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

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For any integers x and y, min(x, y) and max(x, y) denote the [#permalink] New post 29 May 2010, 12:23
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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)
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Re: OG-12 DS #115 [#permalink] New post 29 May 2010, 12:52
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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.
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Re: OG-12 DS #115 [#permalink] New post 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?
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Re: OG-12 DS #115 [#permalink] New post 29 May 2010, 13:43
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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.
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something wrong here? [#permalink] New post 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!
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Re: For any integers x and y, min(x, y) and Max(x, y) denote [#permalink] New post 30 Nov 2011, 12:42
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
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Re: For any integers x and y, min(x, y) and Max(x, y) denote [#permalink] New post 14 Jan 2012, 03:11
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.

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


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?
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Re: For any integers x and y, min(x, y) and Max(x, y) denote [#permalink] New post 20 Dec 2012, 03:40
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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.
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Re: For any integers x and y, min(x, y) and max(x, y) denote the [#permalink] New post 14 Jun 2013, 03:05
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Re: For any integers x and y, min(x, y) and max(x, y) denote the   [#permalink] 14 Jun 2013, 03:05
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