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CAT 2024 Slot 3 — DILR Question 15

TablesEasy
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

CategoryCodenameCarbohydrateProteinFatOther nutrients
CerealC1——012
CerealC2——310
MilletM16210——
MilletM2——716
MilletM356—12—
Pseudo-cerealP166——10
Pseudo-cerealP2—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.

How many foodgrains had a higher amount of carbohydrate per 100 grams of nutrients than M1?

Answer & solution

Answer: 5

Solution

Hard

Each row of nutrients totals 100 g. Fill blanks using the row sums and the multiple-of-5 / multiple-of-4 rules, ordered by Facts 1, 2 and 5, then count carbohydrate values above M1's 62.

Rows sum to 100. Carb blanks are non-zero multiples of 5; protein/fat/other blanks are non-zero multiples of 4. Known carbs: M1=62, M3=56, P1=66.

Solved carbs: C1=80, C2=75, M2=65, P2=70 (with P2 fat=8 so carb=70; M2 prot=12 so carb=65; cereals must exceed all pseudo-cereals, forcing 80 and 75).

1

Pin the unknown carbs. Use Facts 1–2 (pseudo > millet, cereal > pseudo) with the multiple-of-5 rule.

P2: 70+14+8+8=100⇒carb=70⇒ M2 carb=65, (<66, below pseudo-cereals)⇒ C1 carb=80, C2 carb=75 (>70, above all pseudo-cereals)\begin{aligned} &\text{P2: }70+14+8+8=100 \Rightarrow \text{carb}=70\\ &\Rightarrow\ \text{M2 carb}=65,\ \text{(}<66\text{, below pseudo-cereals)}\\ &\Rightarrow\ \text{C1 carb}=80,\ \text{C2 carb}=75\ \text{(}>70\text{, above all pseudo-cereals)} \end{aligned}
2

Count carbohydrate values exceeding M1 = 62.

carbs={C1=80, C2=75, M2=65, P1=66, P2=70}>62⇒ count=5(M3=56 excluded)\begin{aligned} &\text{carbs}=\{C1{=}80,\ C2{=}75,\ M2{=}65,\ P1{=}66,\ P2{=}70\}>62\\ &\Rightarrow\ \text{count}=5 \quad\text{(M3}{=}56\text{ excluded)} \end{aligned}
55
CAT 2024 Slot 3 DILR Q15: How many foodgrains had a higher amount of carbohydrate per 100 grams of nutrients than M1? — Solution | TheCATExam