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

Question

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

Bunuel · Accepted Answer

|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.

kanusha · Answer

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

Kurtosis · Answer

|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

rohit8865 · Answer

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

hero_with_1000_faces · Answer

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.

hero_with_1000_faces · Answer

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!

Bunuel · Answer

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

hero_with_1000_faces · Answer

Thanks Bunuel This Helps

Mansoor50 · Answer

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?

gaiknil · Answer

All possible values of p are 1<=p<=5/3
Formula for the range = Max - Min
q is the set of values of p and we calculated above that p can have values from min 1 to max 5/3 inclusive. 
Hence range = 5/3 -1 = 2/3.

I hope this helps.

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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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