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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, 13:23
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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, 13:52
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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] New post   14 Jan 2012, 04:11
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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] New post   29 May 2010, 14:43
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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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Re: For any integers x and y, min(x, y) and max(x, y) denote the [#permalink] New post   19 Dec 2020, 16:34
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Video solution from Quant Reasoning:
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Re: OG-12 DS #115 [#permalink] New post   29 May 2010, 14:24
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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: For any integers x and y, min(x, y) and Max(x, y) denote [#permalink] New post   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?
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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, 04:40
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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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For any integers x and y, min(x, y) and max(x, y) denote the [#permalink] New post   11 Oct 2016, 09:02
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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] New post   11 Oct 2016, 09:32
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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] New post   01 Sep 2017, 16:05
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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:
Show Spoiler
D


Cheers,
Brent
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For any integers x and y, min(x, y) and max(x, y) denote the [#permalink] New post   16 Jan 2018, 05:05
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Check out our detailed video solution to this problem here:

https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#-soluti ... ciency_377

Edited: Updated the link. Looks like we had to renumber the problems when the new OG came out.
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Re: For any integers x and y, min(x, y) and max(x, y) denote the [#permalink] New post   29 Dec 2020, 14:42
Could somebody explain w = max(10, w) expression? It seems recursive, in order to know w, we have to know w first which doesn't make sense
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For any integers x and y, min(x, y) and max(x, y) denote the [#permalink] New post   29 Dec 2020, 16:17
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Exactly. So this equation is definitely not sufficient for us to infer the value of w. However, we still can infer SOMETHING about w. Check out my video solution.

2020prep2020 wrote:
Could somebody explain w = max(10, w) expression? It seems recursive, in order to know w, we have to know w first which doesn't make sense


Posted from my mobile device
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Re: For any integers x and y, min(x, y) and max(x, y) denote the [#permalink] New post   18 Apr 2021, 08:40
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)


The question statement states 2 functions:
1) max(5,10) = This max function represents the maximum value between the two numbers. So, in this case the answer is 10
2) min(5,10) = This min function represents the minimum value between the two numbers. So, in this case the answer is 5.
Now, question is to find the min(10, w):

min(10, w) = 10, when w>10
min(10, w) = w, when w<10
To answer the question, we will have to know if w<10?
1) w = max(20, z)
From this statement, it's clear that w has to be 20 or greater. Why?
If z < 20: max(20,z) = 20. So, min(10, 20) = 10
if z >20: max(20,z) > 20. So, min(10, greater than 20) = 10.
Satisfied
2) w = max(10,w)
From this statement, it's clear that w has to be greater than 10. Why?
min(10, w) = 10 (as, w>10)
Satisfied.
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Re: For any integers x and y, min(x, y) and max(x, y) denote the [#permalink] New post   20 May 2021, 08:06
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)



Beautiful question, man !


(1) \(w = max(20, z)\) for some integer z

here w is either 20 or z. if \(w=20\) then min(w,10) is 10. if w=z, then z has to be >20, thus assume any integer greater than 20, say 50, if \(w=z=50 \) then, \(min (10,w)=min(10,50)=10\)

sufficient.

(2) \(w = max(10, w)\)

this basically tells us \(w>10\), therefore, min (10,w) must be 10. sufficient.

D
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Re: For any integers x and y, min(x, y) and max(x, y) denote the [#permalink] New post   20 May 2021, 09:41
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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)

Solution:

Question Stem Analysis:

We need to determine the value of min(10, w). Notice that if w ≥ 10, then min(10, w) = 10. However, if w < 10, then min(10, w) = w. That is, if w < 10, we need to determine the value of w.

Statement One Alone:

Notice that max(20, z) = 20 if z < 20 and max(20, z) = z if z ≥ 20. In other words, w is at least 20. Since w ≥ 20, w ≥ 10 and hence min(10, w) = 10. Statement one alone is sufficient.

Statement Two Alone:

Notice that max(10, w) = 10 if w < 10 and max(10, w) = w if w ≥ 10. Since w = max(10, w), we see that w ≥ 10 and hence min(10, w) = 10. Statement two alone is sufficient.

Answer: D
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Re: For any integers x and y, min(x, y) and max(x, y) denote the [#permalink] New post   02 Jul 2021, 01:27
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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)


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Re: For any integers x and y, min(x, y) and max(x, y) denote the [#permalink] New post   19 Sep 2021, 05:31
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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) ?

Here , we need to find which is the min value , 10 or w

If w ≥10, then min(10, w) = 10
if w < 10, then min(10, w) = w
So let's try to find whether w ≥10 or w < 10.

(1) w = max(20, z) for some integer z.

Since w is the max(20, z), we can conclude that w can be 20 or a value greater than 20. i.e., w ≥ 20

As w ≥ 20 , min(10, w) = 10

Statement 1 alone is sufficient.

(2) w = max(10, w)

From the above statement, we can conclude that w ≥ 10
As w ≥ 10 , min(10, w) = 10
Statement 2 alone is sufficient.

Option D is the answer.

Hope this helps,
Clifin J Francis,
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Re: For any integers x and y, min(x, y) and max(x, y) denote the [#permalink] New post   28 Sep 2023, 08:16
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