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.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
If 5 < (8 – x)/3, then which of the following MUST be true? I. 3 <
[#permalink]
18 Feb 2022, 06:00
18 Feb 2022, 06:00
1
1
Bookmarks
00:00
Question Stats:
40% (00:50) correct
60% (01:19) wrong based on 5 sessions
Hide Show timer Statistics
If \(5 < \frac{(8 – x)}{3}\), then which of the following MUST be true?
I. 3 < x
II. |x + 4| > 3
III. –(x + 7) is positive
A) II only
B) III only
C) I and II only
D) II and III only
E) I, II and III
I. 3 < x
II. |x + 4| > 3
III. –(x + 7) is positive
A) II only
B) III only
C) I and II only
D) II and III only
E) I, II and III
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If 5 < (8 – x)/3, then which of the following MUST be true? I. 3 <
[#permalink]
21 Feb 2022, 06:54
21 Feb 2022, 06:54
GreenlightTestPrep wrote:
If \(5 < \frac{(8 – x)}{3}\), then which of the following MUST be true?
I. 3 < x
II. |x + 4| > 3
III. –(x + 7) is positive
A) II only
B) III only
C) I and II only
D) II and III only
E) I, II and III
I. 3 < x
II. |x + 4| > 3
III. –(x + 7) is positive
A) II only
B) III only
C) I and II only
D) II and III only
E) I, II and III
Given: \(5 < \frac{(8 – x)}{3}\)
Multiply both sides of the inequality by \(3\) to get: \(15 < 8 – x\)
Subtract \(8\) from both sides to get: \(7 < -x\)
Multiply both sides by \(-1\) to get: \(-7 > x\) [since I multiplied both sides by a NEGATIVE I had to reverse the direction of the inequality symbol. See the video below for more on this.]
Since we now know \(x < -7\), we are ready to check the statements...
I. 3 < x
If \(x < -7\), it can't be the case that 3 < x.
So, statement I is not true.
II. |x + 4| > 3
If x = -7, then |x + 4| = |(-7) + 4| = |-3| = 3
So, if x is less than -7, then x + 4 will be less than -3, which means |x + 4| will be greater than 3.
So, statement II must be true.
III. –(x + 7) is positive
If we take \(x < -7\) and...
Add 7 to both sides we get: \(x + 7< 0\)
Now multiply both sides by (-1) to get: \(-(x + 7)> 0\)
So, statement III must be true.
Answer: D
RELATED VIDEO
gmatclubot
Re: If 5 < (8 – x)/3, then which of the following MUST be true? I. 3 < [#permalink]
21 Feb 2022, 06:54
Moderators:
