Elementor #7012

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Day 01 / 50

CAT 50 Day Streak – Day 1

30 questions across VARC, DILR & QA · +3 for a correct answer · −1 for a wrong MCQ · no negative marking for TITA

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VARC · Verbal Ability & Reading Comprehension

Q1 – Q10 0/10

Passage · Q1 – Q4

So far, we have told the story of progress as one of humanity climbing out of poverty, isolation, disease and death into abundance, connectedness, health and safety. More fundamentally, it is a story of the expansion of human agency. Our primitive ancestors lived at the mercy of nature. They ate what food they found: what edible plants happened to be growing nearby, what game they could catch. They fashioned tools, clothing, and shelter out of found materials: wood, stone, leaves and grass; the hide, hair, bones, or shells of animals. They might temper these materials with fire, but they could not fundamentally transform them. And as nomads, they were forced to limit their possessions to what could be carried. Until about ten thousand years ago, they did not even have draft animals; they controlled no power sources other than their own muscles.

They had little choice of where to live: when local food resources ran out, they moved on—and they were constantly on the move. They had little choice of what to do with their lives, as any division of labour within the tribe was extremely limited—hunting, foraging, and tool-making—and much of that was determined by social roles. They had little choice of whom to socialise with: they were a part of the community they were born into. When their environment changed, they had to simply react as best they could. They had little to no ability to predict the weather or to grasp climate change. They had no techniques to prevent disease, not even washing hands or boiling water. They fell victim to attacks from wild animals and to raids from other tribes. Estimates of historical world population show very low growth rates for a very long time, which implies high mortality. Although they lived as best they could, although they applied all their intelligence, effort, and will, and although they were surely no less clever and brave than you or I, the life they could create was still merely a tiny enclave carved out of a vast world.

The advent of agriculture and settled society over ten thousand years ago was a major leap forward in human agency. For the first time, we ate not the plants we found and the game we caught in the wild, but the crops we had sown and the livestock we had raised. We chose where to live and we made our homes, finally able to invest in them for the long term. The first settlers and agriculturalists did not have much choice in these things, and their options were poor. They probably worked harder than hunter-gatherers, and they had smaller stature, indicating worse nutrition. Some have interpreted the shift to agriculture as a mistake, even “the worst mistake” in history. More likely, hunter-gatherers were led or forced into agriculture by circumstances beyond their control, such as rising population density or climate change. To call this evolution a “mistake” is ahistorical: a mistake implies a choice, but primitive peoples could not direct the course of their societies, nor even comprehend when a change of this magnitude was occurring. The lesson instead is the extremely limited agency of hunter-gatherer societies: even if they enjoyed their lifestyle, they were unable to keep it when the environment changed.

Q1MCQ

The primary purpose of the passage is to:

ACompare the nutritional advantages of agriculture with those of hunter-gatherer societies.

BDemonstrate that early humans lacked intelligence and creativity compared to modern humans.

CTrace the evolution of human agency from dependence on nature to the beginnings of self-determination.

DArgue that the shift from hunter-gathering to agriculture was a historical mistake.

Solution Answer: C

The passage calls progress “a story of the expansion of human agency”. It moves from ancestors who lived “at the mercy of nature” to agriculture as “a major leap forward in human agency”. That is exactly the arc option C describes.

A picks up only a minor detail about nutrition. B contradicts the author, who says early humans were “no less clever and brave than you or I”. D is the very view the author rejects as ahistorical.

Q2MCQ

Which of the following, if true, would most strengthen the author’s rejection of the view that agriculture was a “mistake”?

AArchaeological evidence shows hunter-gatherers had better health indicators than early farmers.

BClimate changes and increasing populations forced groups into agriculture regardless of preference.

COral histories from primitive tribes suggest they willingly abandoned nomadic life for stability.

DAnthropologists argue that agriculture reduced leisure time compared to hunting and foraging.

Solution Answer: B

The author’s argument is that “a mistake implies a choice”. Hunter-gatherers were likely forced into farming by rising population density or climate change. B confirms that there was no real choice, which directly supports the argument.

A and D show farming made life worse, which supports the “mistake” camp. C says tribes chose willingly, which would weaken the author’s position.

Q3MCQ

If the author’s framework of “human agency” were applied to the Industrial Revolution, which of the following would best align with his perspective?

AWorkers’ poor living conditions prove that industrialisation was a mistake.

BIndustrial advances marked a further expansion of agency, despite initial hardships.

CIndustrial societies were less healthy than agricultural ones, so progress was reversed.

DThe move to industrialisation was purely voluntary, unlike earlier societal shifts.

Solution Answer: B

The author calls agriculture a leap in agency even though early farmers worked harder and were worse nourished. The same logic applied to industrialisation gives B: initial hardships, but a further expansion of agency.

A and C use the “mistake” or “reversal” framing that the author rejects. D introduces a claim about voluntariness that isn’t part of his framework.

Q4MCQ

The author argues that agriculture should not be considered a “mistake” because early humans lacked true choice in the matter. Which of the following, if true, would most weaken this claim?

AEvidence shows that some tribes experimented with small-scale farming while still practising hunting and gathering.

BArchaeological data indicate that the first farmers were shorter and worked harder than hunter-gatherers.

CHunter-gatherer societies often split or migrated to avoid adopting new practices.

DAnthropological studies suggest that agriculture reduced social diversity within tribes.

Solution Answer: A

If tribes deliberately tried small-scale farming while still hunting and gathering, they were weighing two ways of life side by side. That means adopting agriculture was, at least partly, a choice, which strikes at the author’s “no true choice” claim.

B is about hardship, not choice. C concerns avoiding new practices in general, not a decision about farming. D is irrelevant to whether a choice existed.

Q5TITA

Five jumbled-up sentences (labelled 1, 2, 3, 4 and 5), related to a topic, are given below. Four of them can be put together to form a coherent paragraph. Identify the odd sentence and key in the number of that sentence as your answer.

Early European efforts to create a global standard for writing Mayan languages have enabled the preservation of great works of literature like the Popol Vuh and Chilam Balam, but the initial attempts were fraught with miscommunications and rivalries.
A bishop named Diego de Landa convinced a Mayan scribe, Gaspar Antonio Chi, to match, letter for letter, the signs of the Mayan script and the Spanish alphabet.
The scribe’s frustration with de Landa is evident in the last exercise that he completed for the bishop. Asked to pen any sentence in Mayan hieroglyphs, Chi wrote: “I don’t want to.”
When the scribe heard the Spanish pronunciation of the letter ‘b,’ says Pallán, he wrote the sign for bih, which means “road.”
The long line of code-breakers to take on Mayan hieroglyphs started with Spanish colonists in the sixteenth century.

Solution Answer: 1

The coherent paragraph is 5 → 2 → 4 → 3:

5: Code-breaking of Mayan hieroglyphs began with Spanish colonists.
2: Bishop de Landa made the scribe Chi match signs to letters.
4: The ‘b’ → bih (“road”) confusion that followed.
3: Chi’s frustration, ending with “I don’t want to.”

Sentence 1 shifts to a broader theme, a global writing standard and the preservation of literary works, so it doesn’t belong to this anecdote.

Q6TITA

This analysis implicated the axons (output connections) of neurons as well as parts of the cortex and deeper “subcortical” brain regions like the striatum, involved in movement.
These findings tally with brain-imaging studies suggesting dysfunction of some regions in insomnia, and with animal studies implicating these cells in sleep regulation.
It also tagged “medium spiny neurons,” which occupy most of the striatum as well as neurons in other regions, including the hypothalamus.
The researchers then investigated which brain regions and cells these genes frequently turn up in.
In fact, it is probable that insomnia is not a singular condition but a cluster of symptoms grouped, which can have a range of underlying causes.

Solution Answer: 5

The coherent paragraph is 4 → 1 → 3 → 2:

4: Researchers checked where the genes turn up.
1: “This analysis” implicated axons, cortex and striatum.
3: “It also” tagged medium spiny neurons.
2: “These findings” tally with imaging and animal studies.

Sentence 5 makes a general claim that insomnia is a cluster of symptoms. It breaks away from the gene-mapping thread.

Q7MCQ

The passage given below is followed by four alternate summaries. Choose the option that best captures the essence of the passage.

Passage The trees themselves are medicines, too many to name them all: white pines, red spruce, hemlock, fir, beech, maple, birches, and aspen, all of which were known and learned from by Indigenous botanists. Colonist records show that when the French and British invaders arrived here, they were a sickly lot, many near death from scurvy. They describe how Native healers prepared tree teas for them, by which they were restored to health. Northern white cedar earned the French name arborvitae, “tree of life,” for this salvation, which was provided by Indigenous scientists and the trees that carried the medicine. When I am across the Blue Line, I try to drink tree tea every day, a cup of fragrant white pine tea giving me a daily requirement of vitamin C and the knowing that our bodies, mine and the pine’s, are united.

AIndigenous knowledge of medicinal trees once saved European colonists from scurvy, and this tradition continues to be honoured through the daily practice of tree teas that connect humans and nature.

BEuropean colonists, suffering from diseases such as scurvy, introduced Indigenous communities to tree teas, which later became an important cultural practice.

CNative healers used tree-based medicines only during colonial times, but these practices have no relevance in modern health and nutrition.

DTree teas, such as white pine, are valued primarily for their taste, while their role in history and medicine is largely symbolic.

Solution Answer: A

A covers both halves of the passage. Native healers’ tree medicine saved colonists dying of scurvy, and the author still drinks tree tea daily, feeling united with the pine.

B reverses who taught whom. C (“no relevance today”) and D (“valued for taste”, “largely symbolic”) contradict the passage.

Q8MCQ

There is a sentence that is missing in the paragraph below. Look at the paragraph and decide where (option 1, 2, 3, or 4) the following sentence would best fit.

Sentence Between 1933 and 1967, the Lakenhalle was meticulously rebuilt, with old material being reused when that was possible, or new when it wasn’t.

Paragraph Similar rebuilding occurred in Belgium following the First World War. ___(1)___. The town centre of Ypres, which came under intense artillery fire, had been almost completely destroyed, including the Lakenhalle, or cloth hall. ___(2)___. The massive market building, of Gothic design, dates from the thirteenth century, when Ypres was a centre of the flourishing Flemish textile industry. ___(3)___. The library of the Catholic University of Leuven is another Belgian example. It was located in a lakenhalle of more recent vintage, dating back only to the seventeenth century, that was burned to the ground by vindictive German troops. ___(4)___. Its replacement, built with American funds, was a grander version in the same Flemish Renaissance style, and when that building was destroyed in the Second World War, it was carefully restored.

AOption 1

BOption 2

COption 3

DOption 4

Solution Answer: C (Option 3)

The sentence describes rebuilding the Lakenhalle, so it must come after the hall has been introduced (destroyed) and described (the thirteenth-century Gothic building). Blank 3 closes the Ypres story before the paragraph moves on to “another Belgian example”, Leuven.

Blank 2 would interrupt the description of the building. Blank 4 sits inside the Leuven discussion.

Q9MCQ

There is a sentence that is missing in the paragraph below. Look at the paragraph and decide where (option 1, 2, 3, or 4) the following sentence would best fit.

Sentence They are the job creators in cities and towns across this country. They are the heartbeat of American communities.

Paragraph Universities also have an important role to play in supporting small businesses. Research shows that teaching core management skills can improve key business outcomes, such as profitability and growth. ___(1)___. We recommend that business and trade schools increase their focus on small firms and the unique challenges they face. ___(2)___. Whether through executive programs for small-business owners or student consulting projects, universities have a significant opportunity to lean into supporting Main Street entrepreneurs. ___(3)___. Thirty-five million small businesses are the engine of the U.S. economy. ___(4)___. As the nation undergoes rapid and profound policy shifts, we encourage leaders in government and academia to take action to ensure that Main Streets across America not only endure but thrive.

AOption 1

BOption 2

COption 3

DOption 4

Solution Answer: D (Option 4)

“They” needs small businesses as its immediate antecedent. The sentence “Thirty-five million small businesses are the engine of the U.S. economy” supplies it. The missing lines then continue that praise (job creators, heartbeat of communities) before the concluding call to action.

At blanks 1–3, “they” would point to universities or schools, which makes no sense.

Q10TITA

The four sentences (labelled 1, 2, 3 and 4) given below, when properly sequenced, would yield a coherent paragraph. Decide on the proper sequencing of the order of the sentences and key in the sequence of the four numbers as your answer.

Ideally, children would be monitored before puberty and until sexual maturity is reached.
Determining the effect of SBIF on human reproductive development requires a long-term commitment, both on the part of the investigator(s) as well as the subjects.
Furthermore, reproductive capacity should be assessed throughout potential child-bearing years.
This would allow potential differences in reproductive organ development to be discerned.

Solution Answer: 2143

The order runs like this:

2: Introduces the topic and the need for a long-term commitment.
1: Describes the ideal monitoring window, from before puberty to maturity.
4: “This would allow…” gives the benefit of that monitoring.
3: “Furthermore” adds a second requirement, assessment through the child-bearing years.

DILR · Data Interpretation & Logical Reasoning

Q11 – Q20 0/10

Set 1 · Q11 – Q15

Eight trains depart from Delhi to different cities at different times of day. The destination cities are Jaipur, Agra, Nagpur, Mumbai, Kolkata, Bhopal, Patna, and Raipur. The following information is known about them:

The trains departing for Agra and Kolkata depart at a time difference of 12 hours. One of them is the last train to depart.
The train to Jaipur departs at 6:00 am and travels at a speed of 100 km/hr, which is the second-highest speed among all trains.
The train to Bhopal is the first to depart, at a speed of 70 km/hr. The train to Nagpur is the fastest.
Three trains depart after the train to Raipur departs; the next one departs an hour later.
The speed of the train to Patna is half that of the train to Jaipur and departs immediately after the train to Raipur.
The sum of the speeds of the Mumbai and Agra trains is equal to the speed of the Jaipur train.
The train to Mumbai departs at 11:30 am after three trains have already departed.
The train to Agra departs at 7:00 am with a speed of 40 km/hr, which is half the speed of the train to Raipur, departing at 2:00 pm.
One of the trains departs at 2:30 am and another at 4:30 pm.
The speeds of the three fastest trains are in an Arithmetic Progression with a difference of 10 km/h.

Q11MCQ

What is the speed of the train departing at 11:30 am?

A50 km/hr

B70 km/hr

C40 km/hr

D60 km/hr

Solution Answer: D

Timings.

Raipur leaves at 2:00 pm with three trains after it. The next one, Patna, leaves an hour later at 3:00 pm.
Agra leaves at 7:00 am, so Kolkata leaves 12 hours later at 7:00 pm, the last train.
The 4:30 pm slot must then be Nagpur, and the 2:30 am slot is Bhopal, the first train.

Speeds.

Jaipur (100) is second fastest, so the AP of the top three gives Nagpur 110, and the third fastest, 90, goes to Kolkata.
Raipur = 2 × Agra = 80, Patna = 100 ÷ 2 = 50, and Mumbai = 100 − 40 = 60.

#	City	Time	Speed (km/hr)
1	Bhopal	2:30 am	70
2	Jaipur	6:00 am	100
3	Agra	7:00 am	40
4	Mumbai	11:30 am	60
5	Raipur	2:00 pm	80
6	Patna	3:00 pm	50
7	Nagpur	4:30 pm	110
8	Kolkata	7:00 pm	90

The 11:30 am train goes to Mumbai at 60 km/hr.

Q12MCQ

In which of the following triplets are the speeds of the trains not in arithmetic progression?

AAgra, Mumbai, Raipur

BBhopal, Raipur, Jaipur

CPatna, Bhopal, Kolkata

DAgra, Patna, Mumbai

Solution Answer: B

Using the solved speeds:

A: Agra 40, Mumbai 60, Raipur 80 is an AP.
B: Bhopal 70, Raipur 80, Jaipur 100 has gaps of 10 and 20, so it is not an AP.
C: Patna 50, Bhopal 70, Kolkata 90 is an AP.
D: Agra 40, Patna 50, Mumbai 60 is an AP.

Q13MCQ

Arrange the following cities in the ascending order of the departure of their respective trains.

AAgra, Jaipur, Patna, Nagpur

BAgra, Jaipur, Nagpur, Patna

CJaipur, Agra, Patna, Nagpur

DJaipur, Agra, Nagpur, Patna

Solution Answer: C

The departure order is Jaipur (6:00 am), Agra (7:00 am), Patna (3:00 pm), Nagpur (4:30 pm).

Q14TITA

How many trains depart between the trains that depart for Agra and Patna?

Solution Answer: 2

Agra is 3rd (7:00 am) and Patna is 6th (3:00 pm). In between are Mumbai (11:30 am) and Raipur (2:00 pm), so 2 trains.

Q15MCQ

The second slowest train departs for which city?

APatna

BAgra

CMumbai

DRaipur

Solution Answer: A

Speeds in ascending order: Agra 40, Patna 50, Mumbai 60, Bhopal 70, Raipur 80, Kolkata 90, Jaipur 100, Nagpur 110. The second slowest train goes to Patna.

Set 2 · Q16 – Q20

Given below is the division of a number by another. In the representation, each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 has been coded with one letter, with distinct letters representing distinct digits.

Coded long division puzzle for Q16 to Q20

Q16MCQ

What digit does M represent?

Solution Answer: B

Decoding the division gives C = 0, U = 1, S = 2, T = 3, O = 4, M = 5, I = 6, E = 8 and D = 9. The remaining letter stands for 7.

Q17MCQ

Which letter represents the digit 8?

Solution Answer: D

From the decoded division (C = 0, U = 1, S = 2, T = 3, O = 4, M = 5, I = 6, E = 8, D = 9), the digit 8 is E. D = 9, S = 2 and O = 4.

Q18TITA

What is the quotient (OUT)?

Solution Answer: 413

O = 4, U = 1 and T = 3, so the quotient OUT = 413.

Q19MCQ

What is the remainder (IST)?

A623

B413

C321

D432

Solution Answer: A

I = 6, S = 2 and T = 3, so the remainder IST = 623.

Q20TITA

What number is represented by DICES?

Solution Answer: 96082

D = 9, I = 6, C = 0, E = 8 and S = 2, so DICES = 96082.

QA · Quantitative Ability

Q21 – Q30 0/10

Q21MCQ

A ball is dropped from a height of 81 cm. After each bounce, it rises to two-thirds of the previous height. What is the total distance travelled by the ball in the air by the time it strikes the ground for the fifth time?

A422 cm

B341 cm

C260 cm

D211 cm

Solution Answer: B

After the first strike, the ball rises to 54, 36, 24 and 16 cm. It travels each of these heights twice (up and down) before strikes 2 to 5.

Total = 81 + 2(54 + 36 + 24 + 16) = 81 + 2 × 130 = 341 cm.

Q22MCQ

In rhombus ABCD, points M and N are chosen on sides AB and BC, respectively, such that triangle DMN is equilateral and AD = MD. Find the measure of angle ∠ABC.

A100°

B120°

C80°

D90°

Solution Answer: A

Let ∠A = ∠C = α. Since AD = MD, triangle ADM is isosceles, so ∠ADM = 180° − 2α.

DN = DM = AD = DC, so triangle DCN is also isosceles, giving ∠CDN = 180° − 2α.

∠ADC = 180° − α, and it splits as (180° − 2α) + 60° + (180° − 2α). So 420° − 4α = 180° − α, which gives α = 80°.

∠ABC = 180° − 80° = 100°.

Q23TITA

A shopkeeper buys 70 kg of rice for Rs. 1750. If he sells it at the market price, he makes a profit of Rs. 2100. He mixes the rice with some lower-quality rice costing Rs. 10 per kg. Selling this mixture at the same market price, his profit increases to Rs. 3900. Find the quantity (in kg) of the cheaper rice mixed.

Solution Answer: 40

Market price = (1750 + 2100) ÷ 70 = Rs. 55 per kg.

With x kg of cheaper rice: 55(70 + x) − (1750 + 10x) = 3900, so 3850 + 45x − 1750 = 3900, which gives 45x = 1800 and x = 40 kg.

Q24MCQ

a, b, and c are distinct digits. If aabc = (a + b + c)³, find a + b − c.

Solution Answer: D

Detailed solution coming soon.

Q25MCQ

If f(x) = x³3 + x²2 + x6, for all positive integers x, and f(n) − f(n − 1) = 2025, find the value of f(n − 36).

A96

B125

C140

D204

Solution Answer: C

f(x) = x(x + 1)(2x + 1)/6 = 1² + 2² + … + x², the sum of the first x squares.

So f(n) − f(n − 1) = n² = 2025, which gives n = 45. Then (n − 3)/6 = 7.

f(7) = 7 × 8 × 15 ÷ 6 = 140.

Q26TITA

How many real roots does the equation 2010 + x¹⁰ = 11^x + 11^−x have?

Solution Answer: 1

LHS: since x¹⁰ ≥ 0, 20/(10 + x¹⁰) ≤ 2, with equality only at x = 0.

RHS: by AM ≥ GM, 11ˣ + 11⁻ˣ ≥ 2, with equality only at x = 0.

The two sides can be equal only when both equal 2, which happens only at x = 0. So there is exactly 1 real root.

Q27MCQ

ABC is a right-angled triangle, right-angled at B. AB = 12 cm and BC = 9 cm. P is any point on AB. A line from P, parallel to BC, intersects AC at Q. A line from Q, parallel to AB, intersects BC at R. Find the minimum distance PR.

A7.5 cm

B8.4 cm

C7.2 cm

D9 cm

Solution Answer: C

PQ ∥ BC, QR ∥ AB and ∠B = 90°, so PBRQ is a rectangle. Its diagonals are equal, so PR = BQ.

BQ is shortest when it is perpendicular to AC. AC = 15, so the minimum BQ = (12 × 9) ÷ 15 = 7.2 cm.

Q28MCQ

Kamal goes to his village by bicycle. Some portion of the way is uphill, some is flat road, while the rest is downhill. Kamal’s speeds uphill, downhill and on a straight road are 6, 8.4 and 7 km/h, respectively. While going to his village, he took 1 hour and 45 minutes, but while returning, he took 2 hours and 15 minutes. Find the distance between his house and his village.

A12 km

B14 km

C16 km

DCannot be determined

Solution Answer: B

Let the uphill, flat and downhill distances on the way out be u, f and d. On the return trip, uphill and downhill swap.

Adding both trips: (u + d)(1/6 + 1/8.4) + 2f/7 = 1.75 + 2.25 = 4.

Since 1/6 + 1/8.4 = 2/7, this becomes (2/7)(u + d + f) = 4, so the distance u + f + d = 14 km.

Q29TITA

One needs to place 4 distinct balls into 5 distinct boxes. In how many ways can it be done such that exactly 3 of the boxes do not have any balls?

Solution Answer: 140

Exactly 2 boxes must be non-empty. Choose them in ⁵C₂ = 10 ways.

Distributing 4 distinct balls into those 2 boxes with neither empty gives 2⁴ − 2 = 14 ways.

Total = 10 × 14 = 140.

Q30MCQ

Two pipes, A and B, can fill a tank in 75 minutes and 90 minutes, respectively. Both pipes are opened simultaneously. After some time, pipe B is turned off such that the tank is filled in exactly one hour. If instead of pipe B, pipe A were turned off, how much extra time would it take to fill the tank?

A8 minutes 24 seconds

B8 minutes 40 seconds

C7 minutes

D7 minutes 35 seconds

Solution Answer: A

Take the tank as 450 units, so A fills 6 units/min and B fills 5 units/min.

A runs the full 60 min and B runs t min: 360 + 5t = 450, so t = 18 min.

If A is switched off at 18 min instead, 18 × 11 = 198 units are filled. B fills the remaining 252 units in 252 ÷ 5 = 50.4 min, so the total is 68.4 min.

Extra time = 8.4 min = 8 minutes 24 seconds.

Day 1 complete! 🔥

0 / 90

Correct: 0 · Wrong: 0 · Accuracy: 0%

Keep the streak alive. See you tomorrow for Day 2.

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