Question

If each X-Ray occupies 30MB and a new technology reduces space by 60%, what is the total magnetic media memory required to store all the X-Rays in the year 2000? (1MB = \(10^6\) Bytes)

• A. 10,170 TB
• B. 6,780 TB
• C. 1,703,170 TB
• D. None of these

Hint:

Always calculate number of items from known memory, then apply percentage savings directly to total data and convert units.

Answer 1

The Correct Option is B

From the chart, total storage space occupied by X-Rays in 2000 = 16,950 TB
Let the number of X-Ray images be \( n \). Each X-Ray takes 30MB originally.
Total data in MB: \( 30n \Rightarrow 30n \text{ MB} \)
This equals 16,950 TB in original size: \[ 30n \times 10^6 \text{ Bytes} = 16,950 \times 10^{12} \text{ Bytes} \Rightarrow n = \frac{16,950 \times 10^{12}}{30 \times 10^6} = \frac{16,950 \times 10^6}{30} = 565 \times 10^6 \text{ images} \] Now with 60% space saving, only 40% of original size is used:
\[ \text{New total memory} = 30 \times 0.4 = 12 \text{ MB/image} \Rightarrow \text{Total} = 565 \times 10^6 \times 12 = 6,780 \times 10^6 \text{ MB} = \frac{6,780 \times 10^6}{10^6} = \boxed{6,780 \text{ TB}} \]