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Can someone explain how to do this prob

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Can someone explain how to do this prob

by ashblog02 » Sat Nov 06, 2010 7:08 pm
Can anyone explain this prob OG prob 115

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)

In option 1 does it mean z is 10? and 20 is w?I cnt seem to understand the correlation?

Thanks for the help
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by wilson4mba » Sat Nov 06, 2010 8:28 pm
w = max(20,z) will give w >= 20 for any z lets say 1,2 or 30,40. hence min (10.w) will be 10 hence the statement is sufficient.

w=max(10,w) to satisfy this condition we need w >=10 hence min (10,w) will be 10 hence the statement is sufficient.

answer is D
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by goyalsau » Sun Nov 07, 2010 2:47 am
ashblog02 wrote:Can anyone explain this prob OG prob 115

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)

In option 1 does it mean z is 10? and 20 is w?I cnt seem to understand the correlation?

Thanks for the help
in I) statement
If we consider the value of z as 1 to 19 value of then w = 20 { in this case answer of the question is 10 }
If we consider the value of z as 21 to ..... then w = 21 or 21 + { in this case answer is 10 as well }

In both the case answer is 10,
so it should be D

as II statement will also lead to 10 as the answer
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by Geva@EconomistGMAT » Sun Nov 07, 2010 5:35 am
I think this is one of those problems when putting the concept in words helps you make sense. your focus is on the value of min(10, w), or in words "what is the minimum value of w and 10?" This allows two scenarios:
a. if w is greater than 10, then the minimum value of 10,w is simply 10 - only a single value.
b. if w is smaller than 10, life is a bit more complicated - the minimum value of 10,w will be w, and then we need to know if w has a single value or not.

the main idea from stat. (1) is that w is the maximum of 20 and z. You don't know the value of z. Nor do you particularly care: whatever z is, w is the maximum of z and 20.
If z is smaller than 20, then w (being the maximum) will be 20.
If z is greater than 20, then w will equal z - which will be greater than 20.

It follows that whatever the value of w is, it has to be 20 or greater. Going back to our two scenarios, we now effectively know that w is greater than 20 - which means that the answer to the question "what is the minimum value of w and 10) is 10, regardless of the real value of w. Thus, stat. (1) is sufficient.
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