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.
Apr 25Crafting an Impactful Resume: Balancing Detail with Brevity
10:00 AM EDT
-10:30 AM EDT
Showcase your achievements through impactful storytelling! Get ready for an LIVE session on April 25, Learn how to craft compelling narratives on your resume that resonate with admission committees.
Apr 26Get a Top GRE Score with Target Test Prep
12:00 PM EDT
-01:00 PM EDT
The Target Test Prep course represents a quantum leap forward in GRE preparation, a radical reinterpretation of the way that students should study. In fact, more and more Target Test Prep students are scoring 329 and above on the GRE.
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
(x - 3) / (x^2 + 3x + 2) ≥ 1
[#permalink]
24 Sep 2021, 10:39
24 Sep 2021, 10:39
1
1
Bookmarks
00:00
Question Stats:
42% (01:50) correct
57% (02:08) wrong based on 19 sessions
Hide Show timer Statistics
\(\frac{(x - 3)}{(x^2 + 3x + 2)} ≥ 1\)
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
Number of integers which satisfy the above inequality |
1 |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Retired Moderator
Joined: 19 Nov 2020
Posts: 326
Given Kudos: 64
GRE 1: Q160 V152
(x - 3) / (x^2 + 3x + 2) ≥ 1
[#permalink]
24 Sep 2021, 15:04
24 Sep 2021, 15:04
1
let's dissect denominator=0 constraint firstly, \(x^2+3x+2=0\), \((x+1)(x+2)=0\) and x cannot be -1 and/or -2
next, both numerator and denominator must be either positive of negative
we safely multiply as signs of both sides are the same, and it leads to 2 inequalities that follow
\(x-3≥x^2+3x+2\) and \(x^2+3x+2≥x-3\)
\(x^2+2x+5≤0\) and \(x^2+2x+5≥0\) together these satisfy the equation \(x^2+2x+5=0\)
by checking the discriminant of the latter quadratic equation, \(2^2-4*5*1=-16\) we see that it's negative ... and there is not any solution
answer is \(D\)
next, both numerator and denominator must be either positive of negative
we safely multiply as signs of both sides are the same, and it leads to 2 inequalities that follow
\(x-3≥x^2+3x+2\) and \(x^2+3x+2≥x-3\)
\(x^2+2x+5≤0\) and \(x^2+2x+5≥0\) together these satisfy the equation \(x^2+2x+5=0\)
by checking the discriminant of the latter quadratic equation, \(2^2-4*5*1=-16\) we see that it's negative ... and there is not any solution
answer is \(D\)
KarunMendiratta wrote:
\(\frac{(x - 3)}{(x^2 + 3x + 2)} ≥ 1\)
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
Number of integers which satisfy the above inequality |
1 |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
General Discussion
Re: (x - 3) / (x^2 + 3x + 2) ≥ 1
[#permalink]
24 Sep 2021, 21:58
24 Sep 2021, 21:58
motion2020 wrote:
let's dissect denominator=0 constraint firstly, \(x^2+3x+2=0\), \((x+1)(x+2)=0\) and x cannot be -1 and/or -2
next, both numerator and denominator must be either positive of negative
we safely multiply as signs of both sides are the same, and it leads to 2 inequalities that follow
\(x-3≥x^2+3x+2\) and \(x^2+3x+2≥x-3\)
\(x^2+2x+5≤0\) and \(x^2+2x+5≥0\) together these satisfy the equation \(x^2+2x+5=0\)
by checking the discriminant of the latter quadratic equation, \(2^2-4*5*1=-16\) we see that it's negative ... and there is not any solution
answer is \(D\)
interesting problem. More likely to be found in CAT exam.
next, both numerator and denominator must be either positive of negative
we safely multiply as signs of both sides are the same, and it leads to 2 inequalities that follow
\(x-3≥x^2+3x+2\) and \(x^2+3x+2≥x-3\)
\(x^2+2x+5≤0\) and \(x^2+2x+5≥0\) together these satisfy the equation \(x^2+2x+5=0\)
by checking the discriminant of the latter quadratic equation, \(2^2-4*5*1=-16\) we see that it's negative ... and there is not any solution
answer is \(D\)
interesting problem. More likely to be found in CAT exam.
KarunMendiratta wrote:
\(\frac{(x - 3)}{(x^2 + 3x + 2)} ≥ 1\)
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
Number of integers which satisfy the above inequality |
1 |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
