How many integers x are there so that |x-3.5 |

Question

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

Bunuel · Accepted Answer

|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.

Answer: C

sunita123 · Answer

Thanks Bunuel,
But I did not understand this part

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

Bunuel · Answer

Let me ask you a question how does |x| < 1 translate?

sunita123 · Answer

-1<x<1

ok now i got it:).thank you

pacifist85 · Answer

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?

Bunuel · Answer

-x < 2 - 3.5 x > 1.5. For complete solution please read how-many-integers-x-are-there-so-that-x-188429.html#p1441230

pacifist85 · Answer

Yes thank you Bunuel,

I copied it wrong from my notebook..

EMPOWERgmatRichC · Answer

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.

Final Answer:

Show Spoiler

C

GMAT assassins aren't born, they're made,
Rich

MHIKER · Answer

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

Here, x=x - 3.5 and a=2

ydmuley · Answer

|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

CEdward · Answer

Open the modulus.

How many integers xx are there so that |x−3.5|<2?

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

|x−3.5|<2

1. Positive
x - 3.5 < 2 
x < 5.5

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

From the above, we can conclude that 1.5 < x < 5.5

The question asks us which integers would satisfy the inequality. So we have 2, 3, 4, 5. Plug them in to check.

Answer is C.

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

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