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The students in a literature class have been assigned to read pages \(\mathrm{85}\) through \(\mathrm{206}\) of a novel. At exactly two of those pages (the earlier page and the later page), the total number of pages remaining to complete the assignment, not including the page currently being read, is equal to the value expressed by the last two digits of the number on that page. For example, the value expressed by the last two digits of \(\mathrm{107}\) is \(\mathrm{7}\).
Select for Earlier page the number on the earlier page and for Later page the number on the later page. Make only two selections, one in each column.
91
121
153
193
201
203
Let's use a number line to show the reading assignment:
Page: 85 -------- [Current Page] -------- 206
↑ ↑
Start End
Total assignment: pages 85-206 (122 pages total)
At certain pages, a special relationship holds:
For any page X:
Example given: Last two digits of 107 = 07 = 7
We need to find exactly TWO pages where:
\(206 - \text{page number} = \text{last two digits of that page number}\)
Page 91:
Page 121:
Page 153:
Page 193:
Page 201:
Page 203:
Page: 85 ------ 153 -------------- 203 -- 206
↑ ↑
53 pages left 3 pages left
Last digits: 53 Last digits: 03 = 3
✓ ✓
We found exactly two pages where the condition holds:
These are the only two pages from our answer choices that satisfy the special condition.