What is the median of the number of grams of protein in 100 g… | CAT 2024 DILR Slot 3 Q18

Questions on this set: Q15 Q16 Q17 Q18

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 odename. The table has some missing values.

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.

Q18 DI - Reasoning-based DI TYPE IN THE ANSWER

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

Answer: 12

Each row adds up to 100. Missing carbohydrate values are multiples of 5; other missing values are multiples of 4.

P1 and M3: P1 has protein + fat = 24, so P1 protein ≤ 20. It equals 2 × M3 protein, which is a multiple of 8: either 8 or 16. It must also exceed M1's protein of 10 (fact 1). So P1 protein = 16 and P1 fat = 8. Then M3 protein = 8 and M3 other = 100 − 56 − 8 − 12 = 24.
P2: carbohydrate + fat = 78. Its carbohydrate must exceed every millet (at least 62). The options are 70 + 8 or 50 + 28, and only 70 + 8 is large enough. So P2 carbohydrate = 70, fat = 8.
M2: carbohydrate + protein = 77. The options are 65 + 12, 45 + 32, and so on. Its protein must be below 14 (P2's protein), so M2 = 65 carbohydrate, 12 protein. This also keeps it below P1's 66.
C1: carbohydrate + protein = 88, with carbohydrate above 70 (fact 2): 80 + 8. (75 + 13 fails, since 13 is not a multiple of 4.)
C2: carbohydrate + protein = 87: 75 + 12. (80 + 7 fails.)
M1: fat + other = 28. This split is not fixed and is not needed.

Grain	Carb	Protein
C1	80	8
C2	75	12
M1	62	10
M2	65	12
M3	56	8
P1	66	16
P2	70	14

Proteins in order: 8, 8, 10, 12, 12, 14, 16. The middle (4th) value is 12.

Answer: 12

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