December 13, 2018 December 13, 2018 08:00 AM PST 09:00 AM PST What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL. December 14, 2018 December 14, 2018 09:00 AM PST 10:00 AM PST 10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.
Author 
Message 
TAGS:

Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6625
GPA: 3.82

Which of the following is satisfied with x4+x3<2?
[#permalink]
Show Tags
Updated on: 30 Jan 2016, 06:21
Question Stats:
69% (01:31) correct 31% (01:20) wrong based on 830 sessions
HideShow timer Statistics
Which of the following is satisfied with x4+x3<2? A. 1<x<5 B. 2<x<5 C. 2.5<x<4.5 D. 2.5<x<4 E. 3<x<4
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $99 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"
Originally posted by MathRevolution on 27 Jan 2016, 17:24.
Last edited by chetan2u on 30 Jan 2016, 06:21, edited 3 times in total.
Reformatted the question.




Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6625
GPA: 3.82

Re: Which of the following is satisfied with x4+x3<2?
[#permalink]
Show Tags
30 Jan 2016, 05:15
Which of the following is satisfied with x4+x3<2? A. 1<x<5 B. 2<x<5 C. 2.5<x<4.5 D. 2.5<x<4 E. 3<x<4 > If there is addition when there are 2 absolute values, you can just ignore the middle. That is, x4+x3<2 > x4+x3<2 > 2x7<2, 2<2x7<2, 5<2x<9, 5/2<x<9/2 > 2.5<x<4.5 Therefore, the answer is C.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $99 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"




CEO
Joined: 20 Mar 2014
Posts: 2633
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: Which of the following is satisfied with x4+x3<2?
[#permalink]
Show Tags
27 Jan 2016, 18:01
MathRevolution wrote: Which of the following is satisfied with x4+x3<2? A. 1<x<5 B. 2<x<5 C. 2.5<x<4.5 D. 2.5<x<4 E. 3<x<4
* A solution will be posted in two days. Remember that xa represents distance of x from 'a'. As mentioned in the question, x4+x3<2 simply means that you need to find the range of 'x' such that distance of x from 4 + distance of x from 3 < 2. Refer to the attached image, you realize that the distance 'y' when it is in between 3 and 4 will always be <2. For regions x<3 or x>4, the sum of the distances of 'y' from 3 and 4 will be <2 only when y+1+y<2 > 2y+1<2 > y<0.5 or in other words, range of x is > 2.5 < x < 4.5 Attachment:
20160127_205035.jpg [ 6.25 KiB  Viewed 5439 times ]
C is thus the correct answer. Alternate solution: using POE to arrive at the correct answer.Once you know that the sum of the distances of x from 3 and 4 must be < 2, A. 1<x<5 . Try with x=1.5. Clearly the distance of 1.5 from 3 and 4 will be >2. Eliminate.B. 2<x<5 . Take x=2.1. Again, the distances of 2.1 from 3 and 4 (=0.9 and 1.9 respectively) will sum to > 2. Hence Eliminate.C. 2.5<x<4.5. Works for all possible values. Keep.D. 2.5<x<4. Take x=4.2. The distances of 4.2 from 3 and 4 (=1.2 and 0.2 respectively) will sum to < 2 but this value is NOT in the given range, thus incomplete range. Hence Eliminate.E. 3<x<4. Take x=2.6. It works for the given sums of the distances < 2 but is not in the given range, thus incomplete range. Hence eliminate.C is thus the correct answer. Hope this helps.




Manager
Joined: 23 Jul 2014
Posts: 90
Location: India
WE: Information Technology (Computer Software)

Re: Which of the following is satisfied with x4+x3<2?
[#permalink]
Show Tags
27 Jan 2016, 17:55
If we put x=2.51 , 2.501 ... x4+x3 = 1.98 , 1.998 ..... just below 2 Again if we put x= 4.49,4.499..... x4+x3=1.98,1.998 ... just below 2 So Range should be 2.5<x<4.5 Answer (C)
_________________
The Mind ~ Muscle Connection My GMAT Journey is Complete.Going to start the MBA in Information Management from 2016 Good Luck everyone.



Intern
Joined: 03 Feb 2016
Posts: 10

Re: Which of the following is satisfied with x4+x3<2?
[#permalink]
Show Tags
13 Feb 2016, 05:00
Given the modules x4 and x3, we have 2 key points (4 and 3) which give us 3 cases:
1. x<3 x+4x+3<2 > \(x<\frac{5}{2}\) >2.5<x<3 Solution is valid.
2. 3\(\leq{x}\)<4
x+4+x3<2 > 1<2 Solution is valid.
3. 4\(\leq{x}\)
x4+x3<2 > x\(\leq\frac{9}{2}\) > x\(\leq4.5\) Solution is valid.
Therefore x must belong to the interval 2.5<x\(\leq{4.5}\) to satisfy the given inequation.



Manager
Status: Gmat lover
Joined: 27 Mar 2017
Posts: 85
Location: India
GPA: 3.91

Re: Which of the following is satisfied with x4+x3<2?
[#permalink]
Show Tags
15 May 2017, 04:31
A. 1<x<5 B. 2<x<5 C. 2.5<x<4.5
D. 2.5<x<4 E. 3<x<4
_________________
_________________ Rules for posting in verbal Gmat forum, read it before posting anything in verbal forum Giving me + 1 kudos if my post is valuable with you
The more you like my post, the more you share to other's need.
“The great secret of true success, of true happiness, is this: the man or woman who asks for no return, the perfectly unselfish person, is the most successful.” Swami Vivekananda



Manager
Joined: 29 May 2017
Posts: 127
Location: Pakistan
Concentration: Social Entrepreneurship, Sustainability

Re: Which of the following is satisfied with x4+x3<2?
[#permalink]
Show Tags
20 Sep 2018, 02:28
FelixM wrote: Given the modules x4 and x3, we have 2 key points (4 and 3) which give us 3 cases:
1. x<3 x+4x+3<2 > \(x<\frac{5}{2}\) >2.5<x<3 Solution is valid.
2. 3\(\leq{x}\)<4
x+4+x3<2 > 1<2 Solution is valid.
3. 4\(\leq{x}\)
x4+x3<2 > x\(\leq\frac{9}{2}\) > x\(\leq4.5\) Solution is valid.
Therefore x must belong to the interval 2.5<x\(\leq{4.5}\) to satisfy the given inequation. Hi.... I need to learn this key point method......can you send some links please? regards



Manager
Joined: 25 Nov 2017
Posts: 89
Location: India
GPA: 3.56

Re: Which of the following is satisfied with x4+x3<2?
[#permalink]
Show Tags
20 Oct 2018, 04:55
MathRevolution wrote: Which of the following is satisfied with x4+x3<2?
A. 1<x<5 B. 2<x<5 C. 2.5<x<4.5 D. 2.5<x<4 E. 3<x<4
> If there is addition when there are 2 absolute values, you can just ignore the middle. That is, x4+x3<2 > x4+x3<2 > 2x7<2, 2<2x7<2, 5<2x<9, 5/2<x<9/2 > 2.5<x<4.5 Therefore, the answer is C. Hello MathRevolution , If there is addition when there are 2 absolute values, you can just ignore the middleIs this because lal+lbl>=la+bl ?




Re: Which of the following is satisfied with x4+x3<2? &nbs
[#permalink]
20 Oct 2018, 04:55






