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📌 Section 1 is Logical reasoning specially designed for CAT
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SET 1 — 🔍 CAT Level
RAT, a national level entrance test for admission to management schools, has three sections – Verbal Ability (VA), Quantitative Ability (QA), and Data Interpretation (DI). The total maximum marks in the paper is 150, with each section having questions worth 50 marks.
This year, the paper had three types of questions:
1-mark questions
2-mark questions
3-mark questions
There were at least ten questions of each type in the entire paper.
Each of the three sections had at least one question of each of the three types, and the total number of questions in each section was different.
Question 1
The total number of questions in the DI and QA sections together is at least?
Question 2
If the total number of questions in the test was the minimum possible, then the number of questions in the QA section was at most?
Question 3
If the number of questions in the test was the maximum possible, then the number of questions in the DI section was at least?
Question 4
Suchitra, a student who took the test, takes an average of:
10 minutes to attempt one question in DI
8 minutes to attempt one question in QA
4 minutes to attempt one question in VA
If the duration of the test is 150 minutes, what is the maximum total marks she can score?
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✅ Answers & Explanations
Each section has 50 marks.
A section can have:
Minimum questions = 18
Because 1 one-mark + 2 two-mark + 15 three-mark questions = 50 marks
So, 1 + 2 + 15 = 18 questions
Maximum questions = 47
Because 45 one-mark + 1 two-mark + 1 three-mark question = 50 marks
So, 45 + 1 + 1 = 47 questions
Question 1
DI + QA together is at least
To minimize DI + QA, we maximize VA.
But the paper must have at least 10 questions of each type.
One possible arrangement:
Section | 1-mark | 2-mark | 3-mark | Total Questions |
|---|---|---|---|---|
VA | 6 | 7 | 10 | 23 |
QA | 1 | 2 | 15 | 18 |
DI | 3 | 1 | 15 | 19 |
Total questions in QA + DI = 18 + 19 = 37
Answer: 37
Question 2
If total questions is minimum possible, QA was at most
Minimum total questions possible = 60
One possible arrangement:
Section | 1-mark | 2-mark | 3-mark | Total Questions |
|---|---|---|---|---|
VA | 1 | 2 | 15 | 18 |
QA | 6 | 7 | 10 | 23 |
DI | 3 | 1 | 15 | 19 |
So, QA can have at most 23 questions.
Answer: 23
Question 3
If total questions is maximum possible, DI was at least
Maximum total questions possible = 120
One possible arrangement:
Section | 1-mark | 2-mark | 3-mark | Total Questions |
|---|---|---|---|---|
VA | 43 | 2 | 1 | 46 |
QA | 45 | 1 | 1 | 47 |
DI | 12 | 7 | 8 | 27 |
So, DI must have at least 27 questions.
Answer: 27
Question 4
To maximize marks, Suchitra should attempt the fastest scoring section first.
VA takes 4 minutes per question, so it is the best section.
A valid VA section can be:
Type | No. of Questions | Marks |
|---|---|---|
1-mark | 1 | 1 |
2-mark | 2 | 4 |
3-mark | 15 | 45 |
Total | 18 | 50 |
She should skip the 1-mark VA question and attempt the remaining VA questions.
VA marks scored = 49
VA time taken = 17 × 4 = 68 minutes
Remaining time = 150 - 68 = 82 minutes
Now she should attempt QA 3-mark questions.
A valid QA section can have 10 questions of 3 marks each.
Time for 10 QA questions = 10 × 8 = 80 minutes
Marks scored = 10 × 3 = 30
Total time = 68 + 80 = 148 minutes
Total marks = 49 + 30 = 79
So, maximum marks = 79
Why 80 is not possible
To score 80, even if she scores all 50 marks in VA, she still needs 30 marks from QA/DI.
Minimum time for full VA section = 18 × 4 = 72 minutes
Minimum time for 30 marks outside VA = 10 QA questions × 8 = 80 minutes
Total minimum time = 72 + 80 = 152 minutes
But the test duration is only 150 minutes.
Therefore, 80 is impossible.
Final Answer: 79 marks
⚡ Brain teasers are not just about getting the right answer — they train you to think differently under pressure.
Stay consistent with your daily practice, challenge your assumptions, and keep sharpening your reasoning skills.
See you in tomorrow’s challenge!