Data Sufficiency

A local inspection of the 500 houses in a certain subdivision found that 80 percent of the houses in the subdivision had garages and that 45 percent of the houses had swimming pools. What percent of the houses in the subdivision were found to have a garage but not a swimming pool?

The inspection found that 5 percent of the houses in the subdivision had neither a garage nor a swimming pool.
The inspection found that 37.5 percent of the houses in the subdivision that had a garage also had a swimming pool.

Overlapping set Q
Ans:D?

can u explain in details?

pradeepkaushal9518 wrote:A local inspection of the 500 houses in a certain subdivision found that 80 percent of the houses in the subdivision had garages and that 45 percent of the houses had swimming pools. What percent of the houses in the subdivision were found to have a garage but not a swimming pool?

The inspection found that 5 percent of the houses in the subdivision had neither a garage nor a swimming pool.
The inspection found that 37.5 percent of the houses in the subdivision that had a garage also had a swimming pool.

Assume only 100 houses.

n(g) = 80
n(s) = 45
n(g-s) =??

total - neither = 80 +45 - both
100 -neither = 80+45-both
both = 25 + neither

The inspection found that 5 percent of the houses in the subdivision had neither a garage nor a swimming pool.
both = 25+5
both = 30
now, n(g-s) = n(g)-both = 80 - 30 = 50
SUFF

The inspection found that 37.5 percent of the houses in the subdivision that had a garage also had a swimming pool.
37.5 percent of n(g) also had a swimming pool
37.5 percent of 80 = 30
which means both = 30
this is same as above stmt now.
SUFF

pick D.

Hope this helps!!