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The local library has seen a significant decrease in the number of physical books checked out over the last five years. During this same five-year period, the number of digital e-books checked out through the library's online system has tripled. However, overall, the total number of items (physical books plus e-books) checked out from the library has increased by 15 percent over the last five years. Which of the following is most strongly supported by the information above?

  1. The increase in the number of e-books checked out was numerically greater than the decrease in the number of physical books checked out.Answer
  2. B
    The library currently checks out a higher number of e-books than physical books.
  3. C
    Library patrons find e-books more convenient to read than physical books.
  4. D
    The introduction of the library's online e-book system directly caused the decline in physical book checkouts.
  5. E
    Most of the total items checked out from the library over the last five years have been e-books.

Answer

The increase in the number of e-books checked out was numerically greater than the decrease in the number of physical books checked out.
The stimulus establishes a simple mathematical relationship: Total = Physical + Digital. We are told the Total increased, Physical decreased, and Digital increased. The only way for the Total to increase while Physical decreases is if the absolute numerical gain in Digital checkouts is larger than the absolute numerical loss in Physical checkouts. Thus, the statement regarding the numerical difference in their changes is strongly supported as a logical mathematical necessity.

Step-by-Step Solution

1
Identify the components that make up the total checkouts.
Total checkouts = physical books + e-books.
To understand how the parts relate to the whole based on the stimulus.
2
Analyze the individual trends for each component.
Physical book checkouts decreased; e-book checkouts increased (tripled).
To track the directional change of each variable over the five-year period.
3
Analyze the trend for the overall total.
Total checkouts increased by 15 percent.
To compare the net result against the individual component trends.
4
Deduce the mathematical relationship required to produce the overall trend.
For a sum to increase when one part decreases, the other part must increase by a larger absolute amount than the first part decreased.
To determine what must logically be true to reconcile the differing trends.

Key Concept

Synthesizing proportional and numerical trends to draw a valid mathematical deduction without overstepping the provided data.
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