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 |3 - 3x/2| 1, which of the following
[#permalink]
07 Mar 2022, 04:00
07 Mar 2022, 04:00
1
Bookmarks
00:00
Question Stats:
56% (01:43) correct
43% (01:49) wrong based on 44 sessions
Hide Show timer Statistics
If \(|3 - \frac{3x}{2}| ≥ 1\), which of the following is NOT a possible value of \(x\)?
A) \(-\frac{4}{3}\)
B) \(-\frac{1}{3}\)
C) \(\frac{4}{3}\)
D) \(\frac{5}{3}\)
E) \(\frac{8}{3}\)
A) \(-\frac{4}{3}\)
B) \(-\frac{1}{3}\)
C) \(\frac{4}{3}\)
D) \(\frac{5}{3}\)
E) \(\frac{8}{3}\)
Re: If |3 - 3x/2| 1, which of the following
[#permalink]
07 Mar 2022, 11:05
07 Mar 2022, 11:05
1
Upon solving for this abs inequality. 1st we will just take the eq as it is
|3−3x/2|≥1 -----> 3 - 3x/2 => 1 -----> 2 => 3x /2 ----> 4/3 => x
|3−3x/2|≥1------> -3 + 3x/2 => 1 ------> 3x/2 => 4 -----> x =>8x/3
So if you draw these equations on the no. line, you get that x is less than or equal to 4/3 and greater than or equal to 8x/3.
Only option not fulfilling these conditions is D, hence the ans
|3−3x/2|≥1 -----> 3 - 3x/2 => 1 -----> 2 => 3x /2 ----> 4/3 => x
|3−3x/2|≥1------> -3 + 3x/2 => 1 ------> 3x/2 => 4 -----> x =>8x/3
So if you draw these equations on the no. line, you get that x is less than or equal to 4/3 and greater than or equal to 8x/3.
Only option not fulfilling these conditions is D, hence the ans
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If |3 - 3x/2| 1, which of the following
[#permalink]
10 Mar 2022, 13:55
10 Mar 2022, 13:55
3
GreenlightTestPrep wrote:
If \(|3 - \frac{3x}{2}| ≥ 1\), which of the following is NOT a possible value of \(x\)?
A) \(-\frac{4}{3}\)
B) \(-\frac{1}{3}\)
C) \(\frac{4}{3}\)
D) \(\frac{5}{3}\)
E) \(\frac{8}{3}\)
A) \(-\frac{4}{3}\)
B) \(-\frac{1}{3}\)
C) \(\frac{4}{3}\)
D) \(\frac{5}{3}\)
E) \(\frac{8}{3}\)
STRATEGY: As with all GRE Multiple Choice questions, we should immediately ask ourselves, Can I use the answer choices to my advantage?
In this case, we could test the answer choices, but doing so would involve evaluating fractions within fractions, which would be quite time-consuming.
Now we should give ourselves about 10-20 seconds to identify a faster approach.
In this case, it will likely be faster to use algebra to solve the given inequality for x. So let's do that.
Two properties involving absolute value inequalities:
Property #1: If |something| < k, then –k < something < k
Property #2: If |something| > k, then EITHER something > k OR something < -k
Note: these rules assume that k is positive
The given inequality is in the form of Property #2, which means...
Either \(3 - \frac{3x}{2} ≥ 1\) or \(3 - \frac{3x}{2} ≤ -1\).
Let's solve each inequality for \(x\)
Take: \(3 - \frac{3x}{2} ≥ 1\)
Subtract \(3\) from both sides: \(-\frac{3x}{2} ≥ -2\)
Multiply both sides by \(2\) to get: \(-3x ≥ -4\)
Divide both sides by \(-3\) to get: \(x ≤ \frac{4}{3}\) [ since we divided both sides of the inequality by a negative value, we reversed the direction of the inequality symbol]
Take: \(3 - \frac{3x}{2} ≤ -1\)
Subtract \(3\) from both sides: \(-\frac{3x}{2} ≤ -4\)
Multiply both sides by \(2\) to get: \(-3x ≤ -8\)
Divide both sides by \(-3\) to get: \(x ≥ \frac{8}{3}\)
If \(x ≤ \frac{4}{3}\) or \(x ≥ \frac{8}{3}\), then \(x\) cannot equal \(\frac{5}{3}\)
Answer: D
