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CAT 2019 Slot 1 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 · 22 MCQ · 2 TITA

  • Reading Comprehension · 19
  • Verbal Ability · 5

DILR

Data Interpretation & Logical Reasoning

22 questions · 14 MCQ · 8 TITA

  • Logical Reasoning · 14
  • Data Interpretation · 8

QA

Quantitative Ability

22 questions · 14 MCQ · 8 TITA

  • Arithmetic · 10
  • Algebra · 7
  • Geometry · 3
  • Modern Math · 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

As defined by the geographer Yi-Fu Tuan, topophilia is the affective bond between people and place. His 1974 book set forth a wide-ranging exploration of how the emotive ties with the material environment vary greatly from person to person and in intensity, subtlety, and mode of expression. Factors influencing one’s depth of response to the environment include cultural background, gender, race, and historical circumstance, and Tuan also argued that there is a biological and sensory element. Topophilia might not be the strongest of human emotions—indeed, many people feel utterly indifferent toward the environments that shape their lives—but when activated it has the power to elevate a place to become the carrier of emotionally charged events or to be perceived as a symbol.

Aesthetic appreciation is one way in which people respond to the environment. A brilliantly colored rainbow after gloomy afternoon showers, a busy city street alive with human interaction—one might experience the beauty of such landscapes that had seemed quite ordinary only moments before or that are being newly discovered. This is quite the opposite of a second topophilic bond, namely that of the acquired taste for certain landscapes and places that one knows well. When a place is home, or when a space has become the locus of memories or the means of gaining a livelihood, it frequently evokes a deeper set of attachments than those predicated purely on the visual. A third response to the environment also depends on the human senses but may be tactile and olfactory, namely a delight in the feel and smell of air, water, and the earth.

Topophilia—and its very close conceptual twin, sense of place—is an experience that, however elusive, has inspired recent architects and planners. Most notably, new urbanism seeks to counter the perceived placelessness of modern suburbs and the decline of central cities through neo-traditional design motifs. Although motivated by good intentions, such attempts to create places rich in meaning are perhaps bound to disappoint. As Tuan noted, purely aesthetic responses often are suddenly revealed, but their intensity rarely is longlasting. Topophilia is difficult to design for and impossible to quantify, and its most articulate interpreters have been self-reflective philosophers such as Henry David Thoreau, evoking a marvelously intricate sense of place at Walden Pond, and Tuan, describing his deep affinity for the desert.

Topophilia connotes a positive relationship, but it often is useful to explore the darker affiliations between people and place. Patriotism, literally meaning the love of one’s terra patria or homeland, has long been cultivated by governing elites for a range of nationalist projects, including war preparation and ethnic cleansing. Residents of upscale residential developments have disclosed how important it is to maintain their community’s distinct identity, often by casting themselves in a superior social position and by reinforcing class and racial differences. And just as a beloved landscape is suddenly revealed, so too may landscapes of fear cast a dark shadow over a place that makes one feel a sense of dread or anxiety—or topophobia.

Question 1 · MCQ

The word "topophobia" in the passage is used:
  1. A.
    to represent a feeling of dread towards particular spaces and places.
    ✓ Correct
  2. B.
    to signify the fear of studying the complex discipline of topography.
  3. C.
    as a metaphor expressing the failure of the homeland to accommodate non-citizens.
  4. D.
    to signify feelings of fear or anxiety towards topophilic people.
Solution
The passage states: "landscapes of fear cast a dark shadow over a place that makes one feel a sense of dread or anxiety—or topophobia." Thus topophobia means dread toward particular places. Option 1 is correct.

Question 2 · MCQ

Which of the following statements, if true, could be seen as not contradicting the arguments in the passage?
  1. A.
    The most important, even fundamental, response to our environment is our tactile and olfactory response.
  2. B.
    Generally speaking, in a given culture, the ties of the people to their environment vary little in significance or intensity.
  3. C.
    Patriotism, usually seen as a positive feeling, is presented by the author as a darker form of topophilia.
    ✓ Correct
  4. D.
    New Urbanism succeeded in those designs where architects collaborated with their clients.
Solution
The last paragraph presents patriotism as a darker affiliation between people and place, citing its use for nationalist projects like war and ethnic cleansing. Option 3 aligns with this; the others contradict the passage.

Question 3 · MCQ

In the last paragraph, the author uses the example of "Residents of upscale residential developments" to illustrate the:
  1. A.
    introduction of nationalist projects by such elites to produce a sense of dread or topophobia.
  2. B.
    social exclusivism practised by such residents in order to enforce a sense of racial or class superiority.
    ✓ Correct
  3. C.
    manner in which environments are designed to minimise the social exclusion of their clientele.
  4. D.
    sensitive response to race and class problems in upscale residential developments.
Solution
The example immediately follows: "maintain their community’s distinct identity, often by casting themselves in a superior social position and by reinforcing class and racial differences." This illustrates social exclusivism. Option 2.

Question 4 · MCQ

Which one of the following best captures the meaning of the statement, "Topophilia is difficult to design for and impossible to quantify . . ."?
  1. A.
    People’s responses to their environment are usually subjective and so cannot be rendered in design.
    ✓ Correct
  2. B.
    The deep anomie of modern urbanisation led to new urbanism’s intricate sense of place.
  3. C.
    Architects have to objectively quantify spaces and hence cannot be topophilic.
  4. D.
    Philosopher-architects are uniquely suited to develop topophilic design.
Solution
The preceding sentence says attempts to design meaningful places are "bound to disappoint" because aesthetic responses are fleeting and subjective. Hence topophilia cannot be reliably designed or measured. Option 1 captures this.

Question 5 · MCQ

Which one of the following comes closest in meaning to the author’s understanding of topophilia?
  1. A.
    The tendency of many cultures to represent their land as “motherland” or “fatherland” may be seen as an expression of their topophilia
    ✓ Correct
  2. B.
    Nomadic societies are known to have the least affinity for the lands through which they traverse because they tend to be topophobic.
  3. C.
    The French are not overly patriotic, but they will refuse to use English as far as possible, even when they know it well.
  4. D.
    Scientists have found that most creatures, including humans, are either born with or cultivate a strong sense of topography.
Solution
Topophilia is the affective bond between people and place. Calling one’s land "motherland" or "fatherland" expresses a deep emotional attachment to the land itself, mirroring topophilia. Other options refer to topography, language, or nomadism, which are not relevant.

DILR · Data Interpretation & Logical Reasoning

Set

The following table represents addition of two six-digit numbers given in the first and the second rows, while the sum is given in the third row. In the representation, each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 has been coded with one letter among A, B, C, D, E, F, G, H, J, K, with distinct letters representing distinct digits. [See addition table in image]
DILR set, figure 1

Question 1 · TITA (type in the answer)

Which digit does the letter A represent?

Answer: 1

Solution
From the units column: F + F = F ⇒ F = 0 with carry 0.
The sum has 7 digits and starts with A, so the carry from the hundred‑thousands column is A.
The maximum carry from adding two 6‑digit numbers is 1, hence A = 1.
(Also, the equation B + A + c₅ = 11A forces A = 1 as the only non‑zero digit.)

Question 2 · TITA (type in the answer)

Which digit does the letter B represent?

Answer: 9

Solution
With A = 1, the hundred‑thousands column gives: B + 1 + c₅ = 11 ⇒ B + c₅ = 10.
The carry c₅ arises from 2H + c₄ = 10c₅. Since H ≤ 9, 2H + c₄ ≤ 20, so c₅ ∈ {0,1,2}.
c₅ = 2 forces H = 9, c₄ = 2, but then the thousands column requires J − G = 19 (impossible).
c₅ = 0 would give B = 10 (invalid). Hence c₅ = 1 and B = 9.

Question 3 · TITA (type in the answer)

Which among the digits 3, 4, 6 and 7 cannot be represented by the letter D?

Answer: 7

Solution
Set up the column addition with carries. From units: F+F=F ⇒ F=0.
Tens: G+K=10c₂+1; only c₂=1 gives G+K=11.
Hundreds: 1+1=2=10c₃+C ⇒ c₃=0, C=2.
Millions–hundred-thousands carry: c₆=A, B+1+c₅=11A ⇒ A=1, B+c₅=10.
Ten-thousands: H+H+c₄=2H+c₄=10c₅; max 18+1 ⇒ c₅=1, B=9 ⇒ 2H+c₄=10 ⇒ H=5, c₄=0.
Thousands: 1+J=G ⇒ G=J+1.
With G+K=11 and G=J+1, we get K=10−J.
Possible (J,G,K) using remaining digits {3,4,6,7,8}:
• J=3, G=4, K=7 → leaves {6,8} for D,E
• J=6, G=7, K=4 → leaves {3,8} for D,E
• J=7, G=8, K=3 → leaves {4,6} for D,E
D can be 3,4,6,8 but never 7. ∴ 7 cannot be represented by D.

Question 4 · TITA (type in the answer)

Which among the digits 4, 6, 7 and 8 cannot be represented by the letter G?

Answer: 6

Solution
Using the same deduction as above, the possible values for G across the three valid cases are 4 (J=3, K=7), 7 (J=6, K=4), and 8 (J=7, K=3). G never takes the value 6. Hence, 6 cannot be represented by G.

QA · Quantitative Ability

Question 1 · MCQ

If \(m\) and \(n\) are integers such that \((\sqrt{2})^{19} 3^4 4^2 9^m 8^n = 3^n 16^m (\sqrt[4]{64})\) then \(m\) is
  1. A.
    \(-20\)
  2. B.
    \(-12\)
    ✓ Correct
  3. C.
    \(-24\)
  4. D.
    \(-16\)
Solution
Express all terms as powers of 2 and 3.
Left side: \((\sqrt{2})^{19}3^4 4^2 9^m 8^n = 2^{\frac{19}{2}} \cdot 3^4 \cdot 2^4 \cdot 3^{2m} \cdot 2^{3n} = 2^{\frac{19}{2}+4+3n} \cdot 3^{4+2m}\).
Right side: \(3^n 16^m \sqrt[4]{64} = 3^n \cdot 2^{4m} \cdot 2^{\frac{3}{2}} = 2^{4m+\frac{3}{2}} \cdot 3^n\).
Equate exponents:
For 3: \(4+2m = n\).
For 2: \(\frac{19}{2}+4+3n = 4m+\frac{3}{2}\) → multiply by 2: \(19+8+6n = 8m+3\) → \(27+6n = 8m+3\) → \(6n = 8m-24\) → \(3n = 4m-12\).
Substitute \(n = 4+2m\): \(3(4+2m) = 4m-12\) → \(12+6m = 4m-12\) → \(2m = -24\) → \(m = -12\).

Question 2 · MCQ

The income of Amala is \(20\%\) more than that of Bimala and \(20\%\) less than that of Kamala. If Kamala's income goes down by \(4\%\) and Bimala's goes up by \(10\%\), then the percentage by which Kamala's income would exceed Bimala's is nearest to
  1. A.
    31
    ✓ Correct
  2. B.
    28
  3. C.
    32
  4. D.
    29
Solution
Let Bimala's income = B.
Then Amala's income = \(1.2B\).
Amala's income is also \(80%\) of Kamala's, so \(1.2B = 0.8K\) → \(K = 1.5B\).
New Kamala income after \(4%\) decrease: \(K' = 0.96 \times 1.5B = 1.44B\).
New Bimala income after \(10%\) increase: \(B' = 1.10B\).
Percentage excess of Kamala over Bimala = \(\frac{K'-B'}{B'} \times 100 = \frac{0.34B}{1.1B} \times 100 = \frac{34}{1.1} \approx 30.91%\).
Nearest integer is 31.

Question 3 · TITA (type in the answer)

In a class, \(60\%\) of the students are girls and the rest are boys. There are 30 more girls than boys. If \(68\%\) of the students, including 30 boys, pass an examination, the percentage of the girls who do not pass is

Answer: 20

Solution
Let total students = \(T\).
Girls = \(0.6T\), Boys = \(0.4T\).
\(0.6T - 0.4T = 30 \Rightarrow T = 150\).
Then girls = 90, boys = 60.
Pass = \(68%\) of 150 = 102, including 30 boys, so girls pass = 72.
Girls fail = 18. Percentage = \((18/90) \times 100 = 20%\).

Question 4 · MCQ

On selling a pen at \(5\%\) loss and a book at \(15\%\) gain, Karim gains Rs. 7. If he sells the pen at \(5\%\) gain and the book at \(10\%\) gain, he gains Rs. 13. What is the cost price of the book in Rupees?
  1. A.
    80
    ✓ Correct
  2. B.
    85
  3. C.
    95
  4. D.
    100
Solution
Let CP of pen = ₹\(P\), CP of book = ₹\(B\).
Case 1: \(-0.05P + 0.15B = 7\).
Case 2: \(0.05P + 0.10B = 13\).
Adding gives \(0.25B = 20 \Rightarrow B = 80\).
Thus CP of book = ₹80.

Question 5 · MCQ

Corners are cut off from an equilateral triangle T to produce a regular hexagon H. Then, the ratio of the area of H to the area of T is
  1. A.
    5:6
  2. B.
    4:5
  3. C.
    3:4
  4. D.
    2:3
    ✓ Correct
Solution
Let the original equilateral triangle have side length \(3a\). Then the hexagon side length is \(a\).
Area of equilateral triangle T: \( \frac{\sqrt{3}}{4} (3a)^2 = \frac{9\sqrt{3}}{4} a^2 \).
Area of regular hexagon H: \( 6 \times \frac{\sqrt{3}}{4} a^2 = \frac{3\sqrt{3}}{2} a^2 \).
Ratio H : T = \( \frac{3\sqrt{3}}{2} a^2 \div \frac{9\sqrt{3}}{4} a^2 = \frac{3}{2} \times \frac{4}{9} = \frac{2}{3} \).

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