GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
If 2p q 1 and p + 4 3q, which of the following must be true?
[#permalink]
07 Apr 2022, 05:45
07 Apr 2022, 05:45
Expert Reply
1
Bookmarks
00:00
Question Stats:
66% (01:17) correct
33% (02:39) wrong based on 15 sessions
Hide Show timer Statistics
If \(2p ≥ q − 1\) and \(p + 4 ≥ 3q\), which of the following must be true?
(A) \(2p ≥ 3q\)
(B) \(2p + 3q ≥ p + q\)
(C) \(p − 4 ≥ 2q − 1\)
(D) \(3p + 4 ≥ 4q − 1\)
(E) \(2p^2 + 8P ≥ 3q^2 - 3q\)
(A) \(2p ≥ 3q\)
(B) \(2p + 3q ≥ p + q\)
(C) \(p − 4 ≥ 2q − 1\)
(D) \(3p + 4 ≥ 4q − 1\)
(E) \(2p^2 + 8P ≥ 3q^2 - 3q\)
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If 2p q 1 and p + 4 3q, which of the following must be true?
[#permalink]
07 Apr 2022, 05:49
07 Apr 2022, 05:49
Carcass wrote:
If \(2p ≥ q − 1\) and \(p + 4 ≥ 3q\), which of the following must be true?
(A) \(2p ≥ 3q\)
(B) \(2p + 3q ≥ p + q\)
(C) \(p − 4 ≥ 2q − 1\)
(D) \(3p + 4 ≥ 4q − 1\)
(E) \(2p^2 + 8P ≥ 3q^2 - 3q\)
(A) \(2p ≥ 3q\)
(B) \(2p + 3q ≥ p + q\)
(C) \(p − 4 ≥ 2q − 1\)
(D) \(3p + 4 ≥ 4q − 1\)
(E) \(2p^2 + 8P ≥ 3q^2 - 3q\)
Key property: If the inequality symbols of two inequalities are facing the same direction, we can add those inequalities.
That's the case with our given inequalities:
\(2p ≥ q − 1\)
\(p + 4 ≥ 3q\)
Add the inequalities to get: \((2p) + (p + 4) ≥ (q − 1) + (3q)\)
Simplify to get: \(3p+4 ≥ 4q-1\)
Answer: D
gmatclubot
Re: If 2p q 1 and p + 4 3q, which of the following must be true? [#permalink]
07 Apr 2022, 05:49
Moderators:
