Source: Official Guide for the GMAT 13th Ed. Data Sufficiency; #118 Official Guide for the GMAT 2015 14th Ed. Data Sufficiency; #118

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

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)

### 2 Explanations

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bilal muzaffar

what is max min kindly explain i am not getting it abit

Apr 26, 2017 • Comment

Cydney Seigerman, Magoosh Tutor

Happy to help, Bilal :)

In this question, min(x, y) refers to the smaller of the two values listed, x and y. On the other hand, max(x, y) refers to the larger of the two values in parenthesis. For that reason, in the example in the prompt, min(5, 2) is equal to 2, the smaller of the two values in parenthesis, while max(5, 2) is equal to 5, the larger of the two values.

With that in mind, min(10, w) will be the smaller of the two values, either 10 or w. And we need to determine if, based on the statements, we can figure out whether 10 or w is smaller.

Statement 1: We're told w = max(20, z). So, w is the larger value in the set 20 and z. While we don't know the value of z, if z is less than 20, we know the maximum value is 20 and therefore w = 20. If z is greater than 20, than z is the maximum value and w = z. In either case, w > 10. So, we know for sure that min(10, w) = 10, since w is greater than 10.

Statement 2: In the case that w=max(10, w), we are told that w is the larger of the two values in parenthesis. So, we know for sure that w > 10. Again, this is enough information to conclude that min(10, w) is 10, since 10 is less than w.

I hope this clears up your doubts about the meaning of max and min in this question :) Mike McGarry, Magoosh Tutor