.5 to all three parts: $$1.5 \lt x \lt 5.5$$. Since given that $$x$$ is an integer, then it can take the following four values: 2, 3, 4, and 5.

The rule is : lxl<a
=>, -a<x<a

Here, x=x - 3.5 and a=2
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Re: How many integers x are there so that |x-3.5 | < 2  [#permalink]

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22 Jun 2017, 21:25
|x-3.5 | < 2

-2 < x - 3.5 < 2

1.5 < x < 5.5

As per above statement, and as x is an integer.

x can take values of 2,3,4 & 5

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Re: How many integers x are there so that |x-3.5 | < 2  [#permalink]

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Re: How many integers x are there so that |x-3.5 | < 2 &nbs [#permalink] 01 Nov 2018, 10:38
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