Events & Promotions
|
|
GMAT 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 2212:30 AM EDT
-01:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
Apr 1612:00 PM EDT
-11:59 PM EDT
You’re first to know: Save $200 on GMAT prep starting tomorrow, 4/13. Get 6 official practice tests and study with real questions. Be ready to save!
Apr 2301:30 AM EDT
-02:30 AM EDT
Struggling with GMAT Verbal as a non-native speaker? Harsh improved his score from 595 to 695 in just 45 days—and scored a 99 %ile in Verbal (V88)! Learn how smart strategy, clarity, and guided prep helped him gain 100 points.
Apr 2308:00 PM PDT
-09:00 PM PDT
Video explanations + diagnosis of 10 weakest areas + 150+ short videos + study plan!
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
ManishKM1
Current Student
Joined: 22 Apr 2017
Last visit: 03 Jan 2019
Posts: 81
Given Kudos: 75
Location: India
Schools: MBS '20 (D) ISB '19 (D) ESADE '20 (A) IIM (A)
GMAT 1: 620 Q47 V29
GMAT 2: 630 Q49 V26
GMAT 3: 690 Q48 V35
GPA: 3.7
18 Sep 2017, 08:05
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
25% (02:27) correct
75%
(02:40)
wrong
based on 686
sessions
History
Date
Time
Result
Not Attempted Yet
Which of the following is/are true?
I. |3x - 19| > 5 - x holds for all values of x.
II. There is no value of x for which |2x - 10| < 4 - x holds.
III. -|5x - 23| is negative for all values of x.
A. None
B. I only
C. I and II only
D. I and III only
E. I, II and III
Source - Expert's Global
I. |3x - 19| > 5 - x holds for all values of x.
II. There is no value of x for which |2x - 10| < 4 - x holds.
III. -|5x - 23| is negative for all values of x.
A. None
B. I only
C. I and II only
D. I and III only
E. I, II and III
Source - Expert's Global
27 Jan 2023, 14:30
Kudos
Bookmarks
Which of the following is/are true?
I. |3x - 19| > 5 - x holds for all values of x.
II. There is no value of x for which |2x - 10| < 4 - x holds.
III. -|5x - 23| is negative for all values of x.
A. None
B. I only
C. I and II only
D. I and III only
E. I, II and III
I. \(|3x - 19| > 5 - x\) holds for all values of x.
When \(x < \frac{19}{3}\) (notice that \(\frac{19}{3} = 6 \frac{1}{3}\)), \(3x - 19 < 0\) thus in this case \(|3x - 19| = -(3x - 19)\), so we'd get \(-(3x - 19) > 5 - x\):
When \(x \geq \frac{19}{3}\), \(3x - 19 \geq 0\) thus in this case \(|3x - 19| = 3x - 19\), so we'd get 3x - 19 > 5 - x:
\(x < 6 \frac{1}{3}\) and \(x \geq 6 \frac{1}{3}\) give all values of x. So, \(|3x - 19| > 5 - x\) holds for all values of x.
II. There is no value of x for which |2x - 10| < 4 - x holds.
Here notice that x cannot be more than 4, because if it is then the RHS (the right hand side) becomes negative and it cannot be greater than the LHS (the left hand side), which is an absolute value and therefore is always more than or equal to 0.
So, x must be less than or equal to 4. Now, when \(x \leq 4\), \(2x - 10 < 0\) and thus 2x - 10 = -(2x - 10). So, we'd get: -(2x - 10) < 4 - x:
III. -|5x - 23| is negative for all values of x.
This statement says that \(-|5x - 23| < 0\) for all values of x:
This is clearly wrong because when x = 23/5, \(|5x - 23| = 0\), not greater than 0.
Answer: C.
Hope it's clear.
I. |3x - 19| > 5 - x holds for all values of x.
II. There is no value of x for which |2x - 10| < 4 - x holds.
III. -|5x - 23| is negative for all values of x.
A. None
B. I only
C. I and II only
D. I and III only
E. I, II and III
I. \(|3x - 19| > 5 - x\) holds for all values of x.
When \(x < \frac{19}{3}\) (notice that \(\frac{19}{3} = 6 \frac{1}{3}\)), \(3x - 19 < 0\) thus in this case \(|3x - 19| = -(3x - 19)\), so we'd get \(-(3x - 19) > 5 - x\):
- \(-3x + 19 > 5 - x\);
\(14 > 2x\);
\(x < 7\).
When \(x \geq \frac{19}{3}\), \(3x - 19 \geq 0\) thus in this case \(|3x - 19| = 3x - 19\), so we'd get 3x - 19 > 5 - x:
- \(3x - 19 > 5 - x\);
\(4x > 24\);
\(x > 6\).
\(x < 6 \frac{1}{3}\) and \(x \geq 6 \frac{1}{3}\) give all values of x. So, \(|3x - 19| > 5 - x\) holds for all values of x.
II. There is no value of x for which |2x - 10| < 4 - x holds.
Here notice that x cannot be more than 4, because if it is then the RHS (the right hand side) becomes negative and it cannot be greater than the LHS (the left hand side), which is an absolute value and therefore is always more than or equal to 0.
So, x must be less than or equal to 4. Now, when \(x \leq 4\), \(2x - 10 < 0\) and thus 2x - 10 = -(2x - 10). So, we'd get: -(2x - 10) < 4 - x:
- \(-2x + 10 < 4 - x\);
\(x > 6\).
III. -|5x - 23| is negative for all values of x.
This statement says that \(-|5x - 23| < 0\) for all values of x:
- \(|5x - 23| > 0\).
This is clearly wrong because when x = 23/5, \(|5x - 23| = 0\), not greater than 0.
Answer: C.
Hope it's clear.
General Discussion
18 Sep 2017, 08:45
Kudos
Bookmarks
ManishKM1
hi..
you can easily discard option 3, as at some value it will be 0..
1. |3x-19|>5-x holds for all values of x.
x>5 will make the RHS negative but LHS will always be positive or 0 at x = 19/3.
so LHS>RHS.
At negative x the RHS will increase by just x whereas LHS will increase by 3x..
try any value and it will be TRUE
2. There is no value of x for which |2x-10| <4-x holds.
4-x will be negative for x>4, whereas |2x-10| will be POSITIVE
for all negative values of x, again LHS <RHS
try for 0 to 4 also, the statement will be TRUE
3. -|5x-23| is negative for all values of x.
At x = 23/5, -|5x-23|=0
hence FALSE
ans C
