Oct 22 09:00 AM PDT  10:00 AM PDT Watch & learn the Do's and Don’ts for your upcoming interview Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions) Oct 23 08:00 AM PDT  09:00 AM PDT Join an exclusive interview with the people behind the test. If you're taking the GMAT, this is a webinar you cannot afford to miss! Oct 26 07:00 AM PDT  09:00 AM PDT Want to score 90 percentile or higher on GMAT CR? Attend this free webinar to learn how to prethink assumptions and solve the most challenging questions in less than 2 minutes. Oct 27 07:00 AM EDT  09:00 AM PDT Exclusive offer! Get 400+ Practice Questions, 25 Video lessons and 6+ Webinars for FREE.
Author 
Message 
TAGS:

Hide Tags

Current Student
Joined: 27 Apr 2010
Posts: 100

For any integers x and y, min(x, y) and max(x, y) denote the
[#permalink]
Show Tags
29 May 2010, 13:23
Question Stats:
56% (01:36) correct 44% (01:36) wrong based on 2391 sessions
HideShow timer Statistics
For any integers x and y, min(x, y) and max(x, y) denote the minimum and the maximum of x and y, respectively. For example, min (5, 2) = 2 and max(5, 2) = 5. For the integer w, what is the value of min(10, w) ? (1) w = max(20, z) for some integer z. (2) w = max(10, w)
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 58421

Re: OG12 DS #115
[#permalink]
Show Tags
29 May 2010, 13:52
snkrhed wrote: For any integers x and y, min(x, y) and max(x, y) denote the minimum and the maximum of x and y, respectively. For example, min (5, 2) = 2 and max(5, 2) = 5. For the integer w, what is the value of min(10, w) ?
(1) w = max(20, z) for some integer z. (2) w = max(10, w) If \(w\geq{10}\), then \(min(10,w)=10\). If \(w<10\), then \(min(10,w)=w\) and for statement(s) to be sufficient we should be able to get single value of \(w\). (1) \(w = max(20, z)\) > \(w\geq{20}\), hence \(w\geq{10}\), so \(min(10,w)=10\). Sufficient. (2) \(w = max(10, w)\) > \(w\geq{10}\), hence \(min(10,w)=10\). Sufficient. Answer: D. Hope it's clear.
_________________




Intern
Joined: 14 Sep 2010
Posts: 12

Re: For any integers x and y, min(x, y) and Max(x, y) denote
[#permalink]
Show Tags
14 Jan 2012, 04:11
For the integer w, what is the value of min (10, w)?
1) w = max (20, z) for some integer z
2) w = max (10, w)
Min (x,y) or max (x, y) is a selection from x and y.
When x = y, min (x,y) and max (x,y) are the same. Therefore, min (10, w) = 10, if w = 10.
We can also deduce that min (10, w) = 10, if w > 10.
(1) w = max (20, z).
Consider RHS. Variable z, Max can be (a) 20, (b) z (if z > 20) or (c) both.
(a): z < 20. Max(20,z) = 20. w = 20. (b): z > 20. Max(20,z) = z. w > 20. (c): z = 20. Max(20,z) = 20. w = 20.
All values for w are greater than 10. Min (10, w) is 10.
2) w = max (10, w).
w is the maximum value of a set that includes 10. Therefore, all values for w are at least 10 and min (10,w) cannot be below 10.
Posted from my mobile device




Current Student
Joined: 27 Apr 2010
Posts: 100

Re: OG12 DS #115
[#permalink]
Show Tags
29 May 2010, 14:24
If \(w\geq{10}\), then \(min(10,w)=10\). If \(w<10\), then \(min(10,w)=w\) and for statement(s) to be sufficient we should be able to get single value of \(w\).
Can you explain how you deduced this part?



Math Expert
Joined: 02 Sep 2009
Posts: 58421

Re: OG12 DS #115
[#permalink]
Show Tags
29 May 2010, 14:43
snkrhed wrote: If \(w\geq{10}\), then \(min(10,w)=10\). If \(w<10\), then \(min(10,w)=w\) and for statement(s) to be sufficient we should be able to get single value of \(w\).
Can you explain how you deduced this part? The question is \(min(10,w)=?\) Basically the question is: what is the value of least number between \(10\) and \(w\)? Now if \(w\geq{10}\), for instance if \(w=11\), then \(min(10,11)=10\). But if \(w<10\), for instance \(w=9\), then \(min(10,9)=9=w\). (1) \(w = max(20, z)\) > \(max(20, z)=20=w\). when \(z\leq{20}\), so \(w=20>10\) and \(min(10,w)=10\) or \(max(20, z)=z=w\). when \(z>{20}\), so \(w=z>10\) and again \(min(10,w)=10\). Sufficient. (2) \(w = max(10, w)\) > directly tells us that \(w\geq{10}\), hence \(min(10,w)=10\). Sufficient. Answer: D. Hope it's clear.
_________________



Manager
Joined: 21 Feb 2010
Posts: 168

something wrong here?
[#permalink]
Show Tags
20 Jul 2010, 20:22
hello all, this is the question.. for any integers x and y. min(x, y) and max (x, y) denote the minimum and maximum of x and y, respectively. for example, min (5, 2) = 2 and max (5, 2) = 5. for the integer w, what is the value of min (10, w)? 1) w = max ( 20, z) and some integer z. 2) w = max (10, w) explanation: of w is greater than or equals to 10, then min ( 10, w) = 10, and if w is less than 10, then min (10, w) = w. therefore, the value of min (10, w) can be determined if the value of w can be determined. 1) given that w = max (20, z), then w is greater than or equals to 20. hence, w is greater than or equals to 10, and so min ( 10, w) =10, sufficient. 2) given that w = max ( 10, w ), then w is greater than or equals to 10, and so min ( 10, w) = 10, sufficient
i wonder if the z on the first statement is a typo because there are 2 unknown variables in the 1st statement, and how does it get w is greater than or equals to 20 since z is unknown? is it possible that the Z in the statement is a typo and should be W? please comment! thanks!



Manager
Joined: 05 Oct 2011
Posts: 149

Re: For any integers x and y, min(x, y) and Max(x, y) denote
[#permalink]
Show Tags
30 Nov 2011, 13:42
Statement 1 has nice trap built in to catch us under time pressure.
rephrased question is Is \(w\geq10\)? (1) Gives \(w\geq20\) Sufficient. (2) Gives \(w\geq 10\) Sufficient



Intern
Joined: 03 Oct 2009
Posts: 46

Re: For any integers x and y, min(x, y) and Max(x, y) denote
[#permalink]
Show Tags
17 Jan 2012, 20:19
For any integers x and y, min(x, y) and Max(x, y) denote the minimum and the maximum of x and y, respectively. For example, min (5, 2) = 2 and max (5, 2) = 5. For the integer w, what is the value of min(10, w)?
(1) w = max(20, z) for some integer z
Min value of w will be 20.
min(10, w) will be 10
Sufficient
(2) w = max(10, w)
Min value of w will be 10.
min(10, w) will be 10
Sufficient



Manager
Joined: 14 Aug 2012
Posts: 78
Location: United States
GMAT 1: 620 Q43 V33 GMAT 2: 690 Q47 V38

Re: For any integers x and y, min(x, y) and Max(x, y) denote
[#permalink]
Show Tags
27 Aug 2012, 15:34
Thanks for the explanation, I had trouble wrapping my head with the OG explanation but finally got it. Given statement 1, it doesn't matter what the max of 20 or z is it will be at least 20, making 10 the min.



Intern
Joined: 02 Aug 2012
Posts: 10

Re: For any integers x and y, min(x, y) and Max(x, y) denote
[#permalink]
Show Tags
19 Dec 2012, 14:04
Bunuel wrote: icaniwill wrote: Statement 1 has nice trap built in to catch us under time pressure.
rephrased question is Is \(w\geq10\)? (1) Gives \(w\geq20\) Sufficient. (2) Gives \(w\geq 10\) Sufficient Merging similar topics. Please ask if anything remains unclear. I am confused about the rephrasing of the question. I thought that Min (10,10) was not a valid answer. Does there have to be a range greater than zero between the min and max?



Math Expert
Joined: 02 Sep 2009
Posts: 58421

Re: For any integers x and y, min(x, y) and Max(x, y) denote
[#permalink]
Show Tags
20 Dec 2012, 04:40
jogorhu wrote: Bunuel wrote: icaniwill wrote: Statement 1 has nice trap built in to catch us under time pressure.
rephrased question is Is \(w\geq10\)? (1) Gives \(w\geq20\) Sufficient. (2) Gives \(w\geq 10\) Sufficient Merging similar topics. Please ask if anything remains unclear. I am confused about the rephrasing of the question. I thought that Min (10,10) was not a valid answer. Does there have to be a range greater than zero between the min and max? \(min(10,w)=10\) when \(w\geq{10}\); \(min(10,w)=w\) when \(w<10\) As for your other question: min(10,10)=10 and max(10,10)=10 too. Hope it's clear.
_________________



Math Expert
Joined: 02 Sep 2009
Posts: 58421

Re: For any integers x and y, min(x, y) and max(x, y) denote the
[#permalink]
Show Tags
14 Jun 2013, 04:05
Bumping for review and further discussion*. Get a kudos point for an alternative solution! *New project from GMAT Club!!! Check HERE
_________________



Manager
Joined: 11 Jul 2016
Posts: 78

For any integers x and y, min(x, y) and max(x, y) denote the
[#permalink]
Show Tags
11 Oct 2016, 09:02
Bunuel wrote: snkrhed wrote: If \(w\geq{10}\), then \(min(10,w)=10\). If \(w<10\), then \(min(10,w)=w\) and for statement(s) to be sufficient we should be able to get single value of \(w\).
Can you explain how you deduced this part? The question is \(min(10,w)=?\) Basically the question is: what is the value of least number between \(10\) and \(w\)? Now if \(w\geq{10}\), for instance if \(w=11\), then \(min(10,11)=10\). But if \(w<10\), for instance \(w=9\), then \(min(10,9)=9=w\). (1) \(w = max(20, z)\) > \(max(20, z)=20=w\). when \(z\leq{20}\), so \(w=20>10\) and \(min(10,w)=10\) or \(max(20, z)=z=w\). when \(z>{20}\), so \(w=z>10\) and again \(min(10,w)=10\). Sufficient. (2) \(w = max(10, w)\) > directly tells us that \(w\geq{10}\), hence \(min(10,w)=10\). Sufficient. Answer: D. Hope it's clear. From (1) ; w = max (20, z), then w is greater than or equals to 20. How we have reached at this conclusion ? We don't know what is the value of z then how we can determine the max value of w ?Is it because max(5, 2) = 5 as given in the Q stem ? (i.e. selecting first value from the equation)



Math Expert
Joined: 02 Sep 2009
Posts: 58421

Re: For any integers x and y, min(x, y) and max(x, y) denote the
[#permalink]
Show Tags
11 Oct 2016, 09:32
Manonamission wrote: Bunuel wrote: snkrhed wrote: If \(w\geq{10}\), then \(min(10,w)=10\). If \(w<10\), then \(min(10,w)=w\) and for statement(s) to be sufficient we should be able to get single value of \(w\).
Can you explain how you deduced this part? The question is \(min(10,w)=?\) Basically the question is: what is the value of least number between \(10\) and \(w\)? Now if \(w\geq{10}\), for instance if \(w=11\), then \(min(10,11)=10\). But if \(w<10\), for instance \(w=9\), then \(min(10,9)=9=w\). (1) \(w = max(20, z)\) > \(max(20, z)=20=w\). when \(z\leq{20}\), so \(w=20>10\) and \(min(10,w)=10\) or \(max(20, z)=z=w\). when \(z>{20}\), so \(w=z>10\) and again \(min(10,w)=10\). Sufficient. (2) \(w = max(10, w)\) > directly tells us that \(w\geq{10}\), hence \(min(10,w)=10\). Sufficient. Answer: D. Hope it's clear. From (1) ; w = max (20, z), then w is greater than or equals to 20. How we have reached at this conclusion ? We don't know what is the value of z then how we can determine the max value of w ?Is it because max(5, 2) = 5 as given in the Q stem ? (i.e. selecting first value from the equation) No. max(x, y) denote the maximum of x and y. (1) says that \(w = max(20, z)\), so w (the maximum of 20 and z) is 20 if z<=20 or w = z if z>20. Thus, in any case, \(w\geq{20}\).
_________________



Manager
Joined: 18 Oct 2016
Posts: 130
Location: India
WE: Engineering (Energy and Utilities)

Re: For any integers x and y, min(x, y) and max(x, y) denote the
[#permalink]
Show Tags
28 Dec 2016, 00:08
Option D)Min (10,W) ? I: For any integer Z, W = Max (20,Z) : Min (10,W) = Min (10, Max(20,Z)) = Min (10, > 20) = 10 : Sufficient II: W = Max (10,W) : Min (10,W) = Min (10, Max (10,W)) = Min (10, > 10) = 10 : Sufficient
_________________



GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4015
Location: Canada

Re: For any integers x and y, min(x, y) and max(x, y) denote the
[#permalink]
Show Tags
01 Sep 2017, 16:05
snkrhed wrote: For any integers x and y, min(x, y) and max(x, y) denote the minimum and the maximum of x and y, respectively. For example, min (5, 2) = 2 and max(5, 2) = 5. For the integer w, what is the value of min(10, w) ?
(1) w = max(20, z) for some integer z. (2) w = max(10, w) Target question: What is the value of min(10, w)?Statement 1: w = max(20, z) for some integer z. Let's take a closer look at max(20, z) If z < 20, then max(20, z) = 20 If z > 20, then max(20, z) = some value greater than 20 So, max(20, z) must be greater than or equal to 20 Since, w = max(20, z), we can conclude that w is greater than or equal to 20From this, we can conclude that min(10, w) = 10, since 10 will be the lesser value Since we can answer the target question with certainty, statement 1 is SUFFICIENT Statement 2: w = max(10, w) If w = max(10, w), then w is the larger value. In other words, w is greater than or equal to 10If w is greater than or equal to 10, then we can conclude that min(10, w) = 10Since we can answer the target question with certainty, statement 2 is SUFFICIENT Answer: Cheers, Brent
_________________
Test confidently with gmatprepnow.com



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9704
Location: Pune, India

Re: For any integers x and y, min(x, y) and max(x, y) denote the
[#permalink]
Show Tags
16 Jan 2018, 05:05
Check out our detailed video solution to this problem here: https://www.veritasprep.com/gmatsoluti ... ciency_374
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Intern
Joined: 19 Jun 2019
Posts: 2

Re: For any integers x and y, min(x, y) and max(x, y) denote the
[#permalink]
Show Tags
03 Aug 2019, 04:01
Min(10,w) = ?
 Stat 1: if z<20, w=20 and min(10,20) is 10; if z>20, w>20 and min(10, somethinggreaterthan20) is 10  Stat 2: if w>10 then min(10,somethinggreaterthan10) is 10. If w<10, w=10 and min(10,10) is 10




Re: For any integers x and y, min(x, y) and max(x, y) denote the
[#permalink]
03 Aug 2019, 04:01






