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CAT 2025 Slot 2 Question Paper with Solutions

68 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 · 20 MCQ · 4 TITA

  • Reading Comprehension · 16
  • Verbal Ability · 8

DILR

Data Interpretation & Logical Reasoning

22 questions · 11 MCQ · 11 TITA

  • Data Interpretation · 13
  • Logical Reasoning · 9

QA

Quantitative Ability

22 questions · 13 MCQ · 9 TITA

  • Arithmetic · 9
  • Algebra · 8
  • Geometry · 3
  • Number System · 2

Sample questions with solutions

14 of the 68 questions: the first passage, the first DILR set and the first QA questions of the paper.

VARC · Verbal Ability & Reading Comprehension

Passage

Time and again, whenever a population [of Mexican tetra fish] was swept into a cave and survived long enough for natural selection to have its way, the eyes disappeared. “But it’s not that everything has been lost in cavefish . . . Many enhancements have also happened.” . . . Studies have found that cave-dwelling fish can detect lower levels of amino acids than surface fish can. They also have more tastebuds and a higher density of sensitive cells alongside their bodies that let them sense water pressure and flow. . . .

Killing the processes that support the formation of the eye is quite literally what happens. Just like non-cave-dwelling members of the species, all cavefish embryos start making eyes. But after a few hours, cells in the developing eye start dying, until the entire structure has disappeared. [Developmental biologist Misty] Riddle thinks this apparent inefficiency may be unavoidable. “The early development of the brain and the eye are completely intertwined—they happen together,” she says. That means the least disruptive way for eyelessness to evolve may be to start making an eye and then get rid of it. . . .

It’s easy to see why cavefish would be at a disadvantage if they were to maintain expensive tissues they aren’t using. Since relatively little lives or grows in their caves, the fish are likely surviving on a meager diet of mostly bat feces and organic waste that washes in during the rainy season. Researchers keeping cavefish in labs have discovered that, genetically, the creatures are exquisitely adapted to absorbing and storing nutrients. . . .

Fats can be toxic for tissues, [evolutionary physiologist Nicolas] Rohner explains, so they are stored in fat cells. “But when these cells get too big, they can burst, which is why we often see chronic inflammation in humans and other animals that have stored a lot of fat in their tissues.” Yet a 2020 study by Rohner, Krishnan and their colleagues revealed that even very well-fed cavefish had fewer signs of inflammation in their fat tissues than surface fish do. Even in their sparse cave conditions, wild cavefish can sometimes get very fat, says Riddle. This is presumably because, whenever food ends up in the cave, the fish eat as much of it as possible, since there may be nothing else for a long time to come. Intriguingly, Riddle says, their fat is usually bright yellow, because of high levels of carotenoids, the substance in the carrots that your grandmother used to tell you were good for your…eyes.

“The first thing that came to our mind, of course, was that they were accumulating these because they don’t have eyes,” says Riddle. In this species, such ideas can be tested: Scientists can cross surface fish (with eyes) and cavefish (without eyes) and look at what their offspring are like. When that’s done, Riddle says, researchers see no link between eye presence or size and the accumulation of carotenoids. Some eyeless cavefish had fat that was practically white, indicating lower carotenoid levels. Instead, Riddle thinks these carotenoids may be another adaptation to suppress inflammation, which might be important in the wild, as cavefish are likely overeating whenever food arrives.

Question 1 · MCQ

Which one of the following results for the cross between surface fish (with eyes) and cavefish (without eyes) would invalidate Riddle’s inference from the experiment?
  1. A.
    Some offspring with eyes had white fat.
  2. B.
    Some offspring with eyes had yellow fat.
  3. C.
    Some eyeless offspring had white fat.
  4. D.
    Only eyeless offspring had yellow fat.
    ✓ Correct
Solution
Riddle’s cross showed no link between eye presence/size and carotenoid accumulation. Yellow fat indicates high carotenoid levels. If only eyeless offspring had yellow fat, that would show a clear link between eyelessness and carotenoid accumulation, invalidating the no-link inference. The other results are compatible with no link.

Question 2 · MCQ

Which one of the following best explains why the “apparent inefficiency” is “unavoidable”?
  1. A.
    The lack of light in the caves kills the eye cells in the developing Mexican tetra cavefish embryo.
  2. B.
    The inefficiency resulting from eyelessness is compensated by enhancements like more tastebuds in Mexican tetra cavefish.
  3. C.
    Mexican tetra cavefish are similar to non-cave-dwelling variants in their early stages of development.
    ✓ Correct
  4. D.
    The caves have poor and inconsistent availability of food and nutrition for Mexican tetra cavefish.
Solution
The apparent inefficiency is building an eye and then destroying it. Riddle explains that early brain and eye development are intertwined, so the least disruptive route is to begin eye formation like surface fish and then eliminate it. Option 3 captures this shared early developmental path; the other options do not explain the developmental constraint.

Question 3 · MCQ

On the basis of the information in the passage, what is the most likely function of carotenoids in Mexican tetra cavefish?
  1. A.
    To render bright yellow colour to the cavefish.
  2. B.
    To act as a substitute for eyes.
  3. C.
    To help the fat cells store nutrients.
  4. D.
    To control inflammation from the bursting of fat cells.
    ✓ Correct
Solution
The passage states that Riddle thinks carotenoids may be another adaptation to suppress inflammation. This is important because cavefish overeat when food arrives, and fat-cell bursting can cause inflammation. Thus the most likely function is controlling inflammation from bursting fat cells.

Question 4 · MCQ

All of the following statements from the passage describe adaptation in Mexican tetra cavefish EXCEPT:
  1. A.
    “Since relatively little lives or grows in their caves, the fish are likely surviving on a meager diet of mostly bat feces and organic waste that washes in during the rainy season.”
  2. B.
    “‘But when these cells get too big, they can burst, which is why we often see chronic inflammation in humans and other animals that have stored a lot of fat in their tissues.’”
    ✓ Correct
  3. C.
    “It’s easy to see why cavefish would be at a disadvantage if they were to maintain expensive tissues they aren’t using.”
  4. D.
    “Even in their sparse cave conditions, wild cavefish can sometimes get very fat, says Riddle.”
Solution
Option 2 is a general statement about fat cells bursting and chronic inflammation in humans and other animals, not an adaptation specific to Mexican tetra cavefish. The other quoted statements relate to cavefish survival, storage, or fat accumulation in their cave environment.

DILR · Data Interpretation & Logical Reasoning

Set

Ananya Raga, Bhaskar Tala, Charu Veena, and Devendra Sur are four musicians. Each of them started and completed their training as students under each of three Gurus — Pandit Meghnath, Ustad Samiran, and Acharya Raghunath between 2013 and 2024, including both the years. Each Guru trains any student for consecutive years only, for a span of 2, 3, or 4 years, with each Guru having a different span. During some of these years, a student may not have trained under these Gurus; however, they never trained under multiple Gurus in the same year. In none of these years, any of these Gurus trained more than two of these students at the same time. When two students train under the same Guru at the same time, they are referred to as Gurubhai, irrespective of their gender.

The following additional facts are known.
  1. Ustad Samiran never trained more than one of these students in the same year.
  2. Acharya Raghunath did not train any of these students during 2015-2018, as well as during 2021-24.
  3. Ananya and Devendra were never Gurubhai; neither were Bhaskar and Charu. All other pairs of musicians were Gurubhai for exactly 2 years.
  4. In 2013, Ananya and Bhaskar started their trainings under Pandit Meghnath and under Ustad Samiran, respectively.

Question 1 · MCQ

In which of the following years were Ananya and Bhaskar Gurubhai?
  1. A.
    2021
  2. B.
    2018
  3. C.
    2014
  4. D.
    2020
    ✓ Correct
Solution
Raghunath’s span must be 2 because he was allowed only 2013-14 and 2019-20. Since Ananya and Bhaskar started in 2013 under Meghnath and Samiran respectively, they cannot be in Raghunath’s 2013-14 slot; hence both are in Raghunath 2019-20. This forces Charu and Devendra into Raghunath 2013-14. The only consistent spans are Meghnath 4 and Samiran 3, giving the following schedule:
StudentMeghnath (4 yr)Samiran (3 yr)Raghunath (2 yr)
Ananya2013-162022-242019-20
Bhaskar2021-242013-152019-20
Charu2015-182019-212013-14
Devendra2019-222016-182013-14
Ananya and Bhaskar are together under the same Guru only in 2019 and 2020, so the correct year is 2020.

Question 2 · MCQ

In which year did Charu begin her training under Pandit Meghnath?
  1. A.
    2021
  2. B.
    2015
    ✓ Correct
  3. C.
    2016
  4. D.
    2017
Solution
From the forced schedule above, Charu’s training under Pandit Meghnath runs from 2015 to 2018.
StudentMeghnath (4 yr)Samiran (3 yr)Raghunath (2 yr)
Ananya2013-162022-242019-20
Bhaskar2021-242013-152019-20
Charu2015-182019-212013-14
Devendra2019-222016-182013-14
So Charu began Meghnath training in 2015.

Question 3 · MCQ

In which of the following years were Bhaskar and Devendra Gurubhai?
  1. A.
    2018
  2. B.
    2020
  3. C.
    2015
  4. D.
    2022
    ✓ Correct
Solution
From the forced schedule, Bhaskar is under Meghnath in 2021-2024 and Devendra under Meghnath in 2019-2022. Their overlap is 2021 and 2022.
StudentMeghnath (4 yr)Samiran (3 yr)Raghunath (2 yr)
Ananya2013-162022-242019-20
Bhaskar2021-242013-152019-20
Charu2015-182019-212013-14
Devendra2019-222016-182013-14
Hence Bhaskar and Devendra were Gurubhai in 2022.

Question 4 · MCQ

Which of the following statements is TRUE?
  1. A.
    Ananya was training under Ustad Samiran in 2018.
  2. B.
    Charu was training under Ustad Samiran in 2019.
    ✓ Correct
  3. C.
    Ananya was training under Ustad Samiran in 2015.
  4. D.
    Charu was training under Ustad Samiran in 2018.
Solution
Key deductions:
  • Acharya Raghunath is available only in 2013-14 and 2019-20, so AR span = 2.
  • Since Ananya starts with Pandit Meghnath in 2013, and Bhaskar starts with Ustad Samiran in 2013, neither can be with AR in 2013-14. Hence Ananya and Bhaskar are with AR in 2019-20, while Charu and Devendra are with AR in 2013-14.
  • If US span were 4, Bhaskar would occupy US in 2013-16 and Ananya would need US in 2021-24, leaving only 2017-20 for both Charu and Devendra under US; impossible because US trains at most one student per year. So US span = 3 and PM span = 4.
  • The final schedule is:
StudentPMUSAR
Ananya2013-162022-242019-20
Bhaskar2021-242013-152019-20
Charu2015-182019-212013-14
Devendra2019-222016-182013-14
From the table, Charu is under Ustad Samiran in 2019. So option 2 is true.

Question 5 · TITA (type in the answer)

In how many of the years between 2013-24, were only two of these four musicians training under these three Gurus?

Answer: 4

Solution
Use the same final schedule:
StudentPMUSAR
Ananya2013-162022-242019-20
Bhaskar2021-242013-152019-20
Charu2015-182019-212013-14
Devendra2019-222016-182013-14
Year-wise active musicians:
YearActive musiciansCount
2013A,B,C,D4
2014A,B,C,D4
2015A,B,C3
2016A,C,D3
2017C,D2
2018C,D2
2019A,B,C,D4
2020A,B,C,D4
2021B,C,D3
2022A,B,D3
2023A,B2
2024A,B2
Exactly two musicians are training in 2017, 2018, 2023, and 2024, so the answer is 4.

QA · Quantitative Ability

Question 1 · MCQ

The equations \(3x^2 - 5x + p = 0\) and \(2x^2 - 2x + q = 0\) have one common root. The sum of the other roots of these two equations is
  1. A.
    \(\frac{8}{3} + p + \frac{1}{3}q\)
  2. B.
    \(\frac{2}{3} - 2p + \frac{2}{3}q\)
  3. C.
    \(\frac{8}{3} - p + \frac{3}{2}q\)
    ✓ Correct
  4. D.
    \(\frac{2}{3} - p + \frac{3}{2}q\)
Solution
Let the common root be \(a\), and the other roots be \(b\) and \(c\).

From the first equation:
\(a+b=\frac{5}{3}\), \(ab=\frac{p}{3}\), so \(p=5a-3a^2\).

From the second equation:
\(a+c=1\), \(ac=\frac{q}{2}\), so \(q=2a-2a^2\).

Then \(p-\frac{3}{2}q=2a\).

Required sum:
\(b+c=\left(\frac{5}{3}-a\right)+(1-a)=\frac{8}{3}-2a=\frac{8}{3}-p+\frac{3}{2}q\).

Question 2 · MCQ

Let ABCDEF be a regular hexagon and P and Q be the midpoints of AB and CD, respectively. Then, the ratio of the areas of trapezium PBCQ and hexagon ABCDEF is
  1. A.
    6 : 19
  2. B.
    5 : 24
    ✓ Correct
  3. C.
    7 : 24
  4. D.
    6 : 25
Solution
Take side length \(1\). Use coordinates:
\(A=(1,0)\), \(B=\left(\frac{1}{2},\frac{\sqrt{3}}{2}\right)\), \(C=\left(-\frac{1}{2},\frac{\sqrt{3}}{2}\right)\), \(D=(-1,0)\).

Then:
\(P=\left(\frac{3}{4},\frac{\sqrt{3}}{4}\right)\), \(Q=\left(-\frac{3}{4},\frac{\sqrt{3}}{4}\right)\).

In trapezium \(PBCQ\), the parallel sides are:
\(BC=1\), \(PQ=\frac{3}{2}\), and height \(=\frac{\sqrt{3}}{4}\).

Area of \(PBCQ\):
\(\frac{1}{2}\left(1+\frac{3}{2}\right)\cdot\frac{\sqrt{3}}{4}=\frac{5\sqrt{3}}{16}\).

Area of the regular hexagon:
\(6\cdot\frac{\sqrt{3}}{4}=\frac{3\sqrt{3}}{2}\).

Ratio:
\(\frac{5\sqrt{3}/16}{3\sqrt{3}/2}=\frac{5}{24}\).

Thus the ratio is \(5:24\), option 2.

Question 3 · MCQ

If \(\log_{64} x^2 + \log_8 \sqrt{y} + 3\log_{512} (\sqrt{y} z) = 4\), where x, y and z are positive real numbers, then the minimum possible value of (x + y + x) is
  1. A.
    96
  2. B.
    36
  3. C.
    24
  4. D.
    48
    ✓ Correct
Solution
Taking all logs in base 2:

\(\log_{64}x^2=\frac{1}{3}\log_2 x,\quad \log_8\sqrt y=\frac{1}{6}\log_2 y,\quad 3\log_{512}(\sqrt y z)=\frac{1}{6}\log_2 y+\frac{1}{3}\log_2 z.\)

So the equation becomes:
\( \frac{1}{3}(\log_2 x+\log_2 y+\log_2 z)=4 \),
hence \(xyz=2^{12}=4096\).

By AM-GM,
\( x+y+z \ge 3(xyz)^{1/3}=3\cdot 16=48 \).
Equality when \(x=y=z=16\).

The displayed expression \(x+y+x\) appears to be a typo for \(x+y+z\).

Question 4 · MCQ

The set of all real values of \(x\) for which \(x^2 - |x + 9| + x\) > 0, is
  1. A.
    \( (-\infty,-3)\cup(3,\infty) \)
    ✓ Correct
  2. B.
    \( (-9,-3)\cup(3,\infty) \)
  3. C.
    \( (-\infty,-9)\cup(9,\infty) \)
  4. D.
    \( (-\infty,-9)\cup(3,\infty) \)
Solution
Break the domain at \(x=-9\).

For \(x\ge -9\), \(|x+9|=x+9\), so:
\( x^2-(x+9)+x=x^2-9>0 \)
which gives \(x<-3\) or \(x>3\).
Intersecting with \(x\ge -9\) gives:
\( [-9,-3)\cup(3,\infty) \).

For \(x<-9\), \(|x+9|=-(x+9)\), so:
\( x^2+(x+9)+x=x^2+2x+9=(x+1)^2+8>0 \),
always true.

Thus the full solution set is:
\( (-\infty,-3)\cup(3,\infty) \).

Question 5 · MCQ

A certain amount of money was divided among Pinu, Meena, Rinu and Seema. Pinu received 20% of the total amount and Meena received 40% of the remaining amount. If Seema received 20% less than Pinu, the ratio of the amounts received by Pinu and Rinu is
  1. A.
    2 : 1
  2. B.
    5 : 8
    ✓ Correct
  3. C.
    1 : 2
  4. D.
    8 : 5
Solution
Let the total amount be \(T\).
Pinu = \(0.20T\).
Remaining = \(0.80T\), so Meena = \(0.40 \times 0.80T = 0.32T\).
Seema is 20% less than Pinu: \(0.80 \times 0.20T = 0.16T\).
Rinu = \(T - 0.20T - 0.32T - 0.16T = 0.32T\).
Required ratio Pinu : Rinu = \(0.20T : 0.32T = 5 : 8\).
Hence option 2.

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