CAT 2024 Slot 3 — DILR Question 18

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Passage / Data

Answer the following questions based on the information given below.

The table given below shows the amount, in grams, of carbohydrate, protein, fat and all other nutrients, per 100 grams of nutrients in seven foodgrains. The first column shows the foodgrain category and the second column its codename. The table has some missing values.

Table of carbohydrate, protein, fat and other nutrients per 100 g for seven foodgrains

Category	Codename	Carbohydrate	Protein	Fat	Other nutrients
Cereal	C1	—	—	0	12
Cereal	C2	—	—	3	10
Millet	M1	62	10	—	—
Millet	M2	—	—	7	16
Millet	M3	56	—	12	—
Pseudo-cereal	P1	66	—	—	10
Pseudo-cereal	P2	—	14	—	8

The following additional facts are known.
1. Both the pseudo-cereals had higher amounts of carbohydrate as well as higher amounts of protein than any millet.
2. Both the cereals had higher amounts of carbohydrate than any pseudo-cereal.
3. All the missing values of carbohydrate amounts (in grams) for all the foodgrains are non-zero multiples of 5.
4. All the missing values of protein, fat and other nutrients amounts (in grams) for all the foodgrains are non-zero multiples of 4.
5. P1 contained double the amount of protein that M3 contains.

What is the median of the number of grams of protein in 100 grams of nutrients among these food grains?

Answer & solution

Correct answer: 12

Answer: 12

Solution

Hard

Complete every protein value, sort the seven numbers, and take the middle (4th) one.

Protein (g): C1=8, C2=12, M1=10, M2=12, M3=8, P1=16, P2=14 (each derived from its row total and the multiple-of-4 rule with Facts 1–5).

Order the seven protein values and pick the median.

\begin{aligned} &8,\ 8,\ 10,\ 12,\ 12,\ 14,\ 16\\ &\Rightarrow\ \text{median}=\text{4th value}=12 \end{aligned}

12 \text{ g}

CAT 2024 Slot 3 — DILR Question 18

Answer & solution

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