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Print UKCAT Practice Series #001: Distilling the Information in Quantitative Reasoning

We at Career Gym decided to launch a UKCAT practice series to help you increase your UKCAT test score! In this brand new series, our UKCAT test preparation experts walk you through the solution of a sample exercise and give you hints to improve your test-taking strategy.

In this historical first piece we are going to discuss how you can increase your test-solving efficiency by distilling the right information from a UKCAT Quantitative Reasoning exercise.

Here is the UKCAT Quantitative Reasoning exercise we are going to discuss today!  UKCAT Practice Series #001

  • A carpenter makes and sells 5 items of furniture in his workshop.
  • He sells everything he makes.
  • He makes 18 wardrobes during the year.
  • Wardrobes account for 10% of his total profit.

Question: The carpenter sells a wardrobe for five times the price of a cupboard and cupboard sales bring in 25% of his total profit. How many cupboards does he sell in a year?

In this question we are given a lot of information but as the chart and bullet points are for a set of 4 questions it is unlikely that everything is required for each question. We need to distil the information down to what is required for this particular question.

The question is asking about cupboards and also expresses a relationship to wardrobes about which we have extra information. The bullet points tell us that the carpenter makes 18 wardrobes a year and they provide 10% of the total profit. Note that at no point are we given the actual retail price of any piece of furniture. This is not an omission but, as we shall see, unnecessary information.

The chart gives us a breakdown of all five pieces of furniture but we can disregard the bureau, the bedstead and the stool as they are not mentioned in this question. Also, the only pieces of information relevant about the wardrobe and the cupboard are the profit margins of 20% and 15% respectively.

Let us now recap the information we have. The carpenter sells 18 wardrobes at 20% profit providing 10% of his total profit. He also sells a number of cupboards at 15% profit providing 25% of his total profit. The wardrobes cost 5 times as much as the cupboards. We now have everything we need to solve the problem. Just a little hint at this point: you don’t need your calculator to solve this.

Let’s assume for the moment that the price of a cupboard is £C and that the price of a wardrobe is £5C. The profit from a wardrobe is 20% of 5C which is C and he sells 18 of them which gives £18C to the total profit. We know it is 10% of the total so the total profit is £18C/0.1=£180C.

Now we also know that the cupboards account for 25% of the total profit which is £180C*0.25=£45C and the profit from one cupboard is 15% of C or 0.15C. Therefore, the number of cupboards sold is 45C/0.15C=300. Note that the Cs cancel out which is our assumed price of a cupboard i.e. the actual price of any of the furniture is not required information.

 

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