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

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New post 14 Jan 2012, 03:11
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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: OG-12 DS #115  [#permalink]

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New post 29 May 2010, 13:24
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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]

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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]

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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]

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New post 30 Nov 2011, 12:42
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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]

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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]

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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]

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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]

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New post 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


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]

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

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New post 11 Oct 2016, 08:02
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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)
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Re: For any integers x and y, min(x, y) and max(x, y) denote the  [#permalink]

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New post 11 Oct 2016, 08:32
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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, \(w\geq{20}\).
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Re: For any integers x and y, min(x, y) and max(x, y) denote the  [#permalink]

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

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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)


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 20
From 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 10
If w is greater than or equal to 10, then we can conclude that min(10, w) = 10
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer:

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