Max(
*x*,
*y*) equals the greater of
*x* and
*y*. Min(
*x*,
*y*) equals the smaller of
*x* and y. For which of the following values of
*x* would the average of Max(
*x*, 30) and Min(70,
*x*) be greater than
*x*?

Indicate
__all__ such
*x* values.

One way to solve would be to plug/test all of the choices.

*x* |
Max(*x*, 30) |
Min(70, *x*) |
Avg. of Max(*x*, 30) and Min(70, *x*)... |
...greater than *x*? |

-10 |
30 |
-10 |
10 |
YES |

10 |
30 |
10 |
20 |
YES |

30 |
30 |
30 |
30 |
NO |

50 |
50 |
50 |
50 |
NO |

70 |
70 |
70 |
70 |
NO |

90 |
90 |
70 |
80 |
NO |

Alternatively, set up cases that are based on the value of

*x*.

If

*x* > 70, then Max(

*x*, 30) =

*x* and Min(70,

*x*) = 70. So for

*x* > 70, the average in question is (

*x* + 70)/2, which is greater than 70 but less than

*x*.

If 30 ?

*x* ? 70, then Max(

*x*, 30) =

*x* and Min(70,

*x*) =

*x*. So for 30 ?

*x* ? 70, the average is question is (

*x* +

*x*)/2, which is equal to

*x*.

If

*x* < 30, then Max(

*x*, 30) = 30 and Min(70,

*x*) =

*x*. So for

*x* < 30, the average in question is (

*x* + 30)/2, which is greater than

*x*.

The correct answers are -10 and 10 only.