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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If q is the set of positive values for p and |3p – 4| ≤
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BTGmoderatorLU
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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
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Vincen
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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.
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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Scott@TargetTestPrep
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Case 1. Solving for p when (3p - 4) is positive, we have: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
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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