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

Question

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)

(1) w = max(20, z) for some integer z.
(2) w = max(10, w)

Bunuel · Accepted Answer

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.

Study1 · Answer

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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Bunuel · Answer

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.

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=xBG3j-gQvxA

snkrhed · Answer

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?

jogorhu · Answer

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?

Bunuel · Answer

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.

Manonamission · Answer

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)

Bunuel · Answer

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} .

BrentGMATPrepNow · Answer

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:  D

Cheers,
Brent

KarishmaB · Answer

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.

2020prep2020 · Answer

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

avigutman · Answer

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.

Posted from my mobile device

Showmeyaa · Answer

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.

ueh55406 · Answer

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

ScottTargetTestPrep · Answer

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

GMATinsight · Answer

Answer: Option D

Video solution by  GMATinsight

https://www.youtube.com/watch?v=AAQ6WVzpt3M

CrackverbalGMAT · Answer

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)

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,
GMAT SME

SmileAndSolve · Answer

For A: w = max(20,z)
either 20 = max --> w = 20 --> min(10,w) =10
or z = max --> w >20 --> min(10,w) = 10
Either way, in(10,w)= 10

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

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