Percentage 4

guerrero wrote:A lighting store is stocked with 410 fixtures. Some of the fixtures are floor lamps and the rest are table lamps. If 5% of the floor lamps and 30% of the table lamps are imported, what is the smallest possible number of imported lamps stocked at the store?

A. 3
B. 10
C. 13
D. 20
E. 23

any easy approach ?



E

Notice that a greater proportion of the table lamps are imported (30%).
So, to MINIMIZE the number of imported lamps, we must MINIMIZE the number of table lamps.

If 30% of the table lamps are imported, then the number of table lamps must be a multiple of 10 (since 30% = 3/10). In other words, 3 out of every 10 table lamps is imported.
For example, there cannot be 8 table lamps since 30% of 8 is not a whole number.

Likewise, the number of floor lamps must be a multiple of 20 (since 5% = 1/20).

Now that we know the number of table lamps must be a multiple of 10, and the number of floor lamps must be a multiple of 20, let's try to MINIMIZE the number of table lamps.

The smallest possible number table lamps is 10, in which case there are 400 floor lamps.
- Of the 10 table lamps, 30% are imported (3 imported)
- Of the 400 table lamps, 5% are imported (20 imported)

Total number of imported lamps = [spoiler]3 + 20 = 23 = E[/spoiler]

Cheers,
Brent