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22 Aug 2019, 22:41
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Difficulty:
25%
(medium)
Question Stats:
76% (01:09) correct
24%
(01:06)
wrong
based on 98
sessions
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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.
(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.
23 Aug 2019, 01:44
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This is a question involving the usage of percentages and equations. In any question on equations, always identify the unknowns and represent them using variables. The three unknowns in this question are the official height of the skyscraper, the elevation of the roof and the height of the spire.
Let the official height of the skyscraper be x, the elevation be y and the height of the spire be z. Then, as per the question data, x = y + z.
The question asks us to find out the height of the spire as a percentage of its official height. This means, we have to calculate the value of the expression below,
\(\frac{z}{x}\) * 100 which is nothing but \(\frac{z}{(y+z)}\) * 100. Therefore, any statement giving us information about y and z will be sufficient.
Let’s analyse the statements now.
From statement I alone, z = ¼ * y. Therefore, y + z = \(\frac{5}{4}\) * y. Substituting these values in the expression above, we can see that ‘z is 20% of the official height. Statement I alone is sufficient.
Possible answer options are A or D. Answer options B, C and E can be eliminated.
From statement II, although the official height of the skyscraper is known, we do not know the height of the spire. Hence, we cannot calculate the required percentage.
Statement II alone is insufficient. Answer option D can be eliminated.
The correct answer option is A.
In DS questions like these, it’s always a good idea to break down the question stem to form an expression/equation/inequality which can then be used as a basis to look for specific information in the statements.
Hope this helps!
Let the official height of the skyscraper be x, the elevation be y and the height of the spire be z. Then, as per the question data, x = y + z.
The question asks us to find out the height of the spire as a percentage of its official height. This means, we have to calculate the value of the expression below,
\(\frac{z}{x}\) * 100 which is nothing but \(\frac{z}{(y+z)}\) * 100. Therefore, any statement giving us information about y and z will be sufficient.
Let’s analyse the statements now.
From statement I alone, z = ¼ * y. Therefore, y + z = \(\frac{5}{4}\) * y. Substituting these values in the expression above, we can see that ‘z is 20% of the official height. Statement I alone is sufficient.
Possible answer options are A or D. Answer options B, C and E can be eliminated.
From statement II, although the official height of the skyscraper is known, we do not know the height of the spire. Hence, we cannot calculate the required percentage.
Statement II alone is insufficient. Answer option D can be eliminated.
The correct answer option is A.
In DS questions like these, it’s always a good idea to break down the question stem to form an expression/equation/inequality which can then be used as a basis to look for specific information in the statements.
Hope this helps!
23 Aug 2019, 07:50
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The total height is the spire's height plus the roof's height. Statement 1 says the ratio of the spire's height to the roof's height is 1 to 4, so the spire is 1/5 of the total height, or 20% of the total height, and Statement 1 is sufficient. Statement 2 isn't useful so the answer is A.
