May 25 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. May 27 01:00 AM PDT  11:59 PM PDT All GMAT Club Tests are free and open on May 27th for Memorial Day! May 27 10:00 PM PDT  11:00 PM PDT Special savings are here for Magoosh GMAT Prep! Even better  save 20% on the plan of your choice, now through midnight on Tuesday, 5/27 May 30 10:00 PM PDT  11:00 PM PDT Application deadlines are just around the corner, so now’s the time to start studying for the GMAT! Start today and save 25% on your GMAT prep. Valid until May 30th. Jun 01 07:00 AM PDT  09:00 AM PDT Learn reading strategies that can help even nonvoracious reader to master GMAT RC
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 19 Nov 2004
Posts: 44

How many possible integer values are there for x if 4x  3
[#permalink]
Show Tags
Updated on: 20 Oct 2013, 04:03
Question Stats:
62% (01:21) correct 38% (01:24) wrong based on 1317 sessions
HideShow timer Statistics
How many possible integer values are there for x if 4x  3 < 6 ? A. One B. Two C. Three D. Four E. Five What I did here was to separate two scenarios: a. 4x – 3 < 6 and b. 4x – 3 >  6
I simplified x in both scenarios that I ended up in a range of 2.25 < x < .75 Therefore, my answer is 3 integers (2, 1, 0)
I would like to know if this method is correct and if I should use such method for problems that involve absolute value and inequality.
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by cpcalanoc on 19 Dec 2004, 18:33.
Last edited by Bunuel on 20 Oct 2013, 04:03, edited 1 time in total.
Renamed the topic, edited the question and added the OA.




Math Expert
Joined: 02 Sep 2009
Posts: 55271

Re: How many possible integer values are there for x if 4x  3
[#permalink]
Show Tags
20 Oct 2013, 04:08
How many possible integer values are there for x if 4x  3 < 6 ? A. One B. Two C. Three D. Four E. Five \(4x  3 < 6\); Get rid of the modulus: \(6<4x3< 6\); Add 3 to all three parts: \(3<4x< 9\); Divide by 4: \(\frac{3}{4}<x< \frac{9}{4}\) > \(0.75<x< 2.25\). x can take following integer values: 0, 1, and 2. Answer: C.
_________________




Manager
Joined: 26 Dec 2003
Posts: 218
Location: India

u can do this way. Directly substitute the value of x by trial and error method . Start from 0 and move on. u will get 0,1 and 2 as it asked for positive integers



Manager
Joined: 19 Nov 2004
Posts: 58

Cpcalanoc you choose the right way BUT from 4x3<6 => 4x<9 =>
x<2.25
the same mistake in the other
So 0.75 < x < 2.25
then the answer (0, 1, 2)
to Rakesh1239 your answer is right but where you see the word positive?



SVP
Joined: 06 Sep 2013
Posts: 1660
Concentration: Finance

Re: How many possible integer values are there for x if 4x  3
[#permalink]
Show Tags
20 Nov 2013, 05:25
cpcalanoc wrote: How many possible integer values are there for x if 4x  3 < 6 ? A. One B. Two C. Three D. Four E. Five What I did here was to separate two scenarios: a. 4x – 3 < 6 and b. 4x – 3 >  6
I simplified x in both scenarios that I ended up in a range of 2.25 < x < .75 Therefore, my answer is 3 integers (2, 1, 0)
I would like to know if this method is correct and if I should use such method for problems that involve absolute value and inequality. You can try algebraically, If x>=0, then you will have the range 0<=x<9/4 If x<0, you get x>3/4 but this solution is not valid so x must vbe x>=0. Hence, you have 3 integer solutions from the above inequality: 0, 1 and 2. Hope this helps Cheers J



Manager
Status: folding sleeves up
Joined: 26 Apr 2013
Posts: 130
Location: India
Concentration: Finance, Strategy
GMAT 1: 530 Q39 V23 GMAT 2: 560 Q42 V26
GPA: 3.5
WE: Consulting (Computer Hardware)

Re: How many possible integer values are there for x if 4x  3
[#permalink]
Show Tags
26 Mar 2014, 09:06
[quote="cpcalanoc"]How many possible integer values are there for x if 4x  3 < 6 ?
A. One B. Two C. Three D. Four E. Five
Solution: 4x3 < 6
let 4x=a therefore we have a3 < 6 ==> read this as origin is at +3 and we have to move +6 to the right and 6 to the left
(the less than sign represents that the a must be within boundaries )
(36)3(3+6)
now, we have 3<a<9
but a =4x ==> 3<4x<9
dividing all values by +4 we have 0.75 <x < 2.24
Now question says Integer values (not rational ) therefore we have 0,1,2
Hence 3



Manager
Joined: 25 Mar 2013
Posts: 238
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5

Re: How many possible integer values are there for x if 4x  3
[#permalink]
Show Tags
11 Apr 2014, 07:29
My Strategy , X is an integer ( + ,  , 0 ) Principles : Integers ,Module and Inequality Plug In Method Start with 0 , 1 , 1 , 2 as values By Plugging in 4x  3 < 6 Is Yes for 0 , 1, 2 But not with 1 So 3 Values After seeing Bunnel solution we can use Module Basics with a Range in Number line 6<4x  3< 6 , 3<4x<9 , \frac {3}{4} <x< \frac{9}{4}, So  0,75<x< 2.25 So Range from 0 , 1 , 2 If any wrong or any Suggestions in my Strategy pls Correct it
_________________
I welcome analysis on my posts and kudo +1 if helpful. It helps me to improve my craft.Thank you



Intern
Joined: 10 Apr 2014
Posts: 32

Re: How many possible integer values are there for x if 4x  3
[#permalink]
Show Tags
11 Apr 2014, 12:12
kanusha wrote: My Strategy , X is an integer ( + ,  , 0 ) Principles : Integers ,Module and Inequality Plug In Method Start with 0 , 1 , 1 , 2 as values By Plugging in 4x  3 < 6 Is Yes for 0 , 1, 2 But not with 1 So 3 Values After seeing Bunnel solution we can use Module Basics with a Range in Number line 6<4x  3< 6 , 3<4x<9 , \frac {3}{4} <x< \frac{9}{4}, So  0,75<x< 2.25 So Range from 0 , 1 , 2 If any wrong or any Suggestions in my Strategy pls Correct it your strategy is good but suppose if you have lot of integers, how many will you keep plugging? The second method is better as you quickly know the range and based on conceptual understanding. given 4x  3 can take both positive and negative values. It can lie between 6 and 0 or 0 and +6.



Manager
Joined: 08 Sep 2010
Posts: 58

Re: How many possible integer values are there for x if 4x  3
[#permalink]
Show Tags
27 Apr 2014, 09:58
Bunuel wrote: How many possible integer values are there for x if 4x  3 < 6 ?
A. One B. Two C. Three D. Four E. Five
\(4x  3 < 6\);
Get rid of the modulus: \(6<4x3< 6\);
Add 3 to all three parts: \(3<4x< 9\);
Divide by 4: \(\frac{3}{4}<x< \frac{9}{4}\) > \(0.75<x< 2.25\).
x can take following integer values: 0, 1, and 2.
Answer: C. @Bunuel  The question stems talks about how many positive integer values of x. IF we are talking about positive integer then it should be only {1,2} and not {0). Am I missing anything here?



Math Expert
Joined: 02 Sep 2009
Posts: 55271

Re: How many possible integer values are there for x if 4x  3
[#permalink]
Show Tags
28 Apr 2014, 01:34
chanakya84 wrote: Bunuel wrote: How many possible integer values are there for x if 4x  3 < 6 ?
A. One B. Two C. Three D. Four E. Five
\(4x  3 < 6\);
Get rid of the modulus: \(6<4x3< 6\);
Add 3 to all three parts: \(3<4x< 9\);
Divide by 4: \(\frac{3}{4}<x< \frac{9}{4}\) > \(0.75<x< 2.25\).
x can take following integer values: 0, 1, and 2.
Answer: C. @Bunuel  The question stems talks about how many positive integer values of x. IF we are talking about positive integer then it should be only {1,2} and not {0). Am I missing anything here? The question does not specify that the integers must be positive: "how many possible integer values are there for x..." Hope it's clear.
_________________



Manager
Joined: 08 Sep 2010
Posts: 58

Re: How many possible integer values are there for x if 4x  3
[#permalink]
Show Tags
28 Apr 2014, 06:46
Bunuel wrote: chanakya84 wrote: Bunuel wrote: How many possible integer values are there for x if 4x  3 < 6 ?
A. One B. Two C. Three D. Four E. Five
\(4x  3 < 6\);
Get rid of the modulus: \(6<4x3< 6\);
Add 3 to all three parts: \(3<4x< 9\);
Divide by 4: \(\frac{3}{4}<x< \frac{9}{4}\) > \(0.75<x< 2.25\).
x can take following integer values: 0, 1, and 2.
Answer: C. @Bunuel  The question stems talks about how many positive integer values of x. IF we are talking about positive integer then it should be only {1,2} and not {0). Am I missing anything here? The question does not specify that the integers must be positive: "how many possible integer values are there for x..." Hope it's clear. Ahh..my mistake.... Read the question wrong.



Current Student
Status: DONE!
Joined: 05 Sep 2016
Posts: 372

Re: How many possible integer values are there for x if 4x  3
[#permalink]
Show Tags
31 Oct 2016, 13:59
You can figure this out by taking the equation and solving:
SCENARIO 1: (4x  3) < 6 4x<9 x<(9/4)
SCENARIO 2: (4x  3) > 6 4x>3 x>(3/4)
So (0.75)<x<2.25 > The only integers within this range are 0,1,2 > Hence, 3 is the correct answer (C)



Intern
Joined: 06 May 2017
Posts: 5

Re: How many possible integer values are there for x if 4x  3
[#permalink]
Show Tags
11 Sep 2017, 21:33
Hi, I think answer will be B. We can get 1,2 .zero is neither positive or negative and question is asking for positive values only.
PS Any number to the left of zero on a number line; can be integer or noninteger. Note: The number zero is neither positive nor negative
Posted from my mobile device



Math Expert
Joined: 02 Sep 2009
Posts: 55271

Re: How many possible integer values are there for x if 4x  3
[#permalink]
Show Tags
11 Sep 2017, 21:36
paritesh wrote: Hi, I think answer will be B. We can get 1,2 .zero is neither positive or negative and question is asking for positive values only.
PS Any number to the left of zero on a number line; can be integer or noninteger. Note: The number zero is neither positive nor negative
Posted from my mobile device Please read carefully. The question does not specify that the integers must be positive: "how many possible integer values are there for x..." P.S. This doubt is already addressed above. Please read the whole thread before posting. Thank you.
_________________



Intern
Joined: 06 May 2017
Posts: 5

Re: How many possible integer values are there for x if 4x  3
[#permalink]
Show Tags
11 Sep 2017, 21:41
Thanks,I got it I didn't read the question properly
Posted from my mobile device



Manager
Joined: 12 Feb 2017
Posts: 70

Re: How many possible integer values are there for x if 4x  3
[#permalink]
Show Tags
11 Sep 2017, 22:58
4x  3 < 6 remove the modulus Case 1) 4x3 <6 4x<9 x<9/4 x<2.25
Case 2) (4x6)<6 4x3>6 4x>3 x>3/4 x>0.75 Hence 0.75 < x < 2.25
Therefore only possible values for x are 0,1,2.
Hence Option C.
Kudos if it helps.



Senior Manager
Joined: 15 Jan 2017
Posts: 351

Re: How many possible integer values are there for x if 4x  3
[#permalink]
Show Tags
25 Nov 2017, 03:30
Bunuel wrote: How many possible integer values are there for x if 4x  3 < 6 ?
A. One B. Two C. Three D. Four E. Five
\(4x  3 < 6\);
Get rid of the modulus: \(6<4x3< 6\);
Add 3 to all three parts: \(3<4x< 9\);
Divide by 4: \(\frac{3}{4}<x< \frac{9}{4}\) > \(0.75<x< 2.25\).
x can take following integer values: 0, 1, and 2.
Answer: C. Hi! Why is zero seen as an integer here? I understand 1,2 but zero isn't counted as an integer. Please correct my understanding. Thank you!



Math Expert
Joined: 02 Sep 2009
Posts: 55271

Re: How many possible integer values are there for x if 4x  3
[#permalink]
Show Tags
25 Nov 2017, 04:11
Madhavi1990 wrote: Bunuel wrote: How many possible integer values are there for x if 4x  3 < 6 ?
A. One B. Two C. Three D. Four E. Five
\(4x  3 < 6\);
Get rid of the modulus: \(6<4x3< 6\);
Add 3 to all three parts: \(3<4x< 9\);
Divide by 4: \(\frac{3}{4}<x< \frac{9}{4}\) > \(0.75<x< 2.25\).
x can take following integer values: 0, 1, and 2.
Answer: C. Hi! Why is zero seen as an integer here? I understand 1,2 but zero isn't counted as an integer. Please correct my understanding. Thank you! ZERO:1. 0 is an integer.2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even. 3. 0 is neither positive nor negative integer (the only one of this kind). 4. 0 is divisible by EVERY integer except 0 itself. Brush up fundamentals before attempting questions: ALL YOU NEED FOR QUANT ! ! !Ultimate GMAT Quantitative MegathreadHope it helps.
_________________



SVP
Status: It's near  I can see.
Joined: 13 Apr 2013
Posts: 1675
Location: India
Concentration: International Business, Operations
GPA: 3.01
WE: Engineering (Real Estate)

Re: How many possible integer values are there for x if 4x  3
[#permalink]
Show Tags
12 Mar 2018, 06:07
cpcalanoc wrote: How many possible integer values are there for x if 4x  3 < 6 ? A. One B. Two C. Three D. Four E. Five What I did here was to separate two scenarios: a. 4x – 3 < 6 and b. 4x – 3 >  6
I simplified x in both scenarios that I ended up in a range of 2.25 < x < .75 Therefore, my answer is 3 integers (2, 1, 0)
I would like to know if this method is correct and if I should use such method for problems that involve absolute value and inequality. Question: Number of possible values of x which are integer? Given: 4x  3 < 6 6+3 < 4x < 6+3 3/4 < x < 9/4 0.75 < x < 2.25 values are 0, 1, 2 (Three integer values) (C)
_________________
"Do not watch clock; Do what it does. KEEP GOING."



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6239
Location: United States (CA)

Re: How many possible integer values are there for x if 4x  3
[#permalink]
Show Tags
13 Mar 2018, 16:54
cpcalanoc wrote: How many possible integer values are there for x if 4x  3 < 6 ?
A. One B. Two C. Three D. Four E. Five We can first solve when the expression (4x  3) is positive: 4x  3 < 6 4x < 9 x < 9/4 = 2 ¼ Now we can solve when the expression (4x  3) is negative: (4x  3) < 6 4x + 3 < 6 4x < 3 x > 3/4 Thus: 3/4 < x < 2 1/4 So x can be any of 3 integer values: 0, 1, or 2. Answer: C
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.




Re: How many possible integer values are there for x if 4x  3
[#permalink]
13 Mar 2018, 16:54



Go to page
1 2
Next
[ 21 posts ]



