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

Expert replies

Previous Topic Next Topic

BTGmoderatorLU: Moderator; Posts: 2650; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

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

Timer

00:00

Your answer

Difficulty–

right wrong

Pick an answer to see how members did

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!

Source: Beat The GMAT — Problem Solving | Thu Apr 26, 2018 2:39 pm

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10391; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

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

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

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.

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Featured schoolRound 2 closes Jan 7, 2027 53 days left

Chicago Booth

Since 1982, 10 Booth faculty members have received the Nobel Prize in Economic Sciences, more than any other business school.

#3
U.S. News rank: $175,000
Median base salary: 670
Average GMAT Focus: 635
Students in the class

Apply to Booth Visit chicagobooth.edu See the full profile

Photo: Warren LeMay, CC BY-SA 2.0

GMAT Course Reviews

563 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (563 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review