**UKAT** **Question Analysis - Quantitative Reasoning Question 24**

A chocolate lover purchases a 360 g box of powdered drinking chocolate. The label states the foilowing:

**Q24.1 How much fat is contained in 200 ml of whole milk (to the nearest 0.1 g)?**

a. 1.2 g

b. 3.4 g

c. 6.8 g

d. 8.1 g

e. 9.6 g

**024.2 The customer finds whole milk a bit rich and decides to use a mix of semi-skimmed milk and water instead. He then adds 200 ml of the mixed liquid to 18 g of powdered chocolate. The total fat content of the resulting drink is 2.464 g. Given that water does not contain any fat, what volume of semi-skimmed milk did he use?**

a. 56.0 ml

b. 81.5 nI

c. 144.9 ml

d. 118.5 ml

e. 170.4 ml

**Q24.3 The customer uses up the whole box of powdered chocolate, mak-ing hot drinks according to the instructions. How many pints of milk will he have used (1 pint = 570 ml)?**

a.0.35

b. 4.4

c. 7.0

d. 14.1

e.20.0

**Q24.4 The customer is on a diet and, in an effort to reduce his weight, he decides to limit the total daily calories that he gets from the choco-late drink to a strict maximum of 800 kCal. To achieve his objective, he decides to make three chocolate drinks per day using water only (water does not contain any calories) and to make any other choc-olate drink using his usual whole milk.**

**What is the maximum number of whole-milk-based chocolate drinks that he can have in addition to his three daily water-based drinks in order not to breach his resolution?**

a. 0 drink

b. 1 drink

c. 2 drinks

d. 3 drinks

e. 4 drinks

**Q24.5 The customer buys semi-skimmed milk with a label that states that its protein content is 3.3 g per 100 ml. What is the total amount of protein that he will have drunk once he has made drinks with the entire box of chocolate using standard proportions and semi-skimmed milk instead of whole milk (to the nearest gram)?**

a, 66 g

b. 160 g

c. 164 g

d. 244 g

e. 272 g

**Q24.6 The calorific value of food is measured in kCal and is calculated by adding the calorific values of protein, carbohydrate and fat. The cal-orific value of 1 g of protein is 4 kCal and the calorific value of 1 g of carbohydrate is 4 kCal.**

**What is the calorific value of 1 g of fat, to the nearest gram?**

a. 4 kCal

b. 6 kCal

c. 9 kCal

d. 21 kCal

e. 44 kCal

**Answer and Explanation**

**Q24.1 - d: 8.1 g**

A drink made of 18 g of powder and 200 ml of whole milk contains 9.6 g of fat. 100 g of powder contains 8.4 g of fat, therefore 18 g of powder contains 18/100 x 8.4 = 1.512 g. The amount of fat in 200 ml of whole milk is there-fore 9.6 - 1.512 = 8.088 g.

**Q24.2 - a: 56 ml**

The total fat content of 2.464 g contains fat from the chocolate (18/100 x 8.4 = 1.512). Therefore the milk/water mix contains 2.464 - 1.512 = 0.952 g of fat. Since we are told there is no fat in water, this can only come from the semi-skimmed milk. If 100 ml of semi-skimmed milk contains 1.7 g of fat, then to obtain 0.952 g, we need a volume of 0.952 x 100 / 1.7 = 56 ml.

**Q24.3 - c: 7.0 pints**

The box contains 360 g of chocolate (i.e. 20 x 18g). He therefore needs 20 x 200 ml = 4,000 ml of milk which is equivalent to 4000/570 = 7.0 pints.

**024.4 - c: 2 drinks**

One chocolate drink made from water will have the same amount of calories as the 18 g of chocolate powder used to make it, i.e. 372 x 18 / 100 = 66.96 kCal. The three water-based drinks together will therefore account for 3 x 66.96 = 200.88 kCal.

This leaves an allowance of 800 - 200.88 = 599.12 kCal for all other whole-milk-based drinks. We know from the table that each contains 200 kCal and therefore he is just short of being able to make 3 drinks. Since 3 drinks will just about push him over the limit, the answer is 2 drinks.

**Q24.5 - c: 164g**

The box contains 360 g of chocolate; therefore, at a rate of 18 g per drink, the client can make 20 drinks out of the whole box. For these 20 drinks he will require 20 x 200 ml of milk, I.e. 4 litres.

The protein included in the whole box (360 g) of chocolate amounts to 360/100 x 8.9 g = 32.04 g. The protein included in the 4 litres of semi-skimmed milk amounts to 40 x 3.3 g = 132 g.

The total amount of protein is therefore 164.04g.

**Q24.6 - c: 9 kCal**

This can be calculated using either of the two columns. Column 1: (372 - 4 x 8.9 - 4 x 65.2) / 8.4 = 9 Column 2: (200 - 4 x 8.0 - 4 x 20.4) / 9.6 = 9

Drafted by Juno(UCAT Prep)