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

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New post 26 Dec 2016, 11:04
2
18
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

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

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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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New post 26 Dec 2016, 12:06
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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

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

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New post 28 Dec 2016, 10:35
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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
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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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New post 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.
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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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New post 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.

Answer: B.

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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New post 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!
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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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New post 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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Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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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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New post 31 May 2018, 01:51
Thanks Bunuel

This Helps :)
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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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New post 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?
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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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