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

[aspirant2011]

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) for some integer z
2) w=max(10,w)

[spoiler]OA: Will be put later. I am unable to understand OG explanation. Can someone explain the above problem in a more easy way[/spoiler]

[pemdas]

we need to find minimum value out of (10,w) means w can be <,> 10. If w>10 then min(w,10)=10. If w<10, then min(w,10)=w
statement(1) says that w is maximum value out of (20 and some integer z) which means that w is either greater than 20 in this case max(20,z)=z or w is less than 20 and max(20,z)=20. In any way max(20,z)>=20 and 20>10 So min(10,w)=10 Sufficient
statement(2) w=max(10,w) can be interpreted as w>10 since w is maximum value. So min(10,w)=10 Sufficient

hence d

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) for some integer z
2) w=max(10,w)

[spoiler]OA: Will be put later. I am unable to understand OG explanation. Can someone explain the above problem in a more easy way[/spoiler]

[Ashley@VeritasPrep]

The idea is that given a pair of numbers x and y (which could be whatever they want), min(x,y) equals the smaller of the two and max(x,y) equals the larger of the two. So min(x,y) will always equal either x or y (whichever one is less), and max(x,y) will also always equal x or y (whichever one is greater). Therefore, from the get-go, we know that the value of min(10,w) will equal either 10 or w -- and it will equal specifically whichever one of those things is less, 10 or w. From there we move on to the statements.

Does that make the question more intelligible... or still confusing?

[aspirant2011]

yup got it, thanks a lot pemdas and ashley

[mcdesty]

I think this question is ambiguous and here is why...
Statement 1 tells us that w =max(20, z) for some integer z.
Isn't it entirely possible that w could equal z or w could equal 20 if we are not told otherwise?
If it is possible to make such a conclusion, statement one will be insufficient and the answer will be B.
I'm not sure what I am missing here...

[Anurag@Gurome]

Statement 1 tells us that w =max(20, z) for some integer z.
Isn't it entirely possible that w could equal z or w could equal 20 if we are not told otherwise?
If it is possible to make such a conclusion, statement one will be insufficient and the answer will be B.

The following cases are possible,

• 20 > z ---> w = max(20, z) = 20
  20 = z ---> w = max(20, z) = 20
  20 < z ---> w = max(20, z) = z > 20

In all the possible cases w > 10
Hence, min(10, w) = 10

Hope that helps.

[Gaurav 2013-fall]

Good question. Thanks for posting!

[mcdesty]

Statement 1 tells us that w =max(20, z) for some integer z.
Isn't it entirely possible that w could equal z or w could equal 20 if we are not told otherwise?
If it is possible to make such a conclusion, statement one will be insufficient and the answer will be B.

The following cases are possible,

• 20 > z ---> w = max(20, z) = 20
  20 = z ---> w = max(20, z) = 20
  20 < z ---> w = max(20, z) = z > 20

In all the possible cases w > 10
Hence, min(10, w) = 10

Thank you! Looks very easy but a little tricky I guess..

[Scott@TargetTestPrep]

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) for some integer z
2) w=max(10,w)

[spoiler]OA: Will be put later. I am unable to understand OG explanation. Can someone explain the above problem in a more easy way[/spoiler]

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