Skyscraper Height

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The official height of a skyscraper is equal to the elevation of the roof plus the height of the spire atop the roof. The height of the spire on a certain skyscraper is what percent of the official height?

(1) The spire on the skyscraper is 25 percent of the elevation of the roof.

(2) The official height of the skyscraper is 1,000 meters.

Review: Skyscraper Height




Explanation

In this question, there are three variables in play, all of which are heights: the roof height (say, H), the spire height (say, h), and the combined height (H + h). If we have any two, we can get the third. Knowing the percent represented by the roof height would also be sufficient. Or knowing the ratio of the spire to the roof would also be sufficient. On to the statements, separately first.

Statement (1) gives us what we need. It's saying that . That means the combined height is . The spire is one-fifth of the combined height. Sufficient.

Statement (2) gives us the combined height, but no ratio and neither of the component heights. So it's insufficient.

The correct answer is (A).


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