CAT 2024 Question Paper | DILR Slot 3

CAT Questions

CAT 2024 DILR did not have a change in pattern. Atleast two sets were doable in each slot and one of the four sets was extremely tough. Choice of Sets became a crucial factor. Overall this section was at a medium to high level of difficulty.

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.



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.

Question 3 : How many grams of other nutrients were there in 100 grams of nutrients in M3?

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Video Explanation

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Explanatory Answer

Food Grain Category	Codename for Foodgrain	Composition per hundred grams of nutrients in the food grains
		Carbohydrate	Protein	Fat	Other Nutrients
Cereal	C1	CC1	4p	0	12
	C2	CC2	4q	3	10
Millet	M1	62	10	4m	4r
	M2	CM2	4s	7	16
	M3	56	4t	12	4k
Pseudo-Cereal	P1	66	8t	4n	10
	P2	CP2	14	4k	8

P2:

CP2 > 62.
CP2 + 14 + 8 + 4k = 100.
CP2 + 4k = 78.
The only possible value of CP2 being an even multiple of 5 and satisfying the equation is 70.
Hence, 4k = 8.

C1:
CC1 > 66; CC1 + 4p + 0 + 12 = 100; CC1 + 4p = 88.
The only possible value of CC1 being an even multiple of 5 and satisfying the equation is 80.
Hence, 4p = 8.

C2:
CC2 > 66; CC2 + 4q + 3 + 10 = 100; CC2 + 4q = 87.
CC2 is odd.
The only possible value of CC2 being an odd multiple of 5 and satisfying the equation is 75.
Hence, 4q = 12.

Food Grain Category	Codename for Foodgrain	Composition per hundred grams of nutrients in the food grains
		Carbohydrate	Protein	Fat	Other Nutrients
Cereal	C1	80	8	0	12
	C2	75	12	3	10
Millet	M1	62	10	4m	4r
	M2	CM2	4s	7	16
	M3	56	4t	12	4k
Pseudo-Cereal	P1	66	8t	4n	10
	P2	70	14	8	8

M2:
Protein in millet is less than 14. Therefore 4s < 14.
CM2 + 4s + 7 + 16 = 100.
CM2 + 4s = 77.

CM2 = 77 - 4s should be a multiple of 5. 77 - 4 = 71 and 77 - 8 = 69 doesn’t satisfy.
77 - 12 = 65 satisfies. Therefore, CM2 = 65 and 4s = 12.

P1:
66 + 8t + 4n + 10 = 100; Since Protein for P1 should be greater than Protein in Millet. 8t > 10
8t + 4n = 24; 8t > 10.
Therefore 8t = 16 and 4n = 8.

M3:
56 + 4t + 12 + 4k = 100.
56 + 8 + 12 + 4k = 100.
76 + 4k = 100; 4k = 24.

Thus, the final table is,

Food Grain Category	Codename for Foodgrain	Composition per hundred grams of nutrients in the food grains
		Carbohydrate	Protein	Fat	Other Nutrients
Cereal	C1	80	8	0	12
	C2	75	12	3	10
Millet	M1	62	10	4m	4r
	M2	65	12	7	16
	M3	56	8	12	24
Pseudo-Cereal	P1	66	16	8	10
	P2	70	14	8	8

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The question is "How many grams of other nutrients were there in 100 grams of nutrients in M3?"

Solution: From the table, it is known that M3 has 24 grams of other nutrients per 100 grams of nutrients.

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