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Manager  G
Joined: 13 Oct 2013
Posts: 134
Concentration: Strategy, Entrepreneurship
How many integers x are there so that |x-3.5 | < 2  [#permalink]

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Difficulty:   15% (low)

Question Stats: 69% (01:02) correct 31% (01:12) wrong based on 692 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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Kindly press +1 Kudos if my post helped you in any way Math Expert V
Joined: 02 Sep 2009
Posts: 58320
Re: How many integers x are there so that |x-3.5 | < 2  [#permalink]

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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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Manager  G
Joined: 13 Oct 2013
Posts: 134
Concentration: Strategy, Entrepreneurship
Re: How many integers x are there so that |x-3.5 | < 2  [#permalink]

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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 Math Expert V
Joined: 02 Sep 2009
Posts: 58320
How many integers x are there so that |x-3.5 | < 2  [#permalink]

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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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Manager  G
Joined: 13 Oct 2013
Posts: 134
Concentration: Strategy, Entrepreneurship
Re: How many integers x are there so that |x-3.5 | < 2  [#permalink]

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-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.

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Kindly press +1 Kudos if my post helped you in any way Senior Manager  Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 403
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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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, 03:36.
Last edited by pacifist85 on 14 Jan 2015, 03:40, edited 2 times in total.
Math Expert V
Joined: 02 Sep 2009
Posts: 58320
Re: How many integers x are there so that |x-3.5 | < 2  [#permalink]

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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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Senior Manager  Status: Math is psycho-logical
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Re: How many integers x are there so that |x-3.5 | < 2  [#permalink]

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Yes thank you Bunuel,

I copied it wrong from my notebook..
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: How many integers x are there so that |x-3.5 | < 2  [#permalink]

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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.

GMAT assassins aren't born, they're made,
Rich
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Status: No dream is too large, no dreamer is too small
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Posts: 426
Re: How many integers x are there so that |x-3.5 | < 2  [#permalink]

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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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|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

Hence, Answer is C
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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   [#permalink] 01 Nov 2018, 11:38
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