DS Question - 7

A building has two types of apartments, big and small. 65 percent of the apartments are small. The number of occupied big apartments is twice the number of unoccupied small apartments. What percent of the apartments in the building are occupied ?

(1) The number of occupied big apartments is six times the number of unoccupied big apartments.

(2) The building has a total of 160 apartments

Answer - A

Statement (1 ) -- Sufficient.

Percentage occupied = (big & occupied + small & occupied) / total (say, n)

(35/100)n * (6/7) = big & occupied

(small ) - (small & unoccupied) = (small & occupied)

(65/100)n - [(1/2) big & occupied] = small & occupied

(65/100)n - [(1/2) (35/100)n * (6/7)] = small & occupied

Total = [(35/100)n * (6/7) + (65/100)n - (35/100)n * (3/7) ] / n

(multiplied (6/7) by (1/2) here ).

n is removed from the numerator and divisor

(35/100) * (6/7) + (65/100) - (35/100) * (3/7) --- This is approx equal to 0.8

so whatever n is, it is the answer.

Statement (2) -- Insufficient -- 160 total apartments does not give any information regarding any number of occupied apartments -- there could be 2 big and 1 small, or 40 big and 20 small.