Diet formulations from alternative ingredients

CAT 2007 Slot 1 · DILR · Medium · Data Interpretation

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Passage / data set

A health-drink company's R&D department is trying to make various diet formulations, which can be used for certain specific purposes. It is considering a choice of 5 alternative ingredients (O, P, Q, R, and S), which can be used in different proportions in the formulations. The table below gives the composition of these ingredients. The cost per unit of each of these ingredients is O: 150, P: 50, Q: 200, R: 500, S: 100.

IngredientCarbohydrate%Protein%Fat%Minerals%
O50301010
P802000
Q10305010
R550405
S455005

Question 1 of 4

For a recuperating patient, the doctor recommended a diet containing 10% minerals and at least 30% protein. In how many different ways can we prepare this diet by mixing at least two ingredients?

  1. A.

    One

  2. B.

    Two

  3. C.

    Three

  4. D.

    Four

  5. E.

    None

Answer

A

Explanation

Only ingredients O and Q contain 10% minerals. Any mixture of only O and Q will contain 10% minerals. Both O and Q contain 30% protein, so any mix of O and Q contains 30% protein. Thus, mixing O and Q is the only way.

Question 2 of 4

Which among the following is the formulation having the lowest cost per unit for a diet having 10% fat and at least 30% protein? (The diet has to be formed by mixing two ingredients).

  1. A.

    P and Q

  2. B.

    P and S

  3. C.

    P and R

  4. D.

    Q and S

  5. E.

    R and S

Answer

D

Explanation

To get 10% fat using two ingredients, one must have 0% fat and the other > 10% fat. Pair Q (50% fat) and S (0% fat): ratio 1:4 gives 10% fat. Protein =0.2(30%)+0.8(50%)=46%≥30%= 0.2(30\%) + 0.8(50\%) = 46\% \ge 30\%. Cost =1(200)+4(100)5=120= \frac{1(200) + 4(100)}{5} = 120. Pair R (40% fat) and S (0% fat): ratio 1:3 gives 10% fat. Cost =1(500)+3(100)4=200= \frac{1(500) + 3(100)}{4} = 200. Lowest cost is Q and S.

Question 3 of 4

In what proportion P, Q and S should be mixed to make a diet having at least 60% carbohydrate at the lowest cost per unit?

  1. A.

    2:1:3

  2. B.

    4:1:2

  3. C.

    2:1:4

  4. D.

    3:1:2

  5. E.

    4:1:1

Answer

E

Explanation

P has 80% carbohydrate, Q has 10%, S has 45%. Testing options for ≥60%\ge 60\% carbohydrate:

  • 4:1:1   ⟹  4(80)+1(10)+1(45)6=3756=62.5%≥60%\implies \frac{4(80) + 1(10) + 1(45)}{6} = \frac{375}{6} = 62.5\% \ge 60\%. Cost per unit for 4:1:1 =4(50)+1(200)+1(100)6=5006=83.33= \frac{4(50) + 1(200) + 1(100)}{6} = \frac{500}{6} = 83.33. This is the lowest cost among feasible options.

Question 4 of 4

The company is planning to launch a balanced diet required for growth needs of adolescent children. This diet must contain at least 30% each of carbohydrate and protein, no more than 25% fat and at least 5% minerals. Which one of the following combinations of equally mixed ingredients is feasible?

  1. A.

    O and P

  2. B.

    R and S

  3. C.

    P and S

  4. D.

    Q and R

  5. E.

    O and S

Answer

E

Explanation

Equally mixed O and S:

  • Carbohydrate: 50+452=47.5%≥30%\frac{50+45}{2} = 47.5\% \ge 30\%
  • Protein: 30+502=40%≥30%\frac{30+50}{2} = 40\% \ge 30\%
  • Fat: 10+02=5%≤25%\frac{10+0}{2} = 5\% \le 25\%
  • Minerals: 10+52=7.5%≥5%\frac{10+5}{2} = 7.5\% \ge 5\%. All conditions met by O and S.

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