The official height of a skyscraper is equal to the elevation of the

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!