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📌 Section 1 is Logical reasoning specially designed for CAT
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SET 1 — 🔍 CAT Level
An institute recently launched a new online course registration process and, as a result, set up an online helpline to assist students with course-related queries. Students can post their queries on the helpline between 10 AM and 6 PM each day. Every query is resolved by one of the institute's employees the next day. Accordingly, a query posted on Day 1 is resolved on Day 2, a query posted on Day 2 is resolved on Day 3, and so on.
There are four employees responsible for resolving these queries: Dudi, Anu, Tiru, and Sam.
Of all the queries received every day:
40% are valid queries.
The remaining 60% are spam.
Spam queries are discarded and, therefore, not resolved.
The bar graph below shows the number of queries resolved by Anu and Tiru from Day 2 to Day 6.
The additional information is also known:
(i) Each resolved query is handled by exactly one employee. No employee answered more than 40 valid queries on any day.
(ii) Dudi resolved the maximum number of queries every day, while Sam resolved the minimum number of queries every day. The number of queries resolved by each employee on any day is a distinct positive multiple of 5.
(iii) On Day 4, employees resolved queries equivalent to 30% of the total queries posted on Day 4. Similarly, on Day 3, employees resolved queries equivalent to 35% of the total queries posted on Day 1.
(iv) Sam resolved the same number of queries on Day 2 and Day 6, which is 5 less than the number of queries resolved on Day 4.
Question 1
How many queries were resolved on Day 2?
Question 2
Total how many queries were posted on Day 5?
Question 3
Total how many queries were resolved by Dudi on Day 2, Day 3, and Day 4?
90
100
105
110
Question 4
What is the ratio of total queries resolved by Sam on Day 2, Day 3, and Day 4 to the total spam queries posted on Day 1 and Day 4?
1 : 10
1 : 15
2 : 15
1 : 30
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✅ Answers & Explanations
Final Day-wise Table
Day | Anu | Tiru | Sam | Dudi | Total Resolved |
|---|---|---|---|---|---|
Day 2 | 15 | 20 | 10 | 35 | 80 |
Day 3 | 20 | 10 | 5 | 35 | 70 |
Day 4 | 25 | 20 | 15 | 30 | 90 |
Day 5 | 30 | 35 | 15 | 40 | 120 |
Day 6 | 35 | 25 | 10 | 40 | 110 |
Set 1
Valid queries = 40% of queries posted previous day.
Also, from condition (iii):
Day 4 resolved = 30% of Day 4 posted
Day 5 resolved = 40% of Day 4 posted
So,
Day 4 resolved : Day 5 resolved = 30 : 40 = 3 : 4
Hence:
90 : 120 = 3 : 4
Similarly,
Day 3 resolved = 35% of Day 1 posted
Day 2 resolved = 40% of Day 1 posted
So,
Day 3 resolved : Day 2 resolved = 35 : 40 = 7 : 8
Hence:
70 : 80 = 7 : 8
Sam on Day 2 = Sam on Day 6 = 5 less than Sam on Day 4.
So:
Sam Day 2 = 10
Sam Day 4 = 15
Sam Day 6 = 10
Question 1
How many queries were resolved on Day 2?
Day 2 total resolved:
15 + 20 + 10 + 35 = 80
Answer: 80
Question 2
Total how many queries were posted on Day 5?
Queries resolved on Day 6 = valid queries posted on Day 5.
Day 6 resolved = 110
Since valid queries are 40%:
40% of Day 5 posted = 110
Day 5 posted = 110 × 100 / 40 = 275
Answer: 275
Question 3
Total queries resolved by Dudi on Day 2, Day 3, and Day 4
Dudi:
Day 2 = 35
Day 3 = 35
Day 4 = 30
Total = 35 + 35 + 30 = 100
Answer: Option 2) 100
Question 4
Required ratio
Sam on Day 2, Day 3, Day 4:
10 + 5 + 15 = 30
Day 1 posted:
Day 2 resolved = 80 = 40% of Day 1 posted
Day 1 posted = 200
Spam = 60% of 200 = 120
Day 4 posted:
Day 5 resolved = 120 = 40% of Day 4 posted
Day 4 posted = 300
Spam = 60% of 300 = 180
Total spam = 120 + 180 = 300
Ratio = 30 : 300 = 1 : 10
Answer: Option 1) 1 : 10
⚡ 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!