For any integers x and y, min(x, y) and max(x, y) denote the : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 24 Jan 2017, 18:16

### 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

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# For any integers x and y, min(x, y) and max(x, y) denote the

Author Message
TAGS:

### Hide Tags

Manager
Joined: 27 Apr 2010
Posts: 122
Followers: 0

Kudos [?]: 79 [3] , given: 61

For any integers x and y, min(x, y) and max(x, y) denote the [#permalink]

### Show Tags

29 May 2010, 12:23
3
KUDOS
33
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

50% (02:12) correct 50% (01:08) wrong based on 1447 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)
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 36638
Followers: 7106

Kudos [?]: 93670 [12] , given: 10583

### Show Tags

29 May 2010, 12:52
12
KUDOS
Expert's post
13
This post was
BOOKMARKED
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.

Hope it's clear.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 36638
Followers: 7106

Kudos [?]: 93670 [3] , given: 10583

### Show Tags

29 May 2010, 13:43
3
KUDOS
Expert's post
4
This post was
BOOKMARKED
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.

Hope it's clear.
_________________
Manager
Joined: 05 Oct 2011
Posts: 171
Followers: 9

Kudos [?]: 51 [2] , given: 62

Re: For any integers x and y, min(x, y) and Max(x, y) denote [#permalink]

### Show Tags

30 Nov 2011, 12:42
2
KUDOS
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: 14 Sep 2010
Posts: 22
Followers: 0

Kudos [?]: 12 [1] , given: 4

Re: For any integers x and y, min(x, y) and Max(x, y) denote [#permalink]

### Show Tags

14 Jan 2012, 03:11
1
KUDOS
2
This post was
BOOKMARKED
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
Manager
Joined: 27 Apr 2010
Posts: 122
Followers: 0

Kudos [?]: 79 [0], given: 61

### Show Tags

29 May 2010, 13:24
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?
Manager
Joined: 21 Feb 2010
Posts: 212
Followers: 1

Kudos [?]: 29 [0], given: 1

### Show Tags

20 Jul 2010, 19:22
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: 03 Oct 2009
Posts: 62
Followers: 0

Kudos [?]: 101 [0], given: 8

Re: For any integers x and y, min(x, y) and Max(x, y) denote [#permalink]

### Show Tags

17 Jan 2012, 19:19
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
Intern
Joined: 14 Aug 2012
Posts: 5
Followers: 0

Kudos [?]: 1 [0], given: 0

Re: For any integers x and y, min(x, y) and Max(x, y) denote [#permalink]

### Show Tags

27 Aug 2012, 14:34
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: 19
Followers: 0

Kudos [?]: 8 [0], given: 22

Re: For any integers x and y, min(x, y) and Max(x, y) denote [#permalink]

### Show Tags

19 Dec 2012, 13:04
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

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: 36638
Followers: 7106

Kudos [?]: 93670 [0], given: 10583

Re: For any integers x and y, min(x, y) and Max(x, y) denote [#permalink]

### Show Tags

20 Dec 2012, 03:40
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

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: 36638
Followers: 7106

Kudos [?]: 93670 [0], given: 10583

Re: For any integers x and y, min(x, y) and max(x, y) denote the [#permalink]

### Show Tags

14 Jun 2013, 03:05
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

All DS Min/Max Problems to practice: search.php?search_id=tag&tag_id=42
All PS Min/Max Problems to practice: search.php?search_id=tag&tag_id=63

_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13550
Followers: 578

Kudos [?]: 163 [0], given: 0

Re: For any integers x and y, min(x, y) and max(x, y) denote the [#permalink]

### Show Tags

06 Aug 2014, 10:07
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13550
Followers: 578

Kudos [?]: 163 [0], given: 0

Re: For any integers x and y, min(x, y) and max(x, y) denote the [#permalink]

### Show Tags

14 Aug 2015, 07:35
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13550
Followers: 578

Kudos [?]: 163 [0], given: 0

Re: For any integers x and y, min(x, y) and max(x, y) denote the [#permalink]

### Show Tags

22 Aug 2016, 02:23
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Manager
Joined: 11 Jul 2016
Posts: 86
Followers: 0

Kudos [?]: 10 [0], given: 83

For any integers x and y, min(x, y) and max(x, y) denote the [#permalink]

### Show Tags

11 Oct 2016, 08:02
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.

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: 36638
Followers: 7106

Kudos [?]: 93670 [0], given: 10583

Re: For any integers x and y, min(x, y) and max(x, y) denote the [#permalink]

### Show Tags

11 Oct 2016, 08:32
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.

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, $$w\geq{20}$$.
_________________
Intern
Joined: 23 Sep 2011
Posts: 20
Followers: 0

Kudos [?]: 16 [0], given: 26

For any integer x and y, min (x,y) and max (x,y) [#permalink]

### Show Tags

27 Dec 2016, 11:54
For any integer 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) max (10,W)
Math Expert
Joined: 02 Sep 2009
Posts: 36638
Followers: 7106

Kudos [?]: 93670 [0], given: 10583

Re: For any integers x and y, min(x, y) and max(x, y) denote the [#permalink]

### Show Tags

27 Dec 2016, 11:58
interceptor77 wrote:
For any integer 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) max (10,W)

Merging topics. Please refer to the discussion above.
_________________
Intern
Joined: 18 Oct 2016
Posts: 39
Location: India
WE: Engineering (Energy and Utilities)
Followers: 0

Kudos [?]: 13 [0], given: 69

Re: For any integers x and y, min(x, y) and max(x, y) denote the [#permalink]

### Show Tags

27 Dec 2016, 23:08
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
_________________

Press Kudos if you liked the post!

Re: For any integers x and y, min(x, y) and max(x, y) denote the   [#permalink] 27 Dec 2016, 23:08
Similar topics Replies Last post
Similar
Topics:
6 If x + y is an integer, is y an integer? 10 01 Mar 2012, 07:39
19 If y is an integer and y = |x| + x, is y = 0? 8 21 Feb 2012, 21:07
7 If y is an integer and y=|x|+x, is y=0? 19 14 Dec 2010, 21:03
If denotes a mathematical operation, does x y=y x for all x 3 01 Apr 2010, 11:33
7 If x + y is an integer, is y an integer? 4 26 Jul 2008, 09:30
Display posts from previous: Sort by