BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

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

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 2505
Joined: Sun Oct 15, 2017 1:50 pm
Followed by:6 members

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

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

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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!
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
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]
Image
Top
Legendary Member
Posts: 2898
Joined: Thu Sep 07, 2017 2:49 pm
Thanked: 6 times
Followed by:5 members

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.
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8086
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

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]

Image

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

ImageImage
Top
Post new topic Post Reply
• Page 1 of 1