May 20 10:00 PM PDT  11:00 PM PDT Practice the one most important Quant section  Integer Properties, and rapidly improve your skills. May 24 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. 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!
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 55188

Is the range of the integers 6, 3, y, 4, 5, and x greater
[#permalink]
Show Tags
25 Jun 2012, 03:03
Question Stats:
62% (01:48) correct 38% (01:45) wrong based on 1820 sessions
HideShow timer Statistics
Is the range of the integers 6, 3, y, 4, 5, and x greater than 9? (1) y > 3x (2) y > x > 3 Diagnostic Test Question: 32 Page: 25 Difficulty: 650
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Math Expert
Joined: 02 Sep 2009
Posts: 55188

Re: Is the range of the integers 6, 3, y, 4, 5, and x greater
[#permalink]
Show Tags
25 Jun 2012, 03:04
SOLUTIONIs the range of the integers 6, 3, y, 4, 5, and x greater than 9?Given integers are: {3, 4, 5, 6, x, y} (1) y > 3x. If \(x=1\) and \(y=4\) then the range=61=5<9 but if \(x=100\) then the range>9. Not sufficient. (2) y > x > 3. If \(x=4\) and \(y=5\) then the range=63=3<9 but if \(x=100\) then the range>9. Not sufficient. (1)+(2) From \(x > 3\) we have that the least value of \(x\) is 4, and from \(y > 3x=12\) we have that the least value of \(y\) is 13, hence the least value of the range is 133=10>9. Sufficient. Answer: C.
_________________




Current Student
Joined: 29 Mar 2012
Posts: 302
Location: India
GMAT 1: 640 Q50 V26 GMAT 2: 660 Q50 V28 GMAT 3: 730 Q50 V38

Re: Is the range of the integers 6, 3, y, 4, 5, and x greater
[#permalink]
Show Tags
25 Jun 2012, 08:41
Hi,
Range = Largest value  smallest value.
6, 3, y, 4, 5, and x, where x & y are integers
Using (1), y>3x, if x=1, then y = 4, 5,..100.... in each case range can be 5, 6,....So, range is greater than 5. Insufficient.
Using (2), y>x>3. Minimum value of x = 4, y=5,6,7... We can't say whether range is greater than 9.
Combining both statements; \(x_{min} = 4\) & since, y > 3x, \(y_{min}=13,\) thus, 3, 4, 4, 5, 6, & 13 has range (133)=10, which is greater than 9 and on increasing x, range will also increase.
Thus, answer is (C),
Regards,



Math Expert
Joined: 02 Sep 2009
Posts: 55188

Re: Is the range of the integers 6, 3, y, 4, 5, and x greater
[#permalink]
Show Tags
29 Jun 2012, 04:36
SOLUTIONIs the range of the integers 6, 3, y, 4, 5, and x greater than 9?Given integers are: {3, 4, 5, 6, x, y} (1) y > 3x. If \(x=1\) and \(y=4\) then the range=61=5<9 but if \(x=100\) then the range>9. Not sufficient. (2) y > x > 3. If \(x=4\) and \(y=5\) then the range=63=3<9 but if \(x=100\) then the range>9. Not sufficient. (1)+(2) From \(x > 3\) we have that the least value of \(x\) is 4, and from \(y > 3x=12\) we have that the least value of \(y\) is 13, hence the least value of the range is 133=10>9. Sufficient. Answer: C.
_________________



Director
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 685
Location: United States (CA)
Age: 39
GMAT 1: 770 Q47 V48 GMAT 2: 730 Q44 V47 GMAT 3: 750 Q50 V42
WE: Education (Education)

Re: Is the range of the integers 6, 3, y, 4, 5, and x greater
[#permalink]
Show Tags
27 Mar 2016, 19:25
Here is a visual that should help.
Attachments
Screen Shot 20160327 at 7.23.57 PM.png [ 93.38 KiB  Viewed 12281 times ]
_________________
Harvard grad and 99% GMAT scorer, offering expert, private GMAT tutoring and coaching worldwide since 2002. One of the only known humans to have taken the GMAT 5 times and scored in the 700s every time (700, 710, 730, 750, 770), including verified section scores of Q50 / V47, as well as personal bests of 8/8 IR (2 times), 6/6 AWA (4 times), 50/51Q and 48/51V (1 question wrong). You can download my official testtaker score report (all scores within the last 5 years) directly from the Pearson Vue website: https://tinyurl.com/y7knw7bt Date of Birth: 09 December 1979. GMAT Action Plan and Free EBook  McElroy TutoringContact: mcelroy@post.harvard.edu (I do not respond to PMs on GMAT Club.) ...or find me on Reddit: http://www.reddit.com/r/GMATpreparation



Board of Directors
Joined: 17 Jul 2014
Posts: 2555
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: Is the range of the integers 6, 3, y, 4, 5, and x greater
[#permalink]
Show Tags
03 Nov 2016, 06:49
Bunuel wrote: Is the range of the integers 6, 3, y, 4, 5, and x greater than 9? (1) y > 3x (2) y > x > 3 Diagnostic Test Question: 32 Page: 25 Difficulty: 650 pretty easy for a 700 level question... 1. x can be 1, and y can be 4  so the answer is NO x can be 4, and y can be 13  so the answer is YES. 1 alone is insufficient. A and D are out. 2. y>x>3. x can be 4, y =5  answer is no x can be 4, y can be 20  answer is YES. 2 alone is not sufficient. B is out. 1+2. x>3 y>3x minimum value for x is 4. minimum value for y is 13 yes, the range is greater than 9. sufficient. answer is C.



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2823

Re: Is the range of the integers 6, 3, y, 4, 5, and x greater
[#permalink]
Show Tags
29 May 2018, 16:31
Bunuel wrote: Is the range of the integers 6, 3, y, 4, 5, and x greater than 9?
(1) y > 3x (2) y > x > 3 Statement One Alone: y > 3x Statement one is not sufficient to answer the question. For example, if x = 0, y could be 1 and the range is 6  0 = 6, which is less than 9. However, if x = 10, y could be 31 and the range is 31  3 = 28, which is greater than 9. Statement Two Alone: y > x > 3 Statement two is not sufficient to answer the question. For example, if x = 4, y could be 5 and the range is 6  0 = 6, which is less than 9. However, if x = 14, y could be 15 and the range is 15  3 = 12, which is greater than 9. Statements One and Two Together: From the two statements, we know that x > 3 and y > 3x. So the smallest integer x can be is 4 and the smallest integer y can be is 3(4) + 1 = 13. Thus the smallest range of the integers is 13  3 = 10, which is greater 9. Since 10 is the smallest range, any other range of the integers will be greater than 10 and hence greater than 9. 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.



Intern
Joined: 13 Jul 2018
Posts: 11
Concentration: International Business, General Management

Re: Is the range of the integers 6, 3, y, 4, 5, and x greater
[#permalink]
Show Tags
12 Sep 2018, 10:35
In the solution of these questions it is not asked to take minimum value and x and y can take any numbers so why we have solved this by taking minimum values



Senior PS Moderator
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 750
GMAT 1: 740 Q50 V40 GMAT 2: 770 Q51 V42

Re: Is the range of the integers 6, 3, y, 4, 5, and x greater
[#permalink]
Show Tags
16 Oct 2018, 00:05
arpitalewe wrote: In the solution of these questions it is not asked to take minimum value and x and y can take any numbers so why we have solved this by taking minimum values Hi arpitalewe, Welcome to the GMAT Club! So the logic behind trying to take the minimum permissible values for x and y is: we want to see if the minimum permissible value of y is such that range of the given set is greater than 9. If for minimum value this condition holds then for all other values it will hold as well.Hope this solves your doubt. Let me know if you need further clarification or if the above solutions make sense with the above logic. Regards, Gladi
_________________
Regards, Gladi
“Do. Or do not. There is no try.”  Yoda (The Empire Strikes Back)



Director
Joined: 19 Oct 2013
Posts: 511
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)

Is the range of the integers 6, 3, y, 4, 5, and x greater
[#permalink]
Show Tags
16 Oct 2018, 00:28
Statement 1) y > 3x if x = 1 then y must be at least 4 but we cannot tell any further. 61 = 5 > 9 no. If x = 5 y must be at least 16. 16  3 = 13 > 9 yes Insufficient. Statement 2) y > x > 3 we can try the x = 4 and y = 5 we get an answer 63 = 3 > 9 no. Try x = 4 y = 16, 163 = 13 > 9 yes. Insufficient. Now combine (1 and 2) If x = 4 then y at least 13 (given that we took the minimum possible value for x) 13  3 = 10 > 9 Try x = 10 then y at least 31 31  3 = 28 > 9 Sufficient. Answer choice C arpitalewe check the above solution it might help. Also as Gladiator59 explained that the logic is to test if the minimum value satisfies the condition (range > 9) then the maximum will satisfy it too since y > 3x Posted from my mobile device




Is the range of the integers 6, 3, y, 4, 5, and x greater
[#permalink]
16 Oct 2018, 00:28






