Contact lenses

The solution below is taken from the GMATFix App.



-Patrick

BlueDragon2010 wrote:An optometrist charges $150 per pair for soft contact lenses and $85 per pair for hard contact lenses. Last week sh sold 5 more pairs of soft lenses than hard lenses. If her total sales for pairs of contact lenses last week were $1,690, what was the total number of pairs of contact lenses that she sold?

A) 11

B) 13

C) 15

D) 17

E) 19

The total amount of revenue -- $1690 -- is a multiple of 10.
Since the price of each pair of soft lenses is a multiple of 10, the total amount of revenue from the soft lenses must be a multiple of 10.
Implication:
The total amount of revenue from the hard lenses must also be a multiple of 10.
Since the price of each pair of hard lenses is $85, the number of pairs of hard lenses sold must be an EVEN integer.

Case 1: 2 pairs of hard lenses sold
Since 5 more pairs of soft lenses are sold, the number of pairs of soft lenses sold = 2+5 = 7.
Total pairs sold = 2+5 = 7.
Since 7 is not among the answer choices, Case 1 is not viable.

Case 2: 4 pairs of hard lenses sold
Since 5 more pairs of soft lenses are sold, the number of pairs of soft lenses sold = 4+5 = 9.
Total pairs sold = 4+9 = 13.
This is the value in answer choice B.
Check whether Case 2 yields $1690 in revenue:
(4*85) + (9*150) = 340 + 1350 = 1690.
Success!

The correct answer is B.