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CAT 2021 Slot 3 Question Paper with Solutions

66 questions in 120 minutes, in three timed sections. Below: how the paper is built, the topics each section tested, and a solved sample from every section. Take the whole paper in the simulator to get your Score Waterfall, Topic ROI Map and Strategic IQ.

Paper structure and topics

VARC

Verbal Ability & Reading Comprehension

24 questions · 19 MCQ · 5 TITA

Reading Comprehension · 16
Verbal Ability · 8

DILR

Data Interpretation & Logical Reasoning

20 questions · 14 MCQ · 6 TITA

Logical Reasoning · 16
Data Interpretation · 4

QA

Quantitative Ability

22 questions · 14 MCQ · 8 TITA

Arithmetic · 11
Algebra · 7
Geometry · 4

Sample questions with solutions

15 of the 66 questions: the first passage, the first DILR set and the first QA questions of the paper.

VARC · Verbal Ability & Reading Comprehension

Passage

Back in the early 2000s, an awesome thing happened in the New X-Men comics. Our mutant heroes had been battling giant robots called Sentinels for years, but suddenly these mechanical overlords spawned a new threat: Nano-Sentinels! Not content to rule Earth with their metal fists, these tiny robots invaded our bodies at the microscopic level. Infected humans were slowly converted into machines, cell by cell.

Now, a new wave of extremely odd robots is making at least part of the Nano-Sentinels story come true. Using exotic fabrication materials like squishy hydrogels and elastic polymers, researchers are making autonomous devices that are often tiny and that could turn out to be more powerful than an army of Terminators. Some are 1-centimetre blobs that can skate overwater. Others are flat sheets that can roll themselves into tubes, or matchstick-sized plastic coils that act as powerful muscles. No, they won’t be invading our bodies and turning us into Sentinels – which I personally find a little disappointing – but some of them could one day swim through our bloodstream to heal us. They could also clean up pollutants in water or fold themselves into different kinds of vehicles for us to drive. . . .

Unlike a traditional robot, which is made of mechanical parts, these new kinds of robots are made from molecular parts. The principle is the same: both are devices that can move around and do things independently. But a robot made from smart materials might be nothing more than a pink drop of hydrogel. Instead of gears and wires, it’s assembled from two kinds of molecules – some that love water and some that avoid it – which interact to allow the bot to skate on top of a pond.

Sometimes these materials are used to enhance more conventional robots. One team of researchers, for example, has developed a different kind of hydrogel that becomes sticky when exposed to a low-voltage zap of electricity and then stops being sticky when the electricity is switched off. This putty-like gel can be pasted right onto the feet or wheels of a robot. When the robot wants to climb a sheer wall or scoot across the ceiling, it can activate its sticky feet with a few volts. Once it is back on a flat surface again, the robot turns off the adhesive like a light switch.

Robots that are wholly or partly made of gloop aren’t the future that I was promised in science fiction. But it’s definitely the future I want. I’m especially keen on the nanometre-scale “soft robots” that could one day swim through our bodies. Metin Sitti, a director at the Max Planck Institute for Intelligent Systems in Germany, worked with colleagues to prototype these tiny, synthetic beasts using various stretchy materials, such as simple rubber, and seeding them with magnetic microparticles. They are assembled into a finished shape by applying magnetic fields. The results look like flowers or geometric shapes made from Tinkertoy ball and stick modelling kits. They’re guided through tubes of fluid using magnets, and can even stop and cling to the sides of a tube.

Question 1 · MCQ

Which one of the following scenarios, if false, could be seen as supporting the passage?

A.
Some hydrogels turn sticky when an electric current is passed through them; this potentially has very useful applications.
B.
Robots made from smart materials are likely to become part of our everyday lives in the future.
C.
Nano-Sentinel-like robots are likely to be used to inject people to convert them into robots, cell by cell.
✓ Correct
D.
There are two kinds of molecules used to make some nano-robots: one that reacts positively to water and the other negatively.

Solution

The passage explicitly says the new robots "won’t be invading our bodies and turning us into Sentinels." If option 3 were false (i.e., Nano-Sentinel-like robots are NOT likely to be used for such conversion), it would align perfectly with the passage's claim. Thus, the falsehood of option 3 supports the passage.

Question 2 · MCQ

Which one of the following statements, if true, would be the most direct extension of the arguments in the passage?

A.
In the future, robots will be used to search and destroy diseases even in the deepest recesses of the human body.
✓ Correct
B.
X-Men may be created by injecting people with mutant nano-gels that will respond to the brain’s magnetic field.
C.
Sentinel robots will be used in warfare to cause large-scale destructive mutations amongst civilians.
D.
1-centimetre blobs of gel that have nano-robots in them will be used to send messages.

Solution

The passage discusses robots that "could one day swim through our bloodstream to heal us" and prototypes that can navigate tubes using magnets. Option 1 directly extends these ideas: future robots targeting diseases deep inside the body. Other options introduce unsupported sci‑fi or unrelated concepts.

Question 3 · MCQ

Which one of the following statements best captures the sense of the first paragraph?

A.
The X-Men were mutant heroes who now had to battle tiny robots called Nano Sentinels.
✓ Correct
B.
People who were infected by Nano-Sentinel robots became mutants who were called X Men.
C.
Tiny sentinels called X-Men infected people, turning them into mutant robot overlords.
D.
None of the options listed here.

Solution

The first paragraph describes the X‑Men battling Nano‑Sentinels that turn humans into machines. Option 1 correctly captures this: the mutant heroes fought tiny robots. Other options misstate who the X‑Men are or what the Nano‑Sentinels do.

Question 4 · MCQ

Which one of the following statements best summarises the central point of the passage?

A.
Robots will use nano-robots on their feet and wheels to climb walls or move on ceilings.
B.
Once the stuff of science fiction, nano-robots now feature in cutting-edge scientific research.
✓ Correct
C.
Nano-robots made from molecules that react to water have become increasingly useful.
D.
The field of robotics is likely to be feature more and more in comics like the New X-Men

Solution

The passage moves from a sci‑fi comic scenario to real‑world soft‑robot research, emphasizing that these devices are now a reality. Option 2 concisely summarizes this transition: what was once science fiction now appears in cutting‑edge science.

DILR · Data Interpretation & Logical Reasoning

Set

Three reviewers Amal, Bimal, and Komal are tasked with selecting questions from a pool of 13 questions (Q01 to Q13). Questions can be created by external “subject matter experts” (SMEs) or by one of the three reviewers. Each of the reviewers either approves or disapproves a question that is shown to them. Their decisions lead to eventual acceptance or rejection of the question in the manner described below.

If a question is created by an SME, it is reviewed first by Amal, and then by Bimal. If both of them approve the question, then the question is accepted and is not reviewed by Komal. If both disapprove the question, it is rejected and is not reviewed by Komal. If one of them approves the question and the other disapproves it, then the question is reviewed by Komal. Then the question is accepted only if she approves it.

A question created by one of the reviewers is decided upon by the other two. If a question is created by Amal, then it is first reviewed by Bimal. If Bimal approves the question, then it is accepted. Otherwise, it is reviewed by Komal. The question is then accepted only if Komal approves it. A similar process is followed for questions created by Bimal, whose questions are first reviewed by Komal, and then by Amal only if Komal disapproves it. Questions created by Komal are first reviewed by Amal, and then, if required, by Bimal.

The following facts are known about the review process after its completion.

Q02, Q06, Q09, Q11, and Q12 were rejected and the other questions were accepted.
Amal reviewed only Q02, Q03, Q04, Q06, Q08, Q10, Q11, and Q13.
Bimal reviewed only Q02, Q04, Q06 through Q09, Q12, and Q13.
Komal reviewed only Q01 through Q05, Q07, Q08, Q09, Q11, and Q12.

Question 1 · TITA (type in the answer)

How many questions were DEFINITELY created by Amal?

Answer: 3

Solution

From the review lists, the creator of a question never reviews it.

Question	Reviewed by	Possible creator
Q07	Bimal, Komal	Amal
Q09	Bimal, Komal	Amal
Q12	Bimal, Komal	Amal

All other questions either have Amal reviewing them (so cannot be his) or are forced to be others. Only Q07, Q09, Q12 are definitely created by Amal.

Hence, 3.

Question 2 · TITA (type in the answer)

How many questions were DEFINITELY created by Komal?

Answer: 1

Solution

Similarly, a question reviewed by Komal cannot be created by her. The only question created by Komal must not have her in the review list.

Question	Reviewed by	Creator
Q10	Amal only	Komal

Q10 is the only one that is reviewed by Amal alone; it fits Komal-creation (Amal reviewed and approved, so accepted). No other question is definitely Komal's because Q06 and Q13 could also be Komal or SME.

Definitely 1.

Question 3 · TITA (type in the answer)

How many questions were DEFINITELY created by the SMEs?

Answer: 3

Solution

A question reviewed by all three reviewers cannot be created by any of them; therefore it must be created by an SME.

Questions reviewed by Amal, Bimal, and Komal: Q02, Q04, Q08.
These are necessarily SME.

Q06 and Q13 could be SME or Komal, but are not definite.

Hence, 3 questions were definitely created by SMEs.

Question 4 · TITA (type in the answer)

How many questions were DEFINITELY disapproved by Bimal?

Answer: 4

Solution

Bimal reviewed only: Q02, Q04, Q06, Q07, Q08, Q09, Q12, Q13.

Determine his decision on each:

Q06: Rejected, only Amal and Bimal reviewed → both must have disapproved. (Definite disapprove)
Q07: Amal-created, accepted, Komal reviewed → Bimal must have disapproved (to send to Komal). (Disapprove)
Q09: Amal-created, rejected, Komal reviewed → Bimal disapproved. (Disapprove)
Q12: Amal-created, rejected, Komal reviewed → Bimal disapproved. (Disapprove)
Q13: Accepted, either SME (both approve) or Komal-created (Bimal must approve to accept). Bimal definitely approved.
Q02, Q04, Q08: SME, Amal and Bimal disagreed. Bimal could have approved or disapproved; not definite.

Definite disapprovals: Q06, Q07, Q09, Q12 → 4.

Question 5 · MCQ

The approval ratio of a reviewer is the ratio of the number of questions (s)he approved to the number of questions (s)he reviewed. Which option best describes Amal’s approval ratio?

A.
lies between 0.25 and 0.50
B.
either 0.25 or 0.75
C.
0.25
D.
lies between 0.25 and 0.75
✓ Correct

Solution

Amal reviewed 8 questions: Q02, Q03, Q04, Q06, Q08, Q10, Q11, Q13.

Known decisions:

Definitely approved: Q03 (Bimal-created, accepted, Amal had to approve), Q10 (Komal-created, accepted, Amal approved).
Definitely disapproved: Q06 (rejected, both A & B disapproved), Q11 (Bimal-created, rejected, Amal disapproved).
Uncertain (can be approved or disapproved): Q02, Q04, Q08 (SME, Amal may be on either side of disagreement), Q13 (SME → approve; Komal-created → disapprove).

Thus approvals can range from 2 to 6, giving ratio from 2/8 = 0.25 to 6/8 = 0.75.
All intermediate values (0.375, 0.5, 0.625) are possible. So the ratio lies between 0.25 and 0.75.

Question 6 · MCQ

How many questions created by Amal or Bimal were disapproved by at least one of the other reviewers?

A.
2
B.
7
C.
4
D.
5
✓ Correct

Solution

Questions created by Amal or Bimal:

Amal: Q07, Q09, Q12 (3).
Bimal: Q01, Q03, Q05, Q11 (4).

Check each for disapproval by at least one other reviewer:

Q07 (Amal): Bimal disapproved → qualifies.
Q09 (Amal): Bimal & Komal both disapproved → qualifies.
Q12 (Amal): Bimal & Komal both disapproved → qualifies.
Q01 (Bimal): Only Komal reviewed, she approved → does not qualify.
Q03 (Bimal): Komal disapproved → qualifies.
Q05 (Bimal): Only Komal reviewed, she approved → does not qualify.
Q11 (Bimal): Both Komal and Amal disapproved → qualifies.

Total qualifying = 3 (Amal) + 2 (Bimal) = 5.

QA · Quantitative Ability

Question 1 · MCQ

A shop owner bought a total of 64 shirts from a wholesale market that came in two sizes, small and large. The price of a small shirt was INR 50 less than that of a large shirt. She paid a total of INR 5000 for the large shirts, and a total of INR 1800 for the small shirts. Then, the price of a large shirt and a small shirt together, in INR, is

A.
175
B.
150
C.
200
✓ Correct
D.
225

Solution

Let price of large shirt = \(L\), small = \(S = L - 50\).
Let number of large = \(x\), small = \(y\). Given:
\(x + y = 64\), \(Lx = 5000\), \(Sy = 1800\).
Substitute: \(x = \frac{5000}{L}\), \(y = \frac{1800}{L-50}\).
So \(\frac{5000}{L} + \frac{1800}{L-50} = 64\).
Multiply by \(L(L-50)\): \(5000(L-50) + 1800L = 64L(L-50)\).
Simplify: \(6800L - 250000 = 64L^2 - 3200L \Rightarrow 64L^2 - 10000L + 250000 = 0\).
Divide by 8: \(8L^2 - 1250L + 31250 = 0\).
Solve: \(L = \frac{1250 \pm \sqrt{1250^2 - 4 \cdot 8 \cdot 31250}}{16} = \frac{1250 \pm 750}{16}\).
Valid \(L = 125\) (reject \(31.25\) as \(S\) would be negative).
Then \(S = 75\), together \(125 + 75 = 200\).

Question 2 · MCQ

One day, Rahul started a work at 9 AM and Gautam joined him two hours later. They then worked together and completed the work at 5 PM the same day. If both had started at 9 AM and worked together, the work would have been completed 30 minutes earlier. Working alone, the time Rahul would have taken, in hours, to complete the work is

A.
11.5
B.
10
✓ Correct
C.
12.5
D.
12

Solution

Let Rahul’s rate = \(R\) (work/hr), Gautam’s = \(G\).
From 9 AM–5 PM (8 hrs): Rahul works 2 hrs alone, then 6 hrs together:
\(2R + 6(R+G) = 1 \Rightarrow 8R + 6G = 1\).
If both start at 9 AM and finish 30 min earlier (7.5 hrs):
\(7.5(R+G) = 1 \Rightarrow R+G = \frac{2}{15}\).
Substitute \(G = \frac{2}{15} - R\) into first equation:
\(8R + 6\left(\frac{2}{15} - R\right) = 1 \Rightarrow 8R + \frac{12}{15} - 6R = 1 \Rightarrow 2R = \frac{3}{15} = \frac{1}{5}\).
Thus \(R = \frac{1}{10}\), so Rahul alone takes \(10\) hours.

Question 3 · MCQ

In a tournament, a team has played 40 matches so far and won 30% of them. If they win 60% of the remaining matches, their overall win percentage will be 50%. Suppose they win 90% of the remaining matches, then the total number of matches won by the team in the tournament will be

A.
80
B.
78
C.
84
✓ Correct
D.
86

Solution

Won so far: \(40 \times 30% = 12\).
Let remaining matches be \(x\).
\(12 + 0.6x = 0.5(40 + x)\)
\(0.1x = 8\)
\(x = 80\)
Total matches \(= 120\).
Wins with 90% remaining: \(12 + 0.9 \times 80 = 84\).

Question 4 · TITA (type in the answer)

The number of distinct pairs of integers (m,n), satisfying \(|1 + mn| < |m + n| < 5\) is:

Answer: 12

Solution

Condition: \(|1+mn| < |m+n| < 5\).
\(|m+n| < 5\) implies \(m+n \in \{\pm4,\pm3,\pm2,\pm1,0\}\).
\(|m+n|=0\): \(|1+mn|<0\) impossible.
\(|m+n|=1\): need \(|1+mn|=0\) ⇒ \(mn=-1\). Quadratic gives non‑integer roots.
For \(|m+n|=2,3,4\): check integer pairs.
If one of \(m,n\) is 0, condition reduces to \(1 < |\text{other}| < 5\), so the other is \(\pm2,\pm3,\pm4\).
This gives ordered pairs: \((0,\pm2),(0,\pm3),(0,\pm4)\) and their swaps – 12 pairs.
Pairs with both non‑zero fail because \(|1+mn| \ge |m+n|\) for small sum/product.
Hence 12 distinct ordered pairs.

Question 5 · MCQ

For a real number a, if \(\frac{\log_{15} a + \log_{32} a}{(\log_{15} a)(\log_{32} a)} = 4\) then a must lie in the range

A.
2 < a < 3
B.
3 < a < 4
C.
4 < a < 5
✓ Correct
D.
a > 5

Solution

Using \(\frac{\log_{15}a+\log_{32}a}{(\log_{15}a)(\log_{32}a)}=\frac{1}{\log_{32}a}+\frac{1}{\log_{15}a}\),

the equation becomes \(\log_a32+\log_a15=4\) ⇒ \(\log_a(32\cdot15)=4\) ⇒ \(\log_a480=4\).

Hence \(a^4=480\) ⇒ \(a=480^{1/4}=2\cdot30^{1/4}\).

Since \(30^{1/4}\approx2.34\), \(a\approx4.68\), which lies between \(4\) and \(5\).

Answer: Option 3.

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