**UCAT** **Question Analysis - Quantitative Reasoning Question 18**

**Key facts about diamonds: **

**1. The weight of a diamord is measured In carats. A carat is equivalent to 0.2 grams. **

**2. The price of rough diamonds is proportionate to the square of the number of carats and is therefore calculated according to the following formula: Price = (Price of 1 carat) x (Number of carats)^2 **

**3. The price of a 1-carat diamonc varies according to market forces. Currently, a 1-carat rough diamond sells for $125. Hence a 2-carat rough diamond sells for 125 x 2^2= $500, etc. **

**4. Diamonds are exported and imported by countries in rough or polished forms. **

**Diamond import/export figures for Country X for 2008 **

**Q18.1 What is the cost of a rough diamond that weighs 2.6 g? **

a. $2,275

b. $4,225

c. $12,653

d. $18,845

e. $21,125

**Q18.2 How much money would a diamond cutter save by buying a 4-carat diamond and a 7-carat diamond Instead of an 11-carat diamond? **

a. $7,000

b. $9,000

c. $8,125

d. $9,175

e. $12,125

** A diamond cutter has purchased a 5-carat rough diamond and must remove half of it in the process of shaping and polishing the rough diamond. He then sells the polished diamond at 20 times the price of a rough diamond of the same weight.**

**Q18.3 How much profit will he make? **

a. $12,125

b. $12,500

c.$13,225

d. $14,175

e. $15,625

**A diamond cutter has heard rumours that the price of rough diamonds may change soon. He is told that a 4-carat rough diamond might now cost $640. **

**Q18.4 If the new price were to be implemented, what would be the weight of a rough diamond costing $1,960? **

a. 4 carats

b. 5 carats

c. 6 carats

d. 7 carats

e. 8 carats

**Q18.5 What was the total value of exports in Oct-Dec 2007, to the nearest US$ million? **

a. $340m

b. $421m

c. $920m

d. $1,652m

e. $2,117m

**Q18.6 By what percentage has the value of polished imports increased or decreased between 2007 and 2008? **

a. -35.2%

b. -4.04%

c. -3.88%

d. +3.88%

e. +4.04 %

**The diamond industry for Country X expects that, for the first quar-ter of 2009, the net export figure (i.e. the difference between total exports and total imports) will be 20% higher than the average quar-terly net export figure over the period Jan-Sep 2008. **

**Q18.7 What is the expected net export figure for the period Jan-Mar 2009 (to the near-est $ million)?**

a. $70m

b. $413m

c. 6810m

d. $1,033

e. $1,240m

**Q18.8 What Is the average quarterly income from polished exports in 2008? **

a. $428m

b. $1,453m

c. $1,560m

d. $1,937m

e. $3,120m

**Answer and Explanation**

**Q18.1 - e: $21,125 **

A weight of 2.6 g is equivalent to 2.6 / 0.2 = 13 carats. A 13-carat diamond will cost 125 x 132= $21,125.

**Q18.2 - a: $7,000 **

Price of a 4-carat diamond = 125 x 42= $2,000.

Price of a 7-carat diamond = 125 x P= $6,125.

Price of an 11-carat diamond = 125 x 112= $15,125.

Saving = 15,125 - (2,000 + 6,125) = $7,000.

**Q18.3 - b: $12,500**

Price of a 2.5-carat rough diamond = 125 x 2.52= $781.25.

Price of a 5-carat rough diamond = 125 x 52= $3,125.

Profit = 20 x 781.25 - 3125 = $12,500.

**Q18.4 - d: 7 carats **

The new price would give the following equation: $640 = (Price of 1 carat) x 42, i.e. price of 1 carat = $40.

This now gives us the equation 1960 = 40 x c2, where c is the number of carats of the diamond. This gives c2= 1960 / 40 = 49, i.e. c = 7 carats.

**Q18.5 - d: $1,652m **

The question is asking about 2007 values, whilst we are only given 2008 values with % change. It is important to remember that these percentages will be based on the 2007 value. So, for example, if Oct-Dec 2008 polished exports have a value of $428m, and the % change is -62.1% then we have (Oct-Dec 2008 value) = (Oct-Dec 2007 value) x (1 - 0.621).

Therefore Oct-Dec 2007 value for polished exports = 428 / (1 - 0.621) = 1129.29.

Similarly, Oct-Dec 2007 value for rough exports = 141 / (1 - 0.73) = 522.22.

Total exports for Oct-Dec 2007 = 1129.29 + 522.22 = 1651.51.

**Q18.6 - c: -3.88%**

The value of polished imports across 2008 was 594 + 3,787 = $4,381m. The value across 2007 was 594 / (1 - 0.428) + 3,787 / (1 + 0.076) = $4,557.98m.

Ratio of 2008 over 2007 = 4381 / 4557.98 = 0.96117. Change = 1 - 0.96117 = 0.03883, i.e. 3.88% decrease.

**Q18.7 - b: $413m**

The net export figure for the period Jan-Sep 2008 is calculated as: (5,812 + 3,173)- (3,787 + 4,165) = 1,033.

An increase of 20% on the quarterly average will therefore give: 1,033 / 3 (there are 3 quarters in that period) x 1.20 = 413.20.

**Q18.8 - c: $1,560m**

This is simply calculated as the total polished exports over all quarters, di-vided by 4. This gives: (428 + 5812) / 4 = $1,560.

Drafted by Juno Wong(UCAT Prep)