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# If q is the set of possible values for p and |3p – 4| ≤ 1, which of th

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Math Expert
Joined: 02 Sep 2009
Posts: 49960
If q is the set of possible values for p and |3p – 4| ≤ 1, which of th  [#permalink]

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26 Dec 2016, 11:04
2
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45% (medium)

Question Stats:

62% (01:31) correct 38% (01:37) wrong based on 588 sessions

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If q is the set of possible values for p and |3p – 4| ≤ 1, which of the following gives the range of q?

A. 0
B. 2/3
C. 1
D. 5/3
E. 2

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Re: If q is the set of possible values for p and |3p – 4| ≤ 1, which of th  [#permalink]

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26 Dec 2016, 12:06
1
1
|3p – 4| ≤ 1 --> $$-1 \leq {3p - 4} \leq {1}$$ --> $$1 \leq {p} \leq {5/3}$$

Max value of q is 5/3 and min value is 1

Range = 5/3 - 1 = 2/3

Manager
Joined: 25 Mar 2013
Posts: 247
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5
Re: If q is the set of possible values for p and |3p – 4| ≤ 1, which of th  [#permalink]

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28 Dec 2016, 09:18
2
2
Case 1 :
$$3P-4\leq{1}$$
$$P\leq{\frac{5}{3}}$$
Case 2 :
$$3P\leq{-1}$$
$$\frac{P}{1}$$
Range : Larger - Smaller
$$\frac{5}{3} - 1$$
$$\frac{2}{3}$$
B
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Director
Joined: 05 Mar 2015
Posts: 991
Re: If q is the set of possible values for p and |3p – 4| ≤ 1, which of th  [#permalink]

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28 Dec 2016, 10:35
1
1
Bunuel wrote:
If q is the set of possible values for p and |3p – 4| ≤ 1, which of the following gives the range of q?

A. 0
B. 2/3
C. 1
D. 5/3
E. 2

Just square both sides to get
9p^2-24p+15≤0
(3p-5)(p-1)≤0

so 1≤p≤5/3
range = highest-smallest
==5/3-1====2/3==B

Ans B
Manager
Joined: 02 Jan 2016
Posts: 102
Re: If q is the set of possible values for p and |3p – 4| ≤ 1, which of th  [#permalink]

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30 May 2018, 08:10
I do not understand what is being asked.

I could find out the ranges as -1 < = x <= 5/3,

But reducing 5/3-1 doesnt make sense to me, can someone explain.
Math Expert
Joined: 02 Sep 2009
Posts: 49960
Re: If q is the set of possible values for p and |3p – 4| ≤ 1, which of th  [#permalink]

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30 May 2018, 08:53
1
hero_with_1000_faces wrote:
If q is the set of possible values for p and |3p – 4| ≤ 1, which of the following gives the range of q?

A. 0
B. 2/3
C. 1
D. 5/3
E. 2

I do not understand what is being asked.

I could find out the ranges as -1 < = x <= 5/3,

But reducing 5/3-1 doesnt make sense to me, can someone explain.

|3p – 4| ≤ 1;

-1 ≤ 3p – 4 ≤ 1;

3 ≤ 3p ≤ 5;

1 ≤ p ≤ 5/3.

Since q is the set of possible values for p, then the set is composed of all numbers from 1 to 5/3, inclusive. We are asked to find the range of the set q. The range of a set is the difference between the largest and smallest elements of the set. So, the range of q is 5/3 - 1 = 2/3.

Hope it's clear.
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Re: If q is the set of possible values for p and |3p – 4| ≤ 1, which of th  [#permalink]

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30 May 2018, 10:53
Hey Bunuel,

Thanks a lot, thanks a lot man! really appreciate.
Also, I do not clearly recollect, the concept related to this step "-1 ≤ 3p – 4 ≤ 1"
Can you post link for this ? thanks again!
Math Expert
Joined: 02 Sep 2009
Posts: 49960
Re: If q is the set of possible values for p and |3p – 4| ≤ 1, which of th  [#permalink]

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30 May 2018, 22:44
hero_with_1000_faces wrote:
Hey Bunuel,

Thanks a lot, thanks a lot man! really appreciate.
Also, I do not clearly recollect, the concept related to this step "-1 ≤ 3p – 4 ≤ 1"
Can you post link for this ? thanks again!

You can always re-write |x| < a (where a is a positive number) as -a < x < a. For example, |x| < 1 means -1 < x < 1. Similarly we can re-write |3p – 4| ≤ 1 as -1 ≤ 3p – 4 ≤ 1
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Manager
Joined: 02 Jan 2016
Posts: 102
Re: If q is the set of possible values for p and |3p – 4| ≤ 1, which of th  [#permalink]

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31 May 2018, 01:51
Thanks Bunuel

This Helps
Manager
Joined: 29 May 2017
Posts: 72
Location: Pakistan
Concentration: Social Entrepreneurship, Sustainability
Re: If q is the set of possible values for p and |3p – 4| ≤ 1, which of th  [#permalink]

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21 Sep 2018, 05:21
Bunuel wrote:
hero_with_1000_faces wrote:
Hey Bunuel,

Thanks a lot, thanks a lot man! really appreciate.
Also, I do not clearly recollect, the concept related to this step "-1 ≤ 3p – 4 ≤ 1"
Can you post link for this ? thanks again!

You can always re-write |x| < a (where a is a positive number) as -a < x < a. For example, |x| < 1 means -1 < x < 1. Similarly we can re-write |3p – 4| ≤ 1 as -1 ≤ 3p – 4 ≤ 1

Hello...

for practice i did the following:

|3p-4| piecewise is

1. 3p-4 for p>4/3
2. -3p+4 for p< or equal to 4/3

1. gave p less than or equal to 2
2. gave p greater than or equal to 1

so my range is 1 (2-1)

can you please explain where i went wrong?
Re: If q is the set of possible values for p and |3p – 4| ≤ 1, which of th &nbs [#permalink] 21 Sep 2018, 05:21
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# If q is the set of possible values for p and |3p – 4| ≤ 1, which of th

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