**UCAT** **Question Analysis - Quantitative Reasoning Question 7**

The optician Tor Your Eyes Only offers the following prices:

**A client requires bifocal glasses with anti-reflection treatment. He chooses a designer frame, which is 20% more expensive than a classic frame. **

**Q7.1 How much will his glasses cost?**

a. £95.80

b. £106.80

c. £125.80

d. £150.80

e. £172.80

**The shop offers a 25% discount on the whole order to clients over the age of 60. **

**Q7.2 How much would a 65-year-old client pay for vari-focal glasses with a classic frame but no anti-reflection treatment? **

a. £55.50

b. £74.00

c. £84.00

d. £89.60

e. £112.00

**A client is considering buying a classic frame with lenses and anti-reflection treatment. **

**Q7.3 What is the ratio of the total cost of single vision glasses over the total cost of bifocal glasses? **

a.1:3

b.1:2

c.61:89

d.49:72

e.2:3

**Another optician The Apple Of My Eye" sells classic frames with varifocal lenses and anti-reflection treatment for £159.96. **

**Q7.4 What discount would the optician Tor Your Eyes Only need to apply In order to match that price? **

a. 7%

b. 7.53%

C. 8%

d. 8.6%

e. 9%

**Answer and Explanation**

**Q7.1 — d: £150.80 **

The total price (not forgetting to allow for 2 lenses!) will be: 34x1.2 + 2x30 + 2x25 = £150.80.

**Q7.2 — c: £84**

The full price would be 36 + 2x38 = £112. Applying a discount of 25% gives 0.75 x 112 = £84.

**Q7.3 — e: 2:3**

The total cost for single vision is: 26 + 2x15 + 2x20 = 96. The total cost for single vision is: 34 + 2x30 + 2x25 = 144. The ratio is therefore 96/144 = 2/3, i.e. 2:3.

**Q7.4 — a: 7%**

At For Your Eyes Only, varifocal glasses would cost: 36 + 2x38 + 2x30 = £172. This compares to £159.96 at the other shop. 159.96 / 172 = 0.93; hence the discount should be 1 — 0.93 = 0.07, i.e. 7%.

Drafted by Juno Wong(UCAT Prep)