CAT 50 Day Streak Day 2

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CAT 50 Day Streak – Day 2

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

0/30Attempted

0Correct

0Wrong

0Score / 90

VARC · Verbal Ability & Reading Comprehension

Q1 – Q10 0/10

Passage · Q1 – Q4

In most great debates, many possible stances are reduced to two options in a hurry. In American politics, we often frame all debates as “Democrats versus Republicans” and proceed to label every policy or action as belonging to one of those factions. Anybody else, particularly those in the middle, is quickly swept aside and forgotten. According to a new study, this tendency is not only common but is so ingrained in our thinking that you can make a formula to describe it. “We know what happens to people who stay in the middle of the road. They get run down.” – Aneurin Bevan.

A team of researchers at the Santa Fe Institute studied the system using a commonly applied model to try to “solve” for where social boundaries appear on a political scale. The researchers added cognitive and social components — which often drive people into an “us vs. them” style of thinking — to the model’s equations. They hypothesised that people would devise measurable camps of “us” and “them” which would appear in the models. Those who don’t fit cleanly into these roles would tend to be overlooked. The model’s results were compared to data from 1980s surveys, which included questions about respondents’ feelings toward members of other political groups, to verify accuracy. Importantly, during that decade, many people were asked about political independents in the centre, deemed “inbetweeners” by the researchers, as well as about their stance on members of other parties.

Though one might suspect that people viewed those in the middle as potential allies, the tendency to divide the world into two buckets simply excludes those in the middle. The model predicted, and the surveys from the 80s confirmed, that both those on the left and right viewed centrists unfavourably. Lead author Vicky Chuqiao Yang explained the unfortunate situation of these centrists: “By being ‘inbetweeners,’ independents are viewed as unfavourably as the other party by both sides, and left out. So Independents get the worst of both worlds, and there are downstream consequences.”

The authors speculate that this phenomenon could cause those in the middle to drift towards the extremes in hopes of avoiding the ills of being in the middle. Over time, this could lead to a highly polarised society, as nobody is left in the middle at all. These findings are not necessarily limited to politics. The model could be applied to how society views people of indeterminate race or who do not fit cleanly into categories of sexuality, for example. Additionally, because group labels evolve, we should see the formation of entirely new groups and in-betweeners. In the study, the authors note that the model was limited for exactly this reason and hope that future studies will expand on the concept.

Q1MCQ

It can be reasonably inferred from the passage that if centrists continue to be marginalised, then:

APolitical debate will likely become more polarised over time.

BPolitical systems will become more democratic and inclusive.

CCentrist groups will eventually form a dominant third party.

DThe differences between the left and right will gradually dissolve.

Solution Answer: A

The last paragraph says marginalised centrists may “drift towards the extremes”, which “could lead to a highly polarised society, as nobody is left in the middle at all.” That is option A.

B is the opposite of the passage’s warning. C has no support, since centrists are described as excluded, not organising. D contradicts the predicted polarisation.

Q2MCQ

Which of the following, if true, would most strengthen the claim that centrists are marginalised?

AData show the number of registered independents is steadily increasing.

BSurveys reveal centrists enjoy greater trust from both sides of the spectrum.

CEvidence indicates that many centrists hold extreme views privately.

DLongitudinal studies show independents are less likely to be invited to political debates.

Solution Answer: D

Being left out of political debates over a long period is concrete evidence that independents are “swept aside and forgotten”. D directly supports the marginalisation claim.

A is about numbers, not treatment. B shows centrists are trusted, which weakens the claim. C is about centrists’ private views, not how others treat them.

Q3MCQ

The study’s framework could best explain which of the following non-political scenarios?

AA society where bilingual people are celebrated as cultural bridges.

BA workplace where hybrid employees are distrusted by both fully onsite and fully remote colleagues.

CA school where students in the middle grades are given more opportunities than seniors or juniors.

DA family where siblings share equal responsibility without conflict.

Solution Answer: B

The framework says “inbetweeners” who fit neither camp are viewed unfavourably by both sides. Hybrid employees, distrusted by both onsite and remote colleagues, are an exact parallel.

A and C show the middle group being favoured, the opposite of the model. D has no two-camp division at all.

Q4MCQ

Which of the following statements best describes the relationship between the model’s results and the 1980s survey data?

AThe model was developed to explain the observed patterns in the 1980s data; thus, the data served as the model’s ultimate conclusion.

BThe 1980s data provided the initial hypothesis, and the model was subsequently built to predict its statistical components.

CThe model’s predictions were confirmed by the observations found in the 1980s data, establishing the model’s empirical validity.

DThe 1980s data introduced the variable of the “inbetweener,” which the model then successfully incorporated into its cognitive equations.

Solution Answer: C

The passage says the model’s results were compared to the 1980s surveys “to verify accuracy”, and that “the model predicted, and the surveys from the 80s confirmed” the finding. The data validated the model’s predictions.

A and B reverse the order: the hypothesis came from the researchers, not the data. D is wrong because “inbetweeners” is the researchers’ label, not a variable supplied by the data.

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.

Though the sack of Troy has been dated to 1184 BC, the Homeric epics were composed and perhaps written down in the eighth or seventh century.
With a few slips, he was, for instance, very careful not to impose iron on his Bronze Age heroes.
Such historical scrupulosity, however, misses the point.
Homer shows himself acutely aware of the gap between his own day and the period about which he was singing.
For most of them – Sarpedon, Patroclus, Achilles, Ajax – it was a death rendered still more grim by being met at a young age and far from home.

Solution Answer: 5

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

1: There is a time gap between the fall of Troy and the composition of the epics.
4: Homer was aware of that gap.
2: “For instance”, he avoided giving iron to Bronze Age heroes.
3: “Such historical scrupulosity” sums up 2 and pivots with “however”.

Sentence 5 talks about the heroes’ deaths. “Them” has no antecedent, and the topic has nothing to do with Homer’s historical accuracy.

Q6TITA

The COVID-19 pandemic simply accelerated a trend: many of us are now more intimately connected to smartphones than to non-mediated relationships with people.
It is much easier, at least ostensibly, to live in isolation from other people.
Today, thanks mostly to our technologies, people are taking the second path through life much of the time.
Today, we are rapidly becoming ‘tech-vexed’ – my word for the gradual yet relentless seduction of computerised life.
The net result of this insular life is that relationships with ourselves and others take on a new hue.

Solution Answer: 2

The coherent paragraph is 4 → 1 → 3 → 5:

4: Introduces the author’s term “tech-vexed”, the seduction of computerised life.
1: COVID-19 accelerated this trend of being more connected to smartphones than to people.
3: “Thanks mostly to our technologies”, people take the second, mediated path.
5: “The net result of this insular life” concludes.

Sentence 2 is a general remark about how easy isolation is. It says nothing about technology, so it doesn’t fit the paragraph’s thread of technology-driven living.

Q7MCQ

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

Passage If you’re coming at religion from a scientist’s mindset, there’s not much to say. There’s really no evidence either way. We have neither verifiable testimony nor falsifiable claims. When you’re entirely stuck on a physical plane, you cannot say much about the metaphysical one. As Sam Harris says, “I don’t know what happens after the physical brain dies. I don’t think anyone does know.” The only fact we do know is that we will die. And it’s this fact that, for Bill Nye, is so important. Because we do not know what happens after death, and because we’re faced with the possibility that it might be nothing, we turn to life with a kind of vital energy. Death’s approach gives impetus to our mortal existence.

AThe lack of scientific evidence about the afterlife makes death the only certainty, and this uncertainty fuels a greater appreciation and urgency toward life.

BSince science has disproven the existence of the afterlife, figures like Sam Harris and Bill Nye argue that religion has no role in shaping human life.

CReligion and science agree that life after death is nothingness, which is why humans must rely solely on spiritual traditions to find meaning in existence.

DBill Nye and Sam Harris claim that science cannot fully explain what happens after death, proving that the metaphysical realm exists.

Solution Answer: A

The passage makes two points: science has no evidence either way about the afterlife, and the one certainty, death, gives life “vital energy”. A captures both.

B says science has “disproven” the afterlife, but the passage says there is no evidence either way. C invents an agreement between religion and science. D claims the metaphysical is proven, which the passage never says.

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 Retail pricing wars never stop.

Paragraph Customers today have extremely high expectations for prompt, thoughtful, and sympathetic responses. ___(1)___. Digital agents with natural language comprehension, context switching, and complex query resolution capabilities are made possible by agentic AI—all without transferring clients from one bot or agent to another. ___(2)___. They keep learning and getting better over time, which lowers support expenses and boosts client satisfaction. ___(3)___. By examining competitor behavior, inventory levels, purchase probability, and outside variables like seasonality or even popular social topics, agentic AI makes real-time repricing possible. ___(4)___. These agents can execute thousands of simulations and update prices in milliseconds to maximise profit and conversion, in contrast to static pricing algorithms.

AOption 1

BOption 2

COption 3

DOption 4

Solution Answer: C (Option 3)

The first half of the paragraph is about customer service agents. From blank 3 onwards it is about pricing (competitor behaviour, real-time repricing). “Retail pricing wars never stop” is the topic sentence that introduces this shift, so it belongs at blank 3.

Blanks 1 and 2 sit inside the customer-service discussion. Blank 4 would split the repricing explanation after the topic has already been introduced.

Q9TITA

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.

It looks, counterintuitively, as if the future is what determines the motion of the body in the past.
In classical mechanics, for example, there is something called the Lagrangian formulation, which holds that, when moving between two separate points, A and B, a physical body will take the most efficient path.
This does not look like the layer-cake model because, in order for the physical body to take the path of maximal efficiency, point B, which lies in the future, needs to be determined in advance.
In the case of general relativity, there are good reasons for doing this, but in other cases the challenge to the layer-cake model becomes harder to dismiss.

Solution Answer: 4231

The order runs like this:

4: Opens the idea that, outside general relativity, the challenge to the layer-cake model is “harder to dismiss”.
2: “In classical mechanics, for example” gives one such other case, the Lagrangian formulation.
3: Explains why this doesn’t fit the layer-cake model: point B must be fixed in advance.
1: Draws the counterintuitive conclusion that the future seems to determine the past.

Q10TITA

H. floresiensis made stone tools and hunted diminutive elephants, whose own small size stands as another example of insular dwarfism.
In fact, its size conforms to the ecological principle of insular dwarfism, which predicts that animals reduce their body size when their population’s range is limited to a small island environment.
The isolation of H. floresiensis likely contributed to its small brains and stature.
How H. floresiensis arrived at its namesake island is still unknown.

Solution Answer: 3214

The order runs like this:

3: Isolation likely caused the species’ small brain and stature.
2: “In fact, its size” fits the principle of insular dwarfism.
1: The dwarf elephants it hunted are “another example” of insular dwarfism.
4: Closes with an open question: how it reached the island is unknown.

DILR · Data Interpretation & Logical Reasoning

Q11 – Q20 0/10

Set 1 · Q11 – Q15

Eleven people from five societies (Amrapali, Ekansh, Rangoli, Symphony, Trident) own cars of various brands (Honda, Skoda, Ford, Toyota). Each person belongs to one of these societies. One person can have more than one car of any brand. The information about the vehicles owned by these 11 people is given in the table below.

Persons	Honda	Skoda	Ford	Toyota
Ambuj	1	1	1	1
Bindu	2	0	0	1
Chetan	2	0	0	0
Dhanu	0	1	3	0
Edwin	0	1	1	2
Farhat	0	1	2	2
Geeta	0	1	0	1
Harry	0	0	2	1
Ishmeet	0	2	1	0
Jashn	2	0	1	0
Kanta	1	1	1	0

The number of cars owned by these people, society-wise, is also given:

Society	Honda	Skoda	Ford	Toyota
Amrapali	3	2	4	1
Ekansh	2	1	3	2
Rangoli	1	3	2	1
Symphony	2	1	1	2
Trident	0	1	2	2

Q11MCQ

Chetan resides in which society?

AEkansh

BTrident

CSymphony

DCannot be determined

Solution Answer: C

Write each person and society as (Honda, Skoda, Ford, Toyota).

Honda owners. Bindu, Chetan and Jashn own 2 each, and Ambuj and Kanta own 1 each. Rangoli needs 1 Honda (Ambuj or Kanta). Amrapali needs 3, so it gets one 2-Honda person plus Ambuj or Kanta. Ekansh and Symphony (2 each) get one 2-Honda person each. Trident has no Honda owners.

Symphony (2,1,1,2). With Bindu, the remainder (0,1,1,1) can’t be formed. With Jashn, the remainder (0,1,0,2) can’t be formed. With Chetan, the remainder (0,1,1,2) is Edwin. So Symphony = Chetan + Edwin.
Ekansh (2,1,3,2). With Bindu, the remainder (0,1,3,1) is impossible. So it is Jashn + (0,1,2,2), which is either Farhat or Geeta + Harry.
Trident (0,1,2,2) gets whichever of Farhat / Geeta + Harry is left.
Amrapali (3,2,4,1) has Bindu. Adding Ambuj would give 2 Toyotas, so it takes Kanta, and the remainder (0,1,3,0) is Dhanu.
Rangoli (1,3,2,1) = Ambuj + Ishmeet.

Society	Members
Amrapali	Bindu, Kanta, Dhanu
Ekansh	Jashn + (Farhat or Geeta & Harry)
Rangoli	Ambuj, Ishmeet
Symphony	Chetan, Edwin
Trident	(Geeta & Harry) or Farhat

Chetan lives in Symphony.

Q12MCQ

How many people are from Ekansh?

B2 or 3

D3 or 4

Solution Answer: B

Ekansh is either Jashn + Farhat (2 people) or Jashn + Geeta + Harry (3 people). Both fit (2,1,3,2), so the answer is 2 or 3.

Q13TITA

How many people are from Amrapali?

Solution Answer: 3

Amrapali = Bindu (2,0,0,1) + Kanta (1,1,1,0) + Dhanu (0,1,3,0) = (3,2,4,1). That is 3 people.

Q14MCQ

Which of the following is a resident of Rangoli?

AAmbuj

BBindu

CEdwin

DHarry

Solution Answer: A

Rangoli = Ambuj (1,1,1,1) + Ishmeet (0,2,1,0) = (1,3,2,1). Bindu is in Amrapali, Edwin in Symphony, and Harry in Ekansh or Trident. The answer is Ambuj.

Q15MCQ

Which of the following statements may be correct, but not necessarily correct?

AGeeta and Harry are from the same society

BFarhat and Geeta are from different societies

CChetan and Dhanu are from the same society

DGeeta and Jashn are from different societies

Solution Answer: D

A: Geeta and Harry are always together, so this is always true.
B: Farhat and Geeta are always in different societies, so this is always true.
C: Chetan is in Symphony and Dhanu in Amrapali, so this is always false.
D: If Geeta is in Trident, it is true. If Geeta is in Ekansh with Jashn, it is false. It may be correct.

Set 2 · Q16 – Q20

The annual incomes (in lakh Rs.) of six ladies – Gayatri, Heena, Ishani, Jyoti, Kavya and Lekha – are 3, 4, 6, 8, 10 and 16, in no particular order. Each of them saves a different percentage of her annual income among 10%, 20%, 25%, 35%, 40% and 60%, and invests it in a different scheme among Stocks, PPF, Mutual Funds, FOREX, NPS and Crypto, in no particular order. It is also known that:

Ishani saves 25% of her annual income while Heena invests in NPS.
The lady who saves 40% does not invest in PPF.
The average annual income of Gayatri, Heena and Jyoti is Rs. 6 lakhs.
The lady who earns the highest saves Rs. 5.6 lakhs and invests it in FOREX.
The annual income of Kavya is the least among the six. She saves 1/12th of the amount saved by the lady who invests in Mutual Funds.
The sum of the annual incomes of the lady who invests in Stocks and the lady who saves 20% is equal to the sum of the annual incomes of Gayatri and the lady who saves 60%.

Q16TITA

How much does Kavya save? (in Rs.)

Solution Answer: 30000

Highest income is 16, with 5.6 saved, so 35% in FOREX. Kavya has the least income, 3.
G + H + J = 18 from {4, 6, 8, 10, 16}, which forces {4, 6, 8}. So Ishani and Lekha are 10 and 16. Ishani saves 25%, so Ishani = 10 and Lekha = 16.
Kavya saves 10%, 20%, 40% or 60% of 3, i.e. 0.3, 0.6, 1.2 or 1.8. The Mutual Funds lady saves 12 times that: 3.6, 7.2, 14.4 or 21.6. Only 3.6 is achievable (60% of 6). So Kavya saves 10% and the income-6 lady saves 60% in Mutual Funds.
Incomes 4 and 8 take 20% and 40%. Heena (NPS) is 4 or 8.
Last clue: Stocks income + 20%-saver’s income = Gayatri + 6. Gayatri can’t be the 60% lady herself (they are named separately), so Gayatri = 8 or 4. Gayatri = 4 fails. With Gayatri = 8, we need Stocks + 20%-saver = 14, which is 10 + 4. So Ishani is in Stocks, 4 saves 20%, and Gayatri (8) saves 40%.
Heena = 4 (20%, NPS) and Jyoti = 6 (60%, MF). Gayatri’s 40% can’t go to PPF, so Gayatri is in Crypto and Kavya in PPF.

Lady	Income (lakh)	Saves %	Savings (lakh)	Scheme
Gayatri	8	40%	3.2	Crypto
Heena	4	20%	0.8	NPS
Ishani	10	25%	2.5	Stocks
Jyoti	6	60%	3.6	Mutual Funds
Kavya	3	10%	0.3	PPF
Lekha	16	35%	5.6	FOREX

Kavya saves 0.3 lakh = Rs. 30,000.

Q17MCQ

What percent of her salary does Gayatri save?

A20%

B40%

C60%

DCannot be determined

Solution Answer: B

From the solved table (see Q16), Gayatri earns 8 lakh and saves 40% (Rs. 3.2 lakh).

Q18MCQ

In which scheme does Ishani invest?

APPF

BCrypto

CStocks

DMutual Funds

Solution Answer: C

From the last clue, Stocks income + 20%-saver’s income (4) = Gayatri (8) + 60%-saver (6) = 14. So the Stocks investor earns 10, which is Ishani. She invests in Stocks.

Q19MCQ

What are the total savings of the six ladies put together?

ARs. 15 lakhs

BRs. 18 lakhs

CRs. 17 lakhs

DRs. 16 lakhs

Solution Answer: D

Total = 3.2 + 0.8 + 2.5 + 3.6 + 0.3 + 5.6 = Rs. 16 lakhs.

Q20TITA

How many ladies save more than the one who invests in Crypto?

Solution Answer: 2

Gayatri invests in Crypto and saves 3.2 lakh. Jyoti (3.6) and Lekha (5.6) save more, so the answer is 2.

QA · Quantitative Ability

Q21 – Q30 0/10

Q21MCQ

If 4^x = 125 and 8^y = 5, find the value of 2x − yy.

D10

Solution Answer: B

4^x = 2^2x = 125 = 5³, and 8^y = 2^3y = 5, so 5³ = 2^9y.

So 2^2x = 2^9y, which gives 2x = 9y.

(2x − y)/y = (9y − y)/y = 8.

Q22TITA

In the equation x + x + x + … + x = 1260, let the number of x’s be y. If x and y are natural numbers and x > 1, find the smallest possible value of y + x.

Solution Answer: 71

The equation says xy = 1260. For a fixed product, the sum x + y is smallest when the two factors are closest to √1260 ≈ 35.5.

1260 = 35 × 36, so the minimum x + y = 35 + 36 = 71.

Q23MCQ

The sums of n terms of two arithmetic progressions are in the ratio (3n + 8) : (7n + 15). The ratio of their 12^th terms is:

A4 : 9

B3 : 7

C9 : 16

D7 : 16

Solution Answer: D

The ratio of the k^th terms equals the ratio of the sums with n = 2k − 1. For k = 12, n = 23.

(3 × 23 + 8) : (7 × 23 + 15) = 77 : 176 = 7 : 16.

Q24TITA

The number of integers greater than 6000 that can be formed using the digits 3, 5, 6, 7, and 8 without repetition is:

Solution Answer: 192

4-digit numbers: the first digit must be 6, 7 or 8, giving 3 × 4 × 3 × 2 = 72.

5-digit numbers: all of them exceed 6000, giving 5! = 120.

Total = 72 + 120 = 192.

Q25MCQ

An ice cream cone consists of a sphere of vanilla ice cream and a right circular cone that has the same diameter as the sphere. If the ice cream melts, it will exactly fill the cone. Assume that the melted ice cream occupies 75% of the volume of the frozen ice cream. What is the ratio of the cone’s height to its radius?

A2 : 1

B3 : 1

C4 : 1

D16 : 3

Solution Answer: B

Let the common radius be r. The melted volume is 0.75 × (4/3)πr³ = πr³.

This fills the cone: (1/3)πr²h = πr³, so h = 3r.

h : r = 3 : 1.

Q26MCQ

Alisa places 2.5 ounces of coffee into a 5-ounce cup and 2.5 ounces of cream into a second cup of the same size. She then pours half the coffee from the first cup to the second and, after stirring thoroughly, pours half the liquid in the second cup back to the first. What fraction of the liquid in the first cup is now cream?

A1/4

B1/3

C3/7

D2/5

Solution Answer: D

After the first pour: cup 1 has 1.25 coffee, and cup 2 has 1.25 coffee + 2.5 cream = 3.75.

Half of cup 2 (1.875) goes back, carrying 0.625 coffee and 1.25 cream.

Cup 1 now holds 1.875 coffee + 1.25 cream = 3.125. The cream fraction is 1.25 / 3.125 = 2/5.

Q27MCQ

A parallelogram ABCD has ∠ABC = 120°, AB = 16, and BC = 10. Extend CD through D to E so that DE = 4, and label as F the intersection of AD and BE. What is the value of DF?

B1.5

D2.5

Solution Answer: C

DE lies on line CD, which is parallel to AB, so triangles FDE and FAB are similar.

DF : FA = DE : AB = 4 : 16 = 1 : 4. Since AD = BC = 10, DF = 10 × 1/5 = 2.

(The 120° angle isn’t needed.)

Q28MCQ

Two factors of a number N are prime. If N² has 77 factors, find the number of factors of N.

A24

B28

C22

D18

Solution Answer: A

N has exactly two prime factors: N = p^aq^b. Then N² = p^2aq^2b has (2a + 1)(2b + 1) = 77 = 7 × 11 factors, so a = 3 and b = 5.

Factors of N = (3 + 1)(5 + 1) = 24.

Q29MCQ

Anshul invested a sum of money in a bank at 8% rate of interest, compounded annually. Amod also deposited the same amount in the bank. The manager, being a friend of Amod, offered him 10% interest, compounded semiannually. The amount received at the end of the 1st year by Amod was Rs. 2700 more than that received by Anshul. What was the principal amount invested by each of them in the bank?

ARs 135000

BRs 120000

CRs 108000

DRs 90000

Solution Answer: B

Anshul gets 1.08P. Amod gets 10% compounded half-yearly, i.e. 5% per half-year: (1.05)²P = 1.1025P.

Difference: 0.0225P = 2700, so P = Rs 1,20,000.

Q30MCQ

Maya’s mother told her to eat no more than 10 chocolates per day. Also, if in one day she eats more than 7 chocolates, in the next two days she can’t eat more than 5 chocolates. What is the maximum number of chocolates that Maya can eat over a period of 20 consecutive days, following the request of her mother?

A143

B142

C141

D140

Solution Answer: A

A “big” day (10) forces two days of at most 5, giving 20 over 3 days. Three days of 7 give 21. So eating 7 every day beats using big days in the middle.

The exception is the last day: a 10 on day 20 has no following days to penalise. The best plan is 7 × 19 + 10 = 133 + 10 = 143.

Putting the 10 on day 19 instead gives 126 + 10 + 5 = 141, which is lower.

Day 2 complete! 🔥

0 / 90

Correct: 0 · Wrong: 0 · Accuracy: 0%

Keep the streak alive. See you tomorrow for Day 3.

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