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CAT 2024 Slot 3 — DILR Question 16

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 grams of protein were there in 100 grams of nutrients in M2?

Answer & solution

Answer: 12

Solution

Medium

For M2 the row total 100 with fat=7, other=16 leaves carb+protein=77; the multiple rules and Fact 1 (protein below P2's 14) pin protein.

M2: fat =7=7, other =16=16, so carb ++ protein =77=77. Carb is a multiple of 5, protein a multiple of 4. Pseudo-cereals' protein (P2 =14=14) must exceed every millet protein (Fact 1).

1

Solve carb + protein = 77. Carb ≡0 (mod 5)\equiv0\ (\text{mod }5) forces protein ≡2 (mod 5)\equiv2\ (\text{mod }5); the only multiple of 4 that is ≡2 (mod 5)\equiv2\ (\text{mod }5) and below 14 is 12.

protein∈{12,32,… }(mult of 4, gives carb mult of 5)⇒ protein<14 (Fact 1, <P2)⇒ protein=12, carb=65\begin{aligned} &\text{protein}\in\{12,32,\dots\}\quad\text{(mult of 4, gives carb mult of 5)}\\ &\Rightarrow\ \text{protein}<14\ \text{(Fact 1, }<\text{P2)}\\ &\Rightarrow\ \text{protein}=12,\ \text{carb}=65 \end{aligned}
12 g12 \text{ g}
CAT 2024 Slot 3 DILR Q16: How many grams of protein were there in 100 grams of nutrients in M2? — Solution | TheCATExam