Problem Solving

GMAT Paper Tests

An optometrist charges $150 per pair for soft contact lenses and $85 per pair for hard contact lenses. Last week she sold 5 more pairs of soft lenses than hard lenses. If her total sales for pairs 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

OA B

This is an easy one but a time stealer, so make sure you don't make a silly arithmetic mistake.

Now Soft Pair (SP) is sold at $ 150
and Hard Pair (HP) is sold at $ 85

She sold 5 more SP than the HP
so SP - HP = 5 ... ... ... (1) (Difference of the number is 5, SP is more)

and she made a revenue of $1690 in total
So 150(SP) + 85 (HP) = 1690 ... ... ... (2)

Now we have 2 equations and 2 variables so we will be able to solve for both the variable substitution method.

150(5+HP) + 85 (HP) = 1690 ... ... ... (2) (becase SP = 5 + HP)
=> 750 +150HP + 85HP = 1690
=> HP = 4

Substituting HP = 4 in 1st equation
SP - 4 = 5
=> SP = 9

The question asks what is SP + HP, the answer is 9+4 = 11
Correct answer is A