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If q is the set of positive values for p and |3p – 4| ≤

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by BTGmoderatorLU » Thu Apr 26, 2018 2:39 pm

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Answers

A

B

C

D

E

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Difficulty—

If q is the set of positive 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

The OA is B.

Please, can anyone assist me with this PS question? I need help to solve it. Thanks!
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by [email protected] » Thu Apr 26, 2018 9:50 pm
Hi All,

We're told that Q is the set of POSITIVE values for P and |3P - 4| ≤ 1. We're asked which of the following is the RANGE of Q. This question can be solved in a couple of different ways, including Algebraically:

To find the maximum and minimum positive values for P, we need to solve the following equations:

3P - 4 = 1 and 3P - 4 = -1
3P = 5 and 3P = 3
P = 5/3 and P = 1

That range is 5/3 - 1 = 2/3

Final Answer: B

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by Vincen » Fri Apr 27, 2018 7:19 am
Hi BTGmoderatorLU.

I'd solve it as follows: $$\left|3P\ -4\right|\ \le\ 1$$ $$-1\le\ 3P\ -4\le\ 1\ $$ $$3\le\ 3P\ \le\ 5\ $$ $$1\le\ P\ \le\ \frac{5}{3}\ $$ Now, the range of the set $$Q=\left[1,\frac{5}{3}\right]$$ is $$\frac{5}{3}-1=\frac{2}{3}.$$ Hence the correct answer is the option B .

I hope it helps.
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by Scott@TargetTestPrep » Mon Apr 30, 2018 3:45 pm
BTGmoderatorLU wrote:If q is the set of positive 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
Case 1. Solving for p when (3p - 4) is positive, we have:

3p - 4 ≤ 1

3p ≤ 5

p ≤ 5/3

Case 2. Solving for p when (3p - 4) is negative, we have:

-(3p - 4) ≤ 1

3p - 4 ≥ -1

3p ≥ 3

p ≥ 1

Thus, 1 ≤ p ≤ 5/3 and hence the range is 5/3 - 1 = 2/3.

Answer: B

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