The students in a literature class have been assigned to read pages 85 through 206 of a novel. At exactly...
GMAT Two Part Analysis : (TPA) Questions
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.
Phase 1: Owning the Dataset
Visualization
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)
Understanding the Condition
At certain pages, a special relationship holds:
- Pages remaining (not including current page) = Last two digits of the page number
- Pages remaining = \(206 - \text{current page}\)
Phase 2: Understanding the Question
Breaking Down the Condition
For any page X:
- Pages remaining to read = \(206 - X\)
- Last two digits of X = the value when we look at only the final two digits
Example given: Last two digits of 107 = 07 = 7
What We're Looking For
We need to find exactly TWO pages where:
\(206 - \text{page number} = \text{last two digits of that page number}\)
Phase 3: Finding the Answer
Systematic Check of Answer Choices
Page 91:
- Last two digits = 91
- Pages remaining = \(206 - 91 = 115\)
- Does \(115 = 91\)? No ✗
Page 121:
- Last two digits = 21
- Pages remaining = \(206 - 121 = 85\)
- Does \(85 = 21\)? No ✗
Page 153:
- Last two digits = 53
- Pages remaining = \(206 - 153 = 53\)
- Does \(53 = 53\)? Yes! ✓
Page 193:
- Last two digits = 93
- Pages remaining = \(206 - 193 = 13\)
- Does \(13 = 93\)? No ✗
Page 201:
- Last two digits = 01 = 1
- Pages remaining = \(206 - 201 = 5\)
- Does \(5 = 1\)? No ✗
Page 203:
- Last two digits = 03 = 3
- Pages remaining = \(206 - 203 = 3\)
- Does \(3 = 3\)? Yes! ✓
Visual Confirmation
Page: 85 ------ 153 -------------- 203 -- 206
↑ ↑
53 pages left 3 pages left
Last digits: 53 Last digits: 03 = 3
✓ ✓
Phase 4: Solution
We found exactly two pages where the condition holds:
- Earlier page: 153 (because \(206 - 153 = 53\), which equals its last two digits)
- Later page: 203 (because \(206 - 203 = 3\), which equals its last two digits)
These are the only two pages from our answer choices that satisfy the special condition.