In partnership with
📌 Section 1 is Logical reasoning specially designed for CAT
Stop Paying for 10 Tools. One AI Does It All.
Most e-commerce sellers are running their store across 6 to 10 separate tools — and spending more time managing software than growing their business. StoreClaw replaces your entire stack with one autonomous AI engine that monitors competitors, optimizes listings, automates marketing, and tracks real profit across Shopify, Amazon, and beyond.
It doesn't wait for you to ask. It runs 24/7 in the background, so you wake up to a full dashboard instead of a list of things you forgot to check.
Connect your store, and StoreClaw gets to work — no prompts, no complex setup, no six-app stack.
Free to start. No credit card required.
SET 1 — 🔍 CAT Level
Sixteen patients in a hospital must undergo a blood test for a disease. It is known that exactly one of them has the disease. The hospital has only eight testing kits and has decided to pool blood samples of patients into eight vials for the tests. The patients are numbered 1 through 16, and the vials are labelled A, B, C, D, E, F, G, and H. The following table shows the vials into which each patient's blood sample is distributed.
Patient | Vials | Patient | Vials |
|---|---|---|---|
1 | B, D, F, H | 9 | A, D, F, H |
2 | B, D, F, G | 10 | A, D, F, G |
3 | B, D, E, H | 11 | A, D, E, H |
4 | B, D, E, G | 12 | A, D, E, G |
5 | B, C, F, H | 13 | A, C, F, H |
6 | B, C, F, G | 14 | A, C, F, G |
7 | B, C, E, H | 15 | A, C, E, H |
8 | B, C, E, G | 16 | A, C, E, G |
If a patient has the disease, then each vial containing his/her blood sample will test positive. If a vial tests positive, one of the patients whose blood samples were mixed in the vial has the disease. If a vial tests negative, then none of the patients whose blood samples were mixed in the vial has the disease.
Question 1
Suppose vial C tests positive and vials A, E and H test negative. Which patient has the disease?
Patient 8
Patient 2
Patient 6
Patient 14
Question 2
Suppose vial A tests positive and vials D and G test negative. Which of the following vials should we test next to identify the patient with the disease?
Vial E
Vial H
Vial C
Vial B
Question 3
Which of the following combinations of test results is NOT possible?
Vials B and D positive, vials F and H negative
Vials A and E positive, vials C and D negative
Vials A and G positive, vials D and E negative
Vial B positive, vials C, F and H negative
Question 4
Suppose one of the lab assistants accidentally mixed two patients' blood samples before they were distributed to the vials. Which of the following correctly represents the set of all possible numbers of positive test results out of the eight vials?
{5, 6, 7, 8}
{4, 5, 6, 7}
{4, 5}
{4, 5, 6, 7, 8}
My VARC Newsletter for CAT Aspirants
📚 Serious about improving your CAT VARC score?
I run a free daily newsletter designed specifically for CAT aspirants who want consistent improvement in Verbal Ability & Reading Comprehension.
The newsletter includes:
• High-utility vocabulary, Idioms & phrases
• CAT-level Para Jumbles & Odd Sentence Out
• Reading Comprehension practice
• Fill in the blanks & verbal reasoning questions
• Practical explanations and usage examples
Perfect for students struggling with VARC, first-time CAT takers, and working professionals preparing alongside jobs.
Just 10 minutes of daily focused practice can create a huge difference over time.
Join Here: https://vocabwithease.beehiiv.com/
✅ Answers & Explanations
Every patient’s blood goes into four vials, choosing exactly one vial from each pair:
A or B
C or D
E or F
G or H
So each patient has a unique four-vial combination.
For example:
Patient 6 → B, C, F, G
Patient 14 → A, C, F, G
A positive vial contains the diseased patient’s blood.
A negative vial definitely does not contain the diseased patient’s blood.
Question 1
C is positive, while A, E and H are negative.
A negative means the patient must be among 1–8, all of whom are in B.
C positive narrows it to Patients 5, 6, 7 and 8.
E negative removes Patients 7 and 8.
H negative removes Patient 5.
Only Patient 6 remains.
Answer: Option 3 — Patient 6
Question 2
A is positive, while D and G are negative.
A positive means the patient is among 9–16.
D negative removes Patients 9–12.
G negative removes Patients 14 and 16.
Remaining patients:
Patient 13 → A, C, F, H
Patient 15 → A, C, E, H
They differ only in E and F.
So test vial E:
E positive → Patient 15
E negative → Patient 13
Answer: Option 1 — Vial E
Question 3
We must find the impossible result.
Option 1
B and D positive; F and H negative.
That gives B, D, E, G, which is Patient 4.
Possible.
Option 2
A and E positive; C and D negative.
This is impossible because every patient’s blood is placed in either C or D.
Therefore, C and D cannot both be negative when one patient is diseased.
Option 3
A and G positive; D and E negative.
That gives A, C, F, G, which is Patient 14.
Possible.
Option 4
B positive; C, F and H negative.
That gives B, D, E, G, which is Patient 4.
Possible.
Answer: Option 2
Question 4
Normally, one diseased patient produces four positive vials.
If two patients’ samples are mixed, the diseased blood may spread into the vials of both patients.
Depending on how many vials the two patients share, the total number of positive vials can be:
5 positive vials
6 positive vials
7 positive vials
8 positive vials
Also, if the two mixed patients are both healthy, the original diseased patient still produces only four positive vials.
Therefore, all possible numbers are:
{4, 5, 6, 7, 8}
Answer: Option 4
Final Answers
Patient 6
Vial E
Option 2
{4, 5, 6, 7, 8}
⚡ 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!