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For any integers a and b, min(a, b) and max(a, b) denote

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by Gmat_mission » Mon Jun 10, 2019 5:12 am

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For any integers a and b, min(a, b) and max(a, b) denote the minimum and maximum of a and b, respectively.

For example, min(1, 2) = 1 and max(1, 2) = 2.

If x, y, and z are integers, what is max(y, 8)?

(1) min(9, x) = y

(2) min(6, z) = y

[spoiler]OA=B[/spoiler]

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Source: — Data Sufficiency |

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For any integers a and b, min(a, b) and max(a, b) denote

by Brent@GMATPrepNow » Mon Jun 10, 2019 5:55 am
Gmat_mission wrote:For any integers a and b, min(a, b) and max(a, b) denote the minimum and maximum of a and b, respectively.

For example, min(1, 2) = 1 and max(1, 2) = 2.

If x, y, and z are integers, what is max(y, 8)?

(1) min(9, x) = y
(2) min(6, z) = y
Notice that min(3, 4) = 3
Notice that min(2, 2) = 2
Notice that min(1, 11) = 1

KEY PROPERTY:
In general, we can say that, if min(a,b) = c, then we know that c ≤ a and c ≤ b

Target question: What is max(y, 8)?

Statement 1: min(9, x) = y
This tells us that y ≤ 9
Let's test some values of y:
Case a: y = 9. In this case, the answer to the target question is max(y, 8) = max(9, 8)=9
Case b: y = 7. In this case, the answer to the target question is max(y, 8) = max(9, 8)=8
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: min(6, z) = y
This tells us that y ≤ 6
If y ≤ 6, then 8 is ALWAYS GREATER THAN y
So, the answer to the target question is max(y, 8) = 8
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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