**Can you solve this UKCAT Quantitative Reasoning test in 2 minutes?**

Speed is of the essence when doing your UKCAT Quantitative Reasoning test but you can’t afford to sacrifice quality if you’re rushing things too much. You need to keep a cool head, focus on the problem and don’t waste time doing unnecessary calculations. So, are you up to the task yet..?

See if you can solve the Quantitative Reasoning question below in less than 2 minutes.

Don’t read beyond the question until you have finished. Check your watch and start now…!

• The profit margin on "tea" is 40% more than that on "coffee".

• You always sell twice as many coffees as teas.

Q1. Your profit from tea and coffee sales ones day is £60. What is the minimum number of coffees that you could have sold that day (assume you cannot make more than 100% profit on anything)?

A. - 24. B. - 29. C. - 32. D. - 34. E. - 39.

Did you manage it? If you did then well done, assuming of course that you got it right. Let’s go through it together and check.

**The solution**

1. At first glance it may appear that you don’t have enough information to solve this problem but there may be more than you first see.

2. The table gives us the price of tea and coffee as 1.8 and 2.4 respectively; the supplementary information tells us that teas make 50% more profit than coffees but not how much and that we sell twice as many teas as coffees; and the question tells us that the total profit made from teas and coffees is £60.

3. Let’s assume that the number of cups of coffee sold on this day is C and that the profit made on a cup of coffee is P. From the information we have we know that the number of teas sold is 0.5C and that the profit made on a cup of tea is 1.4P.

4. The total profit made of coffees will be:

2.4*C*P = 2.4CP

And the total profit made of teas will be:

1.8*1.4*P*0.5*C = 1.26CP

If we add these together they will total £60:

2.4CP+1.26CP = 3.66CP = £60

CP = 60/3.66 = 16.39

5. Here we have an equation with two unknown values which, in general, is not possible to solve. However, we have another bit of information. The question asks ‘what is the minimum number of coffees sold’. If C*P=16.39 then as either C or P increase the other will decrease and so C will be at a minimum when P is at a maximum.

6. The maximum profit possible is 100% if a cup of teas costs nothing to make and you sell it for 1.80 and the profit on tea is 1.4 times that of coffee and so 1.4*P cannot exceed 100%. At this point P = 1/1.4 and so:

C = 16.39 / (1/1.4)

C = 22.96

7. So we must sell at least 22.96 cups of coffee which must be an integer as you can’t sell a partial cup of coffee, and it must be even because you sell twice as many as you sell of tea. Therefore, the answer is 24.

**Was it difficult? Or challenging? Check our UKCAT practice tests to improve your scores!**