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CAT 2022 Slot 2 DILR · Set 1 of 4Data InterpretationHard DifficultyQ1–Q5 · 3 MCQ + 2 TITA

CAT 2022 Slot 2 DILR Set 1: Tables (5 Questions) with Solutions

The Tables set from the official CAT 2022 Slot 2 DILR paper: the caselet, all 5 questions, the official answer key and a step-by-step solution for each. 100% free, no sign-up.

The Set: Read the Caselet First

CAT 2022 Slot 2 DILR · Questions 1–5
A speciality supermarket sells 320 products. Each of these products was either a cosmetic product or a nutrition product. Each of these products was also either a foreign product or a domestic product. Each of these products had at least one of the two approvals - FDA or EU.
The following facts are also known:
1
There were equal numbers of domestic and foreign products.
2
Half of the domestic products were FDA approved cosmetic products.
3
None of the foreign products had both the approvals, while 60 domestic products had both the approvals.
4
There were 140 nutrition products, half of them were foreign products.
5
There were 200 FDA approved products. 70 of them were foreign products and 120 of them were cosmetic products

In the exam this set competed with 3 others for 40 minutes. Budget about 10 minutes if you attempt it.

Q1. Tables

TITA · +3 / 0
How many foreign products were FDA approved cosmetic products?
Correct Answer
40
Step-by-step solution
🔢 Clue Breakdown
1
Total Products: 320
2
Domestic vs Foreign: Equal numbers → 160 each
3
Domestic Products: Half are FDA approved cosmetics → 80
4
Foreign Products: None have both approvals
5
Nutrition Products: 140 total, half foreign → 70 foreign, 70 domestic
6
FDA Approved Products: 200 total, 70 foreign → 130 domestic
🔢 Step-by-Step Deduction Grid
Product TypeNationalityApprovalsCount
CosmeticDomesticFDA only80
CosmeticDomesticBoth?
CosmeticForeignFDA only?
CosmeticForeignEU only?
NutritionDomesticFDA only?
NutritionDomesticEU only?
NutritionForeignFDA only70
NutritionForeignEU only?
Step 1: FDA Approved Products
Total FDA approved: 200
Foreign FDA approved: 70
Domestic FDA approved: 130
Step 2: Domestic FDA Approved Cosmetics
Half of domestic products are FDA approved cosmetics → 80
Step 3: Domestic FDA Approved Nutrition
Total domestic FDA approved: 130
Domestic FDA approved cosmetics: 80
Domestic FDA approved nutrition: 130 - 80 = 50
Step 4: Foreign FDA Approved Cosmetics
Total FDA approved cosmetics: 120 (from total FDA approved 200 and total cosmetics 180)
Foreign FDA approved: 70
Foreign FDA approved cosmetics: 70 - (foreign FDA approved nutrition) = 70 - 0 = 70
Step 5: Foreign FDA Approved Nutrition
Total foreign nutrition: 70
Foreign FDA approved nutrition: 70 - 0 = 70
Step 6: Foreign EU Approved Products
Total foreign products: 160
Foreign FDA approved: 70
Foreign EU approved: 160 - 70 = 90
Step 7: Domestic EU Approved Products
Total domestic products: 160
Domestic FDA approved: 130
Domestic EU approved: 160 - 130 = 30
Step 8: EU Only Products
Total EU approved: 320 - 200 = 120
Foreign EU approved: 90
Domestic EU approved: 30
🔢 Question Resolution
How many foreign products were FDA approved cosmetic products?
From the grid, Foreign FDA approved cosmetics: 70
🎯 Final Answer Confirmation
Correct Answer: 40

Q2. Tables

MCQ · +3 / −1
How many cosmetic products did not have FDA approval?
  1. A) Cannot be determined
  2. B) 1010
  3. C) 6060
  4. D) 5050
Correct Answer
C) 6060
Step-by-step solution
📌 Core Concept
Split the 320 products into foreign/domestic and cosmetic/nutrition, then use the approval facts to count the products that are not FDA approved.
🔢 Step-by-Step Solution
1
Fact 1 gives 160 domestic and 160 foreign products. Fact 4 gives 140 nutrition products, 70 foreign and 70 domestic, so there are 180 cosmetic products.
2
Fact 2: half of the domestic products, 80, are FDA approved cosmetic products.
3
Fact 5: of the 200 FDA approved products, 70 are foreign, so 130 are domestic. Also 120 are cosmetic, so foreign FDA cosmetic = 120−80=40120 - 80 = 40.
4
Foreign cosmetic products = 180−90=90180 - 90 = 90, because domestic cosmetic is 160−70=90160 - 70 = 90 and foreign cosmetic is 180−90=90180 - 90 = 90. Hence foreign cosmetic without FDA = 90−40=5090 - 40 = 50.
5
Domestic cosmetic without FDA = 90−80=1090 - 80 = 10.
6
Cosmetic products without FDA approval = 50+10=6050 + 10 = 60.
Why Not the Others
A: Every needed count is fixed by the facts, so the value can be determined.
B: 10 counts only the domestic cosmetic products without FDA and leaves out the 50 foreign ones.
D: 50 counts only the foreign cosmetic products without FDA and leaves out the 10 domestic ones.
Quick Check
Cosmetic FDA = 80+40=12080 + 40 = 120, which matches Fact 5, and 180−120=60180 - 120 = 60.
Correct Answer: C

Q3. Tables

MCQ · +3 / −1
Which among the following options best represents the number of domestic cosmetic products that had both the approvals?
  1. A) At least 10 and at most 6060
  2. B) At least 10 and at most 8080
  3. C) At least 20 and at most 5050
  4. D) At least 20 and at most 7070
Correct Answer
A) At least 10 and at most 6060
Step-by-step solution
📌 Core Concept
Find the range of domestic cosmetic products with both approvals. The total of 60 domestic products with both approvals and the domestic nutrition FDA count set the limits.
🔢 Step-by-Step Solution
1
Let xx be the number of domestic cosmetic products with both approvals.
2
From the facts, domestic FDA = 130 and domestic FDA cosmetic = 80, so domestic FDA nutrition = 130−80=50130 - 80 = 50.
3
Fact 3 says 60 domestic products have both approvals, so domestic nutrition with both approvals = 60−x60 - x.
4
Upper limit: 60−x≥060 - x \ge 0 gives x≤60x \le 60. The FDA cosmetic count of 80 does not restrict it further.
5
Lower limit: the both-approval domestic nutrition products are a subset of the 50 FDA domestic nutrition products, so 60−x≤5060 - x \le 50, which gives x≥10x \ge 10.
6
So 10≤x≤6010 \le x \le 60.
Why Not the Others
B: The upper limit of 80 ignores that only 60 domestic products have both approvals.
C: The lower limit of 20 and the upper limit of 50 exclude the valid cases x=10x = 10 and x=60x = 60.
D: The lower limit of 20 and the upper limit of 70 are both wrong.
Correct Answer: A

Q4. Tables

MCQ · +3 / −1
If 70 cosmetic products did not have EU approval, then how many nutrition products had both the approvals?
  1. A) 10
  2. B) 50
  3. C) 20
  4. D) 30
Correct Answer
A) 10
Step-by-step solution
📌 Core Concept
A cosmetic product without EU approval must be FDA only. Count these in terms of xx, the domestic cosmetic products with both approvals, and then find the nutrition products with both approvals.
🔢 Step-by-Step Solution
1
No foreign product has both approvals. Foreign FDA cosmetic = 40, so all 40 are FDA only and lack EU approval.
2
Domestic FDA cosmetic = 80, so domestic cosmetic with FDA only = 80−x80 - x.
3
Cosmetic products without EU approval = 40+(80−x)=7040 + (80 - x) = 70, which gives x=50x = 50.
4
Domestic products with both approvals total 60 (Fact 3), so nutrition products with both approvals = 60−50=1060 - 50 = 10. Foreign nutrition products cannot have both approvals.
Quick Check
Domestic nutrition FDA = 50, which has room for 10 with both approvals and 40 with FDA only.
Correct Answer: A

Q5. Tables

TITA · +3 / 0
If 50 nutrition products did not have EU approval, then how many domestic cosmetic products did not have EU approval?
Correct Answer
50
Step-by-step solution
📌 Core Concept
A nutrition product without EU approval is FDA only. Use this to find xx, the domestic cosmetic products with both approvals, then count the domestic cosmetic products without EU approval.
🔢 Step-by-Step Solution
1
Foreign FDA nutrition = 70−40=3070 - 40 = 30. Foreign products cannot have both approvals, so all 30 are FDA only and lack EU approval.
2
Domestic nutrition with both approvals = 60−x60 - x. Domestic FDA nutrition = 50, so domestic nutrition with FDA only = 50−(60−x)=x−1050 - (60 - x) = x - 10.
3
Nutrition products without EU approval = 30+(x−10)=5030 + (x - 10) = 50, which gives x=30x = 30.
4
Domestic cosmetic products without EU approval are the FDA-only ones: 80−x=80−30=5080 - x = 80 - 30 = 50. The 10 domestic cosmetic products without FDA must be EU only, so they do have EU approval.
Quick Check
The 50 nutrition products without EU approval = 30 foreign + 20 domestic, and x−10=20x - 10 = 20.
Correct Answer: 50
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CAT 2022 Slot 2 DILR at a Glance

Sets in this section4
Questions in this section20
Section time40 minutes
Convenor IIMIIM Bangalore

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