CAT 2024 Slot 3 DILR Set 1 Q1–Q4

A DILR caselet from the Data Interpretation & Logical Reasoning (DILR) section of CAT 2024 Slot 3, with 4 questions (Charts & Tables). Answers are CAT's official key.

The set

This set relies on a figure in the original paper, which is not reproduced here. The questions and answers are 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.

[Figure in the original paper]

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 1

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

TITA: type in the answer. There are no options and no negative marking.

Answer: 5 Charts & Tables TITA

Solution

  1. Each row sums to 100. P2: carb + fat \(= 78\), carb a multiple of 5 and above every millet (so \(> 62\)), fat a multiple of 4: carb \(= 70\), fat \(= 8\).
  2. Cereals beat 70 in carb. C1: carb + protein \(= 88\) forces carb \(= 80\), protein \(= 8\). C2: carb + protein \(= 87\) forces carb \(= 75\), protein \(= 12\).
  3. P1: protein + fat \(= 24\), protein \(= 2 \times\) M3's protein (a multiple of 4) and \(> 10\) (M1's protein), so P1 protein \(= 16\), fat \(= 8\); M3 protein \(= 8\), other \(= 100 - 56 - 8 - 12 = 24\).
  4. M2: carb + protein \(= 77\), protein a multiple of 4 below 14 (P2's protein), carb a multiple of 5 below 66: protein \(= 12\), carb \(= 65\).
  5. Carbohydrates: C1 80, C2 75, M2 65, P1 66, P2 70 all exceed M1's 62 (M3 is 56). Answer: 5.

Question 2

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

TITA: type in the answer. There are no options and no negative marking.

Answer: 12 Charts & Tables TITA

Solution

  1. Each row sums to 100. P2: carb + fat \(= 78\), carb a multiple of 5 and above every millet (so \(> 62\)), fat a multiple of 4: carb \(= 70\), fat \(= 8\).
  2. Cereals beat 70 in carb. C1: carb + protein \(= 88\) forces carb \(= 80\), protein \(= 8\). C2: carb + protein \(= 87\) forces carb \(= 75\), protein \(= 12\).
  3. P1: protein + fat \(= 24\), protein \(= 2 \times\) M3's protein (a multiple of 4) and \(> 10\) (M1's protein), so P1 protein \(= 16\), fat \(= 8\); M3 protein \(= 8\), other \(= 100 - 56 - 8 - 12 = 24\).
  4. M2: carb + protein \(= 77\), protein a multiple of 4 below 14 (P2's protein), carb a multiple of 5 below 66: protein \(= 12\), carb \(= 65\).
  5. So M2 has 12 g protein.

Question 3

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

TITA: type in the answer. There are no options and no negative marking.

Answer: 24 Charts & Tables TITA

Solution

  1. Each row sums to 100. P2: carb + fat \(= 78\), carb a multiple of 5 and above every millet (so \(> 62\)), fat a multiple of 4: carb \(= 70\), fat \(= 8\).
  2. Cereals beat 70 in carb. C1: carb + protein \(= 88\) forces carb \(= 80\), protein \(= 8\). C2: carb + protein \(= 87\) forces carb \(= 75\), protein \(= 12\).
  3. P1: protein + fat \(= 24\), protein \(= 2 \times\) M3's protein (a multiple of 4) and \(> 10\) (M1's protein), so P1 protein \(= 16\), fat \(= 8\); M3 protein \(= 8\), other \(= 100 - 56 - 8 - 12 = 24\).
  4. M2: carb + protein \(= 77\), protein a multiple of 4 below 14 (P2's protein), carb a multiple of 5 below 66: protein \(= 12\), carb \(= 65\).
  5. M3's other nutrients \(= 24\) g.

Question 4

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

TITA: type in the answer. There are no options and no negative marking.

Answer: 12 Charts & Tables TITA

Solution

  1. Each row sums to 100. P2: carb + fat \(= 78\), carb a multiple of 5 and above every millet (so \(> 62\)), fat a multiple of 4: carb \(= 70\), fat \(= 8\).
  2. Cereals beat 70 in carb. C1: carb + protein \(= 88\) forces carb \(= 80\), protein \(= 8\). C2: carb + protein \(= 87\) forces carb \(= 75\), protein \(= 12\).
  3. P1: protein + fat \(= 24\), protein \(= 2 \times\) M3's protein (a multiple of 4) and \(> 10\) (M1's protein), so P1 protein \(= 16\), fat \(= 8\); M3 protein \(= 8\), other \(= 100 - 56 - 8 - 12 = 24\).
  4. M2: carb + protein \(= 77\), protein a multiple of 4 below 14 (P2's protein), carb a multiple of 5 below 66: protein \(= 12\), carb \(= 65\).
  5. Proteins: 8, 12, 10, 12, 8, 16, 14. Sorted 8, 8, 10, 12, 12, 14, 16; median \(= 12\).

Same concept in other years

See every question on Table with missing entries completed from additional clues.

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