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05 Aug 2026, 22:29
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Starting at the beginning of 2007, a research lab’s data archive increased by 20% each year for a whole number of years. If no data was deleted during this period, how many gigabytes of data were in the archive at the end of the period?
(1) By the end of the period, the amount of data in the archive had increased by 44%.
(2) If 360 gigabytes of data had been deleted at the beginning of the final year of the period, the amount of data in the archive at the end of the period would have been 12% less than its actual amount at the end of the period.
(1) By the end of the period, the amount of data in the archive had increased by 44%.
(2) If 360 gigabytes of data had been deleted at the beginning of the final year of the period, the amount of data in the archive at the end of the period would have been 12% less than its actual amount at the end of the period.
05 Aug 2026, 22:29
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Official Solution:
Starting at the beginning of 2007, a research lab’s data archive increased by 20% each year for a whole number of years. If no data was deleted during this period, how many gigabytes of data were in the archive at the end of the period?
Let \(F\) be the actual amount of data, in gigabytes, in the archive at the end of the period.
(1) By the end of the period, the amount of data in the archive had increased by \(44\%\).
Since the archive increased by \(20\%\) each year, a \(44\%\) total increase means the period lasted 2 years, because:
\(1.2 * 1.2 = 1.44\)
However, this does not tell us the starting amount of data, so we cannot determine the final amount of data.
Not sufficient.
(2) If 360 gigabytes of data had been deleted at the beginning of the final year of the period, the amount of data in the archive at the end of the period would have been \(12\%\) less than its actual amount at the end of the period.
If 360 gigabytes had been deleted at the beginning of the final year, those 360 gigabytes would not have increased by \(20\%\) during the final year.
So the final amount would have been lower by:
\(360 * 1.2 = 432\)
Statement (2) says that this decrease would have been \(12\%\) of the actual final amount. So:
\(432 = 0.12F\)
\(F = 3,600\)
Sufficient.
Answer: B
Starting at the beginning of 2007, a research lab’s data archive increased by 20% each year for a whole number of years. If no data was deleted during this period, how many gigabytes of data were in the archive at the end of the period?
Let \(F\) be the actual amount of data, in gigabytes, in the archive at the end of the period.
(1) By the end of the period, the amount of data in the archive had increased by \(44\%\).
Since the archive increased by \(20\%\) each year, a \(44\%\) total increase means the period lasted 2 years, because:
\(1.2 * 1.2 = 1.44\)
However, this does not tell us the starting amount of data, so we cannot determine the final amount of data.
Not sufficient.
(2) If 360 gigabytes of data had been deleted at the beginning of the final year of the period, the amount of data in the archive at the end of the period would have been \(12\%\) less than its actual amount at the end of the period.
If 360 gigabytes had been deleted at the beginning of the final year, those 360 gigabytes would not have increased by \(20\%\) during the final year.
So the final amount would have been lower by:
\(360 * 1.2 = 432\)
Statement (2) says that this decrease would have been \(12\%\) of the actual final amount. So:
\(432 = 0.12F\)
\(F = 3,600\)
Sufficient.
Answer: B
