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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]

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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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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.

Hope it's clear.
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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?

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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.

Hope it's clear.
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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!

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

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30 Nov 2011, 13:42
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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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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: For any integers x and y, min(x, y) and Max(x, y) denote [#permalink]

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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

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

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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.

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

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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

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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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

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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14 Jun 2013, 04:05
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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

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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.

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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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.

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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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
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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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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

[Reveal] Spoiler:
D

Cheers,
Brent
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Re: For any integers x and y, min(x, y) and max(x, y) denote the   [#permalink] 01 Sep 2017, 16:05
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