It is an odd number. it is greater than 142. it is less than 156. rounded to the nearest ten, the rounded value is less than the mystery number. rounded to the nearest hundred, the rounded value is greater than the mystery number.

The odd numbers between 142 and 156 are these:

143, 145, 147, 149, 151, 153, and 155.

Of these, 143 to the nearest ten is 140.

Likewise, 151 to the nearest ten is 150.

And, 153 to the nearest ten is 150.

Of the seven original numbers, 143, 151, and 153 round to a nearest ten that
 is less than the possible mystery number.

To the nearest hundred, 143 goes to 100; 151 goes to 200, and 153 goes to 200.

Of those three, only two round to a nearest hundred that is bigger than the mystery number.

  151 and 153 are the mystery numbers.

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