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# Which of the following could be n if |2n – 3| < 1?

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Math Expert
Joined: 02 Sep 2009
Posts: 44639
Which of the following could be n if |2n – 3| < 1? [#permalink]

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14 Dec 2016, 06:01
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5% (low)

Question Stats:

78% (00:48) correct 22% (00:54) wrong based on 318 sessions

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Which of the following could be n if |2n – 3| < 1?

A. -4/3
B. -1
C. 4/3
D. 1
E. 0
[Reveal] Spoiler: OA

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Re: Which of the following could be n if |2n – 3| < 1? [#permalink]

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14 Dec 2016, 08:21
Bunuel wrote:
Which of the following could be n if |2n – 3| < 1?

A. -4/3
B. -1
C. 4/3
D. 1
E. 0

Plug in the values of n from the options and check -

A. If n = -4/3 ; |2n – 3| = 5.67

B. If n = -1 ; |2n – 3| = 5

C. If n = 4/3 ; |2n – 3| = 1/3 < 1

D. If n = 1 ; |2n – 3| = 1

E. If n = 0 ; |2n – 3| = 3

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Re: Which of the following could be n if |2n – 3| < 1? [#permalink]

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14 Dec 2016, 09:42
Bunuel wrote:
Which of the following could be n if |2n – 3| < 1?

A. -4/3
B. -1
C. 4/3
D. 1
E. 0

sq. both sides to get
4n^2+9-12n<1
4n^2-12n+8<0
(2n-2)(n-4)<0

so break even points are 1 & 4 (shown below)
any number between 1& 4 willsatisfy the equation asked

thus 4/3 lies in between 1 & 4 will be answer

Ans C
Attachments

number.jpg [ 5.43 KiB | Viewed 2222 times ]

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Re: Which of the following could be n if |2n – 3| < 1? [#permalink]

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15 Dec 2016, 17:52
1
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Expert's post
Bunuel wrote:
Which of the following could be n if |2n – 3| < 1?

A. -4/3
B. -1
C. 4/3
D. 1
E. 0

Let’s solve the given inequality for when (2n - 3) is positive and then when (2n - 3) is negative.

When (2n - 3) is positive, we have:

2n - 3 < 1

2n < 4

n < 2

Now we can solve for when (2n - 3) is negative:

-(2n - 3) < 1

-2n + 3 < 1

-2n < -2

n > 1

Thus, 1 < n < 2, so n could equal 4/3.

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Re: Which of the following could be n if |2n – 3| < 1? [#permalink]

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01 Jan 2017, 16:08
2
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-1 <2n - 3< 1
3-1 < 2n < 1+3
$$\frac{2}{2} < n < \frac{4}{2}$$
1 < n < 2
C
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Re: Which of the following could be n if |2n – 3| < 1? [#permalink]

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12 Nov 2017, 11:27
kanusha wrote:
-1 <2n - 3< 1
3-1 < 2n < 1+3
$$\frac{2}{2} < n < \frac{4}{2}$$
1 < n < 2
C

This is by far the fastest method and should take no more than 30 seconds.
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Which of the following could be n if |2n – 3| < 1? [#permalink]

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09 Mar 2018, 05:27
Bunuel wrote:
Which of the following could be n if |2n – 3| < 1?

A. -4/3
B. -1
C. 4/3
D. 1
E. 0

Using POE:

A & B are out as they will add with 3 to get the value larger than 1.

D & E are out as they will yield |-1| = 1, & |-3| = 3

Hence (C)
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Re: Which of the following could be n if |2n – 3| < 1? [#permalink]

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09 Mar 2018, 05:47
|2n-3| < 1

For cases when 2n-3>0 and 2n-3<0 we have two cases -
Step 1) -1 < 2n-3 < 1 (writing both inequalities together)
Step 2) simplify by adding 3 to all sides and dividing by 2.
2 < 2n < 4
1< n < 2

Hence C) fits best.
Re: Which of the following could be n if |2n – 3| < 1?   [#permalink] 09 Mar 2018, 05:47
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