Suppose that you are buying a house. You and your realtor have determined that the most expensive house you can afford is the 34th percentile. The 34th percentile of housing prices is $240,000 in the town you want to move to. In this town, can you afford 34% of the houses or 66% of the houses?

You can afford 34% of the houses.

Step-by-step explanation:

Interpretation of a percentile

When a value V is said to be in the xth percentile of a set, x% of the values in the set are lower than V and (100-x) % of the values in the set are higher than V.

In this problem:

The most expensive house you can afford is the 34th percentile. The 34th percentile of housing prices is $240,000.

Values higher than $240,000 are above the 34th percentile. So 66% of the houses are above $240,000.

Values lower than $240,000 are below the 34th percentile. So 34% of the houses are below $240,000.

Can you afford 34% of the houses or 66% of the houses?

You can afford houses of at most $240,000.

34% of those houses are at most $240,000.

So you can afford 34% of the houses.