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CAT 2023 Slot 1 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 · 20 MCQ · 4 TITA

  • Reading Comprehension · 16
  • Verbal Ability · 8

DILR

Data Interpretation & Logical Reasoning

20 questions · 12 MCQ · 8 TITA

  • Logical Reasoning · 13
  • Data Interpretation · 7

QA

Quantitative Ability

22 questions · 14 MCQ · 8 TITA

  • Algebra · 9
  • Arithmetic · 9
  • Geometry · 3
  • Number System · 1

Sample questions with solutions

14 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

For early postcolonial literature, the world of the novel was often the nation. Postcolonial novels were usually [concerned with] national questions. Sometimes the whole story of the novel was taken as an allegory of the nation, whether India or Tanzania. This was important for supporting anti-colonial nationalism, but could also be limiting - land-focused and inward looking.

My new book "Writing Ocean Worlds" explores another kind of world of the novel: not the village or nation, but the Indian Ocean world. The book describes a set of novels in which the Indian Ocean is at the centre of the story. It focuses on the novelists Amitav Ghosh, Abdulrazak Gurnah, Lindsey Collen and Joseph Conrad [who have] centred the Indian Ocean world in the majority of their novels. . . Their work reveals a world that is outward-looking full of movement, border-crossing and south-south interconnection. They are all very different - from colonially inclined (Conrad) to radically anti-capitalist (Collen), but together draw on and shape a wider sense of Indian Ocean space through themes, images, metaphors and language. This has the effect of remapping the world in the reader's mind, as centred in the interconnected global south. ...

The Indian Ocean world is a term used to describe the very long-lasting connections among the coasts of East Africa, the Arab coasts, and South and East Asia. These connections were made possible by the geography of the Indian Ocean. For much of history, travel by sea was much easier than by land, which meant that port cities very far apart were often more easily connected to each other than to much closer inland cities. Historical and archaeological evidence suggests that what we now call globalisation first appeared in the Indian Ocean. This is the interconnected oceanic world referenced and produced by the novels in my book.

For their part Ghosh, Gurnah, Collen and even Conrad reference a different set of histories and geographies than the ones most commonly found in fiction in English. Those [commonly found ones] are mostly centred in Europe or the US, assume a background of Christianity and whiteness, and mention places like Paris and New York. The novels in [my] book highlight instead a largely Islamic space, feature characters of colour and centralise the ports of Malindi, Mombasa, Aden, Java and Bombay. . . . It is a densely imagined, richly sensory image of a southern cosmopolitan culture which provides for an enlarged sense of place in the world.

This remapping is particularly powerful for the representation of Africa. In the fiction, sailors and travellers are not all European. . . African, as well as Indian and Arab characters, are traders, nakhodas (dhow ship captains), runaways, villains, missionaries and activists. This does not mean that Indian Ocean Africa is romanticised. Migration is often a matter of force; travel is portrayed as abandonment rather than adventure, freedoms are kept from women and slavery is rife. What it does mean is that the African part of the Indian Ocean world plays an active role in its long, rich history and therefore in that of the wider world.

Question 1 · MCQ

On the basis of the nature of the relationship between the items in each pair below, choose the odd pair out:
  1. A.
    Postcolonial novels : Anti-colonial nationalism
  2. B.
    Indian Ocean novels : Outward-looking
  3. C.
    Indian Ocean world : Slavery
  4. D.
    Postcolonial novels : Border-crossing
    ✓ Correct
Solution
The passage states that early postcolonial novels were "land-focused and inward looking" and concerned with national allegories. In contrast, "border-crossing" is a characteristic of the Indian Ocean novels, which reveal a world that is "outward-looking full of movement, border-crossing and south-south interconnection." Therefore, pairing postcolonial novels with border-crossing is incorrect and makes it the odd pair out.

Question 2 · MCQ

All of the following statements, if true, would weaken the passage's claim about the relationship between mainstream English-language fiction and Indian Ocean novels EXCEPT:
  1. A.
    the depiction of Africa in most Indian Ocean novels is driven by a postcolonial nostalgia for an idyllic past.
  2. B.
    most mainstream English-language novels have historically privileged the Christian, white, male experience of travel and adventure.
    ✓ Correct
  3. C.
    the depiction of Africa in most Indian Ocean novels is driven by an Orientalist imagination of its cultural crudeness.
  4. D.
    very few mainstream English-language novels have historically been set in American and European metropolitan centres.
Solution
The passage claims that mainstream English-language fiction is "mostly centred in Europe or the US, assume a background of Christianity and whiteness." Option B supports this claim by stating that mainstream English-language novels have historically privileged the Christian, white, male experience. Since it strengthens rather than weakens the passage's claim, it is the correct choice.

Question 3 · MCQ

Which one of the following statements is not true about migration in the Indian Ocean world?
  1. A.
    The Indian Ocean world's migration networks were shaped by religious and commercial histories of the region.
  2. B.
    Migration in the Indian Ocean world was an ambivalent experience.
  3. C.
    Geographical location rather than geographical proximity determined the choice of destination for migrants.
  4. D.
    The Indian Ocean world's migration networks connected the global north with the global south.
    ✓ Correct
Solution
The passage explicitly describes the Indian Ocean world as an "interconnected global south" characterized by "south-south interconnection." It does not mention connecting the global north with the global south. Therefore, Option D is not true.

Question 4 · MCQ

All of the following claims contribute to the "remapping" discussed by the passage, EXCEPT:
  1. A.
    the global south, as opposed to the global north, was the first centre of globalisation.
  2. B.
    cosmopolitanism originated in the West and travelled to the East through globalisation.
    ✓ Correct
  3. C.
    Indian Ocean novels have gone beyond the specifics of national concerns to explore rich regional pasts.
  4. D.
    the world of early international trade and commerce was not the sole domain of white Europeans.
Solution
The passage highlights a "southern cosmopolitan culture" and argues that globalisation first appeared in the Indian Ocean (the global south). Claiming that cosmopolitanism originated in the West and travelled to the East directly contradicts this southern-centric remapping, making Option B the correct exception.

DILR · Data Interpretation & Logical Reasoning

Set

Faculty members in a management school can belong to one of four departments – Finance and Accounting (F&A), Marketing and Strategy (M&S), Operations and Quants (O&Q) and Behaviour and Human Resources (B&H). The numbers of faculty members in F&A, M&S, O&Q and B&H departments are 9, 7, 5 and 3 respectively. Prof. Pakrasi, Prof. Qureshi, Prof. Ramaswamy and Prof. Samuel are four members of the school's faculty who were candidates for the post of the Dean of the school. Only one of the candidates was from O&Q. Every faculty member, including the four candidates, voted for the post. In each department, all the faculty members who were not candidates voted for the same candidate. The rules for the election are listed below.
  1. There cannot be more than two candidates from a single department.
  2. A candidate cannot vote for himself/herself.
  3. Faculty members cannot vote for a candidate from their own department.
After the election, it was observed that Prof. Pakrasi received 3 votes, Prof. Qureshi received 14 votes, Prof. Ramaswamy received 6 votes and Prof. Samuel received 1 vote. Prof. Pakrasi voted for Prof. Ramaswamy, Prof. Qureshi for Prof. Samuel, Prof. Ramaswamy for Prof. Qureshi and Prof. Samuel for Prof. Pakrasi.

Question 1 · MCQ

Which two candidates can belong to the same department?
  1. A.
    Prof. Pakrasi and Prof. Qureshi
    ✓ Correct
  2. B.
    Prof. Qureshi and Prof. Ramaswamy
  3. C.
    Prof. Pakrasi and Prof. Samuel
  4. D.
    Prof. Ramaswamy and Prof. Samuel
Solution
1. Identify Voting Blocks
  • Total Faculty = 24 (\(9+7+5+3\)). Total votes received = 24 (\(3+14+6+1\)).
  • Non-candidates vote in departmental blocks: F&A(\(9 - c_F\)), M&S(\(7 - c_M\)), O&Q(\(5 - c_O\)), B&H(\(3 - c_B\)).
  • We are given exactly 1 candidate is from O&Q (\(c_O = 1\)), leaving an O&Q block of 4 voters.
2. Deduce the Vote Distribution
Subtract the known individual candidate votes to find the block votes:
  • S (1 vote): Q voted for S. S received 0 block votes.
  • P (3 votes): S voted for P. The remaining 2 votes must come from a single block. Only B&H (\(3 - c_B\)) can yield 2. So, \(c_B = 1\). (B&H block voted for P).
  • R (6 votes): P voted for R. The remaining 5 votes must come from a single block. Only M&S (\(7 - c_M\)) can yield 5. So, \(c_M = 2\). (M&S block voted for R).
  • Q (14 votes): R voted for Q. The remaining 13 votes must come from the remaining blocks: F&A + O&Q. We know O&Q is 4. F&A (\(9 - c_F\)) must be 9. So, \(c_F = 0\). (F&A and O&Q voted for Q).
3. Determine Candidate Departments
  • The 4 candidates belong to: M&S (2), O&Q (1), B&H (1).
  • We need to find the two candidates in M&S.
  • Rule 3 states faculty cannot vote for candidates in their own department. This applies to the candidates themselves: P\(\rightarrow\)R, Q\(\rightarrow\)S, R\(\rightarrow\)Q, and S\(\rightarrow\)P. Therefore, the pairs (P,R), (Q,S), (R,Q), and (S,P) cannot share a department.
  • This leaves only two possible pairs for the M&S department: (P, Q) or (R, S).
  • Since the M&S block voted for R, R cannot belong to M&S.
  • Therefore, the two candidates in M&S must be Pakrasi (P) and Qureshi (Q).
Conclusion
Option A. Prof. Pakrasi and Prof. Qureshi is the correct answer.

Question 2 · MCQ

Which of the following can be the number of votes that Prof. Qureshi received from a single department?
  1. A.
    7
  2. B.
    8
  3. C.
    6
  4. D.
    9
    ✓ Correct
Solution
1. Non-Candidate Block Recap
From our previous logic, we identified the number of non-candidates (block voters) in each department:
  • F&A: 9 voters (0 candidates)
  • M&S: 5 voters (2 candidates: P, Q)
  • O&Q: 4 voters (1 candidate)
  • B&H: 2 voters (1 candidate)
2. Tracing Qureshi's Votes
Qureshi (Q) received a total of 14 votes:
  • 1 individual vote came from Candidate R.
  • The remaining 13 votes must come from the non-candidate voting blocks.
  • Looking at our block sizes (9, 5, 4, 2), the only combination that sums to 13 is F&A (9) + O&Q (4).
3. Single Department Totals for Qureshi
Let's look at how many total votes Q got from these specific departments:
  • F&A Department: Gives its entire block of 9 votes. Since there are no candidates in F&A, no extra individual votes can come from here. Total = 9.
  • O&Q Department: Gives its block of 4 votes, plus potentially 1 more if Candidate R belongs to O&Q. Total = 4 or 5.
The F&A department provided exactly 9 votes to Qureshi.

Conclusion
Option D. 9 is the correct answer.

Question 3 · MCQ

If Prof. Samuel belongs to B&H, which of the following statements is/are true?
Statement A: Prof. Pakrasi belongs to M&S.
Statement B: Prof. Ramaswamy belongs to O&Q.
  1. A.
    Only statement A
  2. B.
    Both statements A and B
    ✓ Correct
  3. C.
    Neither statement A nor statement B
  4. D.
    Only statement B
Solution
1. Established Context
  • Candidates per Department slots: M&S (2), O&Q (1), B&H (1), F&A (0).
  • M&S Candidates: We previously deduced the two M&S candidates must be Pakrasi (P) and Qureshi (Q). (This is because the M&S block voted for R, so R can't be in M&S, leaving P and Q as the only valid pair that doesn't violate the "cannot vote for own department" rule).
2. Evaluating the Statements
  • Statement A (Prof. Pakrasi belongs to M&S): This is universally True based on the core deductions, regardless of the new condition.
  • Statement B (Prof. Ramaswamy belongs to O&Q): The "If" condition places Samuel (S) in B&H. With P and Q in M&S, and S in B&H, the only remaining candidate is Ramaswamy (R). He must take the only remaining slot, which is in O&Q. Therefore, this is also True.
Conclusion
Both Statement A and Statement B are true.

Question 4 · MCQ

What best can be concluded about the candidate from O&Q?
  1. A.
    It was either Prof. Ramaswamy or Prof. Samuel.
    ✓ Correct
  2. B.
    It was Prof. Samuel.
  3. C.
    It was either Prof. Pakrasi or Prof. Qureshi.
  4. D.
    It was Prof. Ramaswamy.
Solution
Based on our core deductions from the puzzle:
  1. We definitively placed Prof. Pakrasi and Prof. Qureshi in the Marketing and Strategy (M&S) department.
  2. The remaining candidates are Prof. Ramaswamy and Prof. Samuel.
  3. The remaining candidate slots are exactly one in O&Q and one in B&H.
Without additional conditions (like the "If..." scenario in the previous question), we cannot definitively pin Ramaswamy or Samuel to just one department. The O&Q candidate could be either of them.

Conclusion
Option A. It was either Prof. Ramaswamy or Prof. Samuel. is the correct answer.

Question 5 · MCQ

Which of the following statements is/are true?
Statement A: Non-candidates from M&S voted for Prof. Qureshi.
Statement B: Non-candidates from F&A voted for Prof. Qureshi.
  1. A.
    Neither statement A nor statement B
  2. B.
    Both statements A and B
  3. C.
    Only statement A
  4. D.
    Only statement B
    ✓ Correct
Solution
Based on our core deductions from the voting blocks:

1. Evaluating the Statements
  • Statement A (Non-candidates from M&S voted for Prof. Qureshi): We established that the M&S block of 5 voters gave their votes to Ramaswamy. Furthermore, since Qureshi belongs to the M&S department, the M&S block cannot vote for him anyway due to the rules. This statement is False.
  • Statement B (Non-candidates from F&A voted for Prof. Qureshi): We established that Qureshi's 13 block votes came from the combination of the F&A block (9) and the O&Q block (4). This statement is True.
Conclusion
Option D. Only statement B is the correct answer.

QA · Quantitative Ability

Question 1 · MCQ

If \(x\) and \(y\) are real numbers such that \(x^2 + (x-2y-1)^2 = -4y(x+y)\), then the value \(x-2y\) is
  1. A.
    1
    ✓ Correct
  2. B.
    2
  3. C.
    -1
  4. D.
    0
Solution
Expand the given equation:

\(x^2 + (x-2y-1)^2 = -4y(x+y)\)

\(x^2 + x^2 + 4y^2 + 1 - 4xy - 2x + 4y = -4xy - 4y^2\)

Bring all terms to the left side:

\(2x^2 + 8y^2 - 2x + 4y + 1 = 0\)

Divide by 2 and group the terms to complete the squares:

\((x^2 - x + \frac{1}{4}) + (4y^2 + 2y + \frac{1}{4}) = 0\)

\((x - \frac{1}{2})^2 + (2y + \frac{1}{2})^2 = 0\)

Since the sum of squares of real numbers is zero, each term must be zero:

\(x - \frac{1}{2} = 0 \implies x = \frac{1}{2}\)

\(2y + \frac{1}{2} = 0 \implies y = -\frac{1}{4}\)

Calculate \(x - 2y\) :

\(x - 2y = \frac{1}{2} - 2(-\frac{1}{4}) = 1\)

Question 2 · MCQ

If \(\sqrt{5x+9} + \sqrt{5x-9} = 3(2+\sqrt{2})\), then \(\sqrt{10x+9}\) is equal to
  1. A.
    \(3\sqrt{7}\)
    ✓ Correct
  2. B.
    \(4 \sqrt{5}\)
  3. C.
    \(3\sqrt{31}\)
  4. D.
    \(2\sqrt{7}\)
Solution
Let \(a = \sqrt{5x+9}\) and \(b = \sqrt{5x-9}\) .

We are given \(a + b = 3(2+\sqrt{2}) = 6 + 3\sqrt{2}\) .

Notice that \(a^2 - b^2 = (5x+9) - (5x-9) = 18\) .

Using the identity \(a^2 - b^2 = (a+b)(a-b)\) , we find \(a - b\) :

\(a - b = \frac{18}{6 + 3\sqrt{2}} = \frac{18(6 - 3\sqrt{2})}{36 - 18} = 6 - 3\sqrt{2}\)

Adding the equations for \(a+b\) and \(a-b\) :

\(2a = 12 \implies a = 6\)

Substitute \(a\) back to find \(x\) :

\(\sqrt{5x+9} = 6 \implies 5x+9 = 36 \implies 5x = 27\)

We need to find \(\sqrt{10x+9}\) :

\(\sqrt{10x+9} = \sqrt{2(5x) + 9} = \sqrt{2(27) + 9} = \sqrt{63} = 3\sqrt{7}\)

Question 3 · MCQ

Let \(n\) be the least positive integer such that 168 is a factor of \(1134^n\). If \(m\) is the least positive integer such that \(1134^n\) is a factor of \(168^m\), then \(m+n\) equals
  1. A.
    15
    ✓ Correct
  2. B.
    12
  3. C.
    24
  4. D.
    9
Solution
Prime factorize the given numbers:
\(168 = 2^3 \times 3 \times 7\)
\(1134 = 2 \times 3^4 \times 7\)

For 168 to be a factor of \(1134^n = 2^n \times 3^{4n} \times 7^n\), the powers of each prime factor in \(1134^n\) must be at least those in 168:
\(n \ge 3\), \(4n \ge 1\), and \(n \ge 1\).
The least positive integer satisfying these conditions is \(n = 3\).

Substitute \(n = 3\) to find \(1134^3 = 2^3 \times 3^{12} \times 7^3\).
For \(1134^3\) to be a factor of \(168^m = 2^{3m} \times 3^m \times 7^m\), we must have:
\(3m \ge 3 \implies m \ge 1\)
\(m \ge 12\)
\(m \ge 3\)
The least positive integer satisfying these conditions is \(m = 12\).

Thus, \(m + n = 12 + 3 = 15\).

Question 4 · MCQ

If \(x\) and \(y\) are positive real numbers such that \(\log_x(x^2+12)=4\) and \(3\log_y x=1\), then \(x+y\) equals
  1. A.
    11
  2. B.
    20
  3. C.
    10
    ✓ Correct
  4. D.
    68
Solution
From the first equation, \(\log_x(x^2+12) = 4\):
\(x^4 = x^2 + 12\)
\(x^4 - x^2 - 12 = 0\)
\((x^2 - 4)(x^2 + 3) = 0\)
Since \(x\) must be a positive real number (and the base of a logarithm cannot be 1), \(x^2 = 4 \implies x = 2\).

From the second equation, \(3\log_y x = 1\):
\(\log_y x = \frac{1}{3}\)
\(y^{1/3} = x\)
\(y = x^3\)

Substitute \(x = 2\):
\(y = 2^3 = 8\)

Finally, \(x + y = 2 + 8 = 10\).

Question 5 · TITA (type in the answer)

The number of integer solutions of equation \(2|x|(x^2+1)=5x^2\) is

Answer: 3

Solution
Let \( y = |x| \). Since \( x^2 = |x|^2 = y^2 \), the equation becomes:
\( 2y(y^2 + 1) = 5y^2 \)
\( 2y^3 - 5y^2 + 2y = 0 \)
\( y(2y^2 - 5y + 2) = 0 \)
\( y(2y - 1)(y - 2) = 0 \)
The possible values for \( y \) are \( 0, \frac{1}{2}, 2 \).
Substituting back \( y = |x| \):
If \( |x| = 0 \), then \( x = 0 \).
If \( |x| = \frac{1}{2} \), then \( x = \pm \frac{1}{2} \) (not integers).
If \( |x| = 2 \), then \( x = \pm 2 \).
The integer solutions are \( -2, 0, 2 \), giving a total of 3 integer solutions.

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