OG 12 | VICs

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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)

Please explain statement 1. I did not get it.

[das.ashmita]

Hi Nishat

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

According to this sentence

if z<20 say 19 ,
then w = 20

if z>20 say 21 ,
then w = z = 21

Since we dont know the exact value of z, we cant determine the value of w.
But as per both cases, w is at least 20.
Therefore min(10,w) = 10

Hence SUFF

(2) w = max(10, w)

As per this statement, w>10

therefore min(10, w) = 10 for all values of 10.
Hence SUFF


ANS D

Hope it helps

[GMATGuruNY]

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)

Please explain statement 1. I did not get it.

The value of min(10,w) is equal to the MINIMUM of 10 and w.
If 10<w, then the MINIMUM of 10 and w is 10.

Statement 1: w = max(20, z) for some integer z.
In other words, w is equal to the MAXIMUM of 20 and z.

Case 1: 20<z
In this case, the MAXIMUM value is z, which is greater than 20 and thus GREATER THAN 10.

Case 2: z≤20
In this case, the MAXIMUM value is 20, which is GREATER THAN 10.

In each case, the MAXIMUM value -- in other words, the value of w -- is GREATER THAN 10.
Thus, w>10.
Since 10<w, min(10,w) = 10.
SUFFICIENT.

Statement 2: w = max(10, w)
Thus, of 10 and w, the MAXIMUM value is w.
In other words, w>10.
Since 10<w, min(10,w) = 10.
SUFFICIENT.

The correct answer is D.

[Anurag@Gurome]

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)

Please explain statement 1. I did not get it.

If w > 10, min(10, w) = 10
If w < 10, min(10, w) = w

Statement 1: w = max(20, z)
This means w is maximum of 20 and z. Hence, w is more than or equal to 20.
Therefore, w > 10 --> min(10, w) = 10

Sufficient

Statement 2: w = max(10, w)
This means w is maximum of 10 and w. Hence, w > 10.
Therefore, min(10, w) = 10

Sufficient

The correct answer is D.