CAT 50 Day Streak Day 20

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CAT 50 Day Streak – Day 20

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

Many people in the twenty-first century spend a great deal of time thinking about their emotions: where they come from, how they show up in our bodies, and whether they drive us toward productive or destructive acts. As historians Damien Boquet and Piroska Nagy write, ideas about this topic in Europe changed dramatically in the High Middle Ages. Intellectual life in medieval Europe was thoroughly bound up in Christianity, and, early on, this often translated to viewing human feelings in stark terms of good and evil. For example, Gregory the Great, a Church Father from the early medieval period, wrote that even though it was necessary to slake one’s thirst, the pleasure of tasting a drink could contain an element of sin.

Boquet and Nagy write that this began to change in the late eleventh century, thanks partly to new translations of Arabic texts. Christian intellectuals increasingly accepted input from classical and contemporary non-Christian sources, particularly in emerging urban schools, which were beginning to replace monastic cloisters as centers of learning in Europe. In this context, feelings like anger, joy, sadness, fear, and shame could be understood through humoral medicine, a longstanding framework for addressing the body’s needs. Joy, for example, represented the movement of the body’s heat outward from the heart—something that was beneficial to the body in small doses but potentially dangerous or even lethal in sudden, sharp bursts.

Around the same time, Boquet and Nagy write, Christian thinkers increasingly came to view emotional feeling as an aspect of human nature that did not necessarily have a moral weight in and of itself. As French philosopher and theologian Peter Abelard wrote in the 1130s, “the sin is not the desire for the wife of another, but rather to consent to this desire.” For Abelard, having tendencies toward wrong thoughts or actions might be a natural defect of the soul, but it was not itself evil—and, in fact, it provided the opportunity for a person to virtuously triumph over their innate drive toward wrath, luxury, or other evils.

Working with emotion to improve virtue became part of the job of religious authorities. For example, William of Auvergne, who served as bishop of Paris in the thirteenth century, described the need to convert fleeting passions such as love and joy into lasting dispositions—and to avoid allowing hate, pain, or anger to congeal similarly. This process might involve cultivating appropriate feelings during penance, such as promoting “virtuous shame,” which encourages contrition, and avoiding “arrogant shame,” which discourages it. In place of a stoic effort to avoid the influence of emotion, thirteenth-century thinkers, including Thomas Aquinas, sought to use reason to direct the passions correctly, turning them into tools for self-improvement. “The way to salvation proposed by late medieval thinkers was no longer bound in an austere dialectic opposing spiritual and carnal man but instead proceeded from the new understanding of the divine project as expressed by the physical world,” Boquet and Nagy write.

Q1MCQ

It can be inferred that prior to the late eleventh century, a Christian thinker like Gregory the Great would have been most likely to agree with which of the following statements?

AThe experience of shame can be a virtuous tool for encouraging contrition.

BA physiological imbalance, such as an excess of heat from the heart, is the true cause of sin.

CConsenting to a sinful desire is a greater moral failing than simply having the desire.

DThe pleasure derived from a necessary act, like tasting a drink, can be a moral failing.

Solution Answer: D

Gregory wrote that even though drinking is necessary, “the pleasure of tasting a drink could contain an element of sin.” D restates this.

A (“virtuous shame”) comes from William of Auvergne in the 13th century. B draws on humoral medicine, which entered later and wasn’t used to explain sin. C is Abelard’s 1130s view.

Q2MCQ

The final quote from Boquet and Nagy (“The way to salvation... proceeded from the new understanding of the divine project as expressed by the physical world”) implies that:

Athe late medieval church began to see the physical body and its emotions as a valid expression of divine creation, rather than just an obstacle to spirituality.

Blate medieval thinkers abandoned the concept of salvation in favor of a new focus on the “divine project.”

Cthe physical world and its passions were newly understood as being superior to the spiritual world.

Dthe “austere dialectic” was perfected and became the primary path to understanding the divine.

Solution Answer: A

The quote says salvation was “no longer bound” to setting spiritual against carnal man, and now came from the divine project “as expressed by the physical world”. In other words, the body and its passions became part of God’s design rather than just an obstacle.

B: salvation itself remains the goal. C: “superior” overstates a reconciliation. D: the austere dialectic was left behind, not perfected.

Q3MCQ

According to the passage, the humoral medicine framework understood joy as:

Aa fleeting passion that religious authorities sought to convert into a lasting disposition.

Ba physical phenomenon that could be beneficial in moderation but harmful in excess.

Ca natural defect of the soul that provided an opportunity to demonstrate virtue.

Da purely spiritual state that was entirely separate from the body’s heat.

Solution Answer: B

In humoral medicine, joy was heat moving outward from the heart, “beneficial … in small doses but potentially dangerous or even lethal in sudden, sharp bursts.”

A is William of Auvergne’s religious view, not humoral medicine. C is Abelard’s idea about wrong tendencies. D contradicts the heat-based physical description.

Q4MCQ

Which of the following, if true, would most weaken the passage’s explanation for the changes in emotional theory in the High Middle Ages?

AModern science has conclusively proven that the humoral theory of medicine is factually incorrect.

BThomas Aquinas and Peter Abelard are discovered to have had significant disagreements on other theological matters.

CHistorical evidence shows that new translations of Arabic texts in the late eleventh century were exclusively focused on mathematics and astronomy.

DResearch confirms that monastic cloisters continued to produce significant scholarly work well into the thirteenth century.

Solution Answer: C

The passage credits the change “partly to new translations of Arabic texts”, which brought in frameworks like humoral medicine. If those translations covered only maths and astronomy, they couldn’t have shaped thinking about emotion, and the explanation is undercut.

A: whether humoral theory is true today is irrelevant to its historical influence. B: disagreements on other matters don’t matter here. D: urban schools only “were beginning to replace” cloisters, so continued monastic work doesn’t contradict the passage.

Q5TITA

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.

The two basic types of writing—hieroglyphs, which were used for monuments and display, and the cursive form known as hieratic—were invented at much the same time in late predynastic Egypt.
Writing was chiefly used for administration, and until about 2650 BCE, no continuous texts are preserved.
Writing was a major instrument in the centralization of the Egyptian state and its self-presentation.
The only extant literary texts written before the early Middle Kingdom seem to have been lists of important traditional information and possibly medical treatises.

Solution Answer: 3124

The order runs like this:

3: Writing was central to the Egyptian state’s centralisation and self-presentation (general thesis).
1: The two types of writing (hieroglyphs and hieratic) were invented together.
2: Writing was used mainly for administration, with no continuous texts before 2650 BCE.
4: The only early literary texts are lists and possibly medical treatises.

Q6TITA

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.

The accommodations I received in school, like my black-and-white enlarged textbooks or a seat at the front of the room, made me feel different and alone.
Seeing disability in this more empowering light, I feel it as just one part of my identity that makes me resilient and resourceful.
I wanted my books in colour and to sit with my friends.
Three times a week, that rubber ball reminded me that, just because I was born a certain way, my world and my potential had limits.
During gym class, when we played softball, I hit the ball off a tee.

Solution Answer: 2

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

1: School accommodations made the author feel different and alone.
3: The author wanted coloured books and to sit with friends.
5: In gym class, the author hit the ball off a tee.
4: “That rubber ball” reminded the author of limits.

Sentence 2 refers to “this more empowering light”, which is never set up. It belongs to a later, positive reframing, while the other four recall feeling limited.

Q7MCQ

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 A lack of political socialization is not merely a personal failing to Elliott.

Paragraph ___(1)___. Elliott is concerned about politically “unsocialized” citizens, who do not know what is going on or how to participate. ___(2)___. He claims unsocialized citizens create externalities. They are more susceptible to undemocratic arguments that discount democracy’s benefits or make promises democratic institutions can’t fulfill. ___(3)___. Politically unsocialized citizens are the most at risk of endorsing Constant’s Bonapartist despots. ___(4)___. Besides that, they are unable to see, respond to, and avoid participating in injustices in their communities.

AOption 1

BOption 2

COption 3

DOption 4

Solution Answer: B (Option 2)

Once “unsocialized” citizens are introduced, the sentence says it is “not merely a personal failing”. The next sentence explains why: “He claims unsocialized citizens create externalities”, meaning costs for others.

At 1, the term hasn’t been introduced yet. At 3 and 4, the externalities argument is already under way.

Q8TITA

Medicine, social reform, benevolent people and institutions had relaxed the struggle for existence.
For others who were inspired by Darwin and Malthus, the problem was exactly the opposite: human societies had become unlike processes of the natural world.
Malthus’s ideas emerged at a time when Britain was being socially reconfigured.
In 1867, the poet Matthew Arnold felt this loss when he described the spiritual emptiness created by evolution in terms of a retreating ocean heard only as a ‘melancholy, long, withdrawing roar’.
For Arnold, the fact that humans were part of an aimless natural process was a source of anguish.

Solution Answer: 3

The coherent paragraph is 4 → 5 → 2 → 1:

4: Arnold felt the spiritual loss caused by evolution.
5: For Arnold, being part of an aimless natural process was anguish.
2: “For others”, the problem was the opposite: society had become unlike nature.
1: Medicine and reform had relaxed the struggle for existence (why society was unlike nature).

Sentence 3 changes the subject to the historical setting of Malthus’s ideas. It doesn’t fit the contrast between the two reactions to evolution.

Q9MCQ

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

Passage Time also exerts pressure on the receiving end of language. A listener’s memory for the bare form of language, untethered from meaning, is fleeting. (Notice how much harder it is to remember a nonsensical list of syllables than a meaningful phrase of the same length: ‘lep blintasp lorset ap lep howd’, versus ‘the smartest person in the room’.) To avoid the accumulation of free-floating phonetic bits, the listener races to extract meaning from the first sounds that drop from a speaker’s mouth. If you hear ‘the cap—’, you are automatically rifling through your vocabulary to decide whether this snippet of speech refers to a hat or whether it will continue as ‘the captain’, ‘the capital’, or ‘the cappuccino’.

AThe human brain retains meaningless sounds more effectively than meaningful phrases.

BListeners process speech by rapidly attaching meaning to sounds as they are heard.

CSpeakers must slow down to help listeners retain what they say.

DUnderstanding language depends primarily on memorising phonetic details.

Solution Answer: B

Memory for meaningless sound fades fast, so listeners “race to extract meaning from the first sounds”. B says exactly this.

A reverses the syllables example. C advises speakers, which the passage never does. D: the passage stresses meaning over phonetic detail.

Q10TITA

Sentences given in the question below, when properly sequenced, form a coherent paragraph. The first and last sentences are A and F, and the four in between are labelled 1, 2, 3, and 4. Choose the most logical order of these four sentences to construct a coherent paragraph from sentences A to F.

“The Enigma of Reason,” “The Knowledge Illusion,” and “Denying to the Grave” were all written before the November election.
And yet they anticipate Kellyanne Conway and the rise of “alternative facts.”
Rational agents would be able to think their way to a solution.
These days, it can feel as if the entire country has been given over to a vast psychological experiment being run either by no one or by Steve Bannon.
But, on this matter, the literature is not reassuring.
The books suggest that rational thinking might be less common than we assume.

Solution Answer: 1324

The order runs like this:

A: The books were written before the election.
1: “And yet they anticipate” alternative facts.
3: Today it feels like a vast psychological experiment.
2: Rational agents would think their way out.
4: “But” the literature is not reassuring.
F: Rational thinking may be rarer than we assume.

DILR · Data Interpretation & Logical Reasoning

Q11 – Q20 0/10

Set 1 · Q11 – Q15

There are some pens in a box. Each pen has either a transparent or an opaque body, is either a gel pen or a ball pen, and is either red or blue. Further, it is known that:

3/5 of the pens in the box have a transparent body.
2/7 of the opaque pens are red, and 3/7 of the red pens have a transparent body.
3/8 of the opaque pens are gel, whereas 2/5 of the gel pens are opaque.
1/8 of the number of blue ball pens is equal to red gel pens.
1/8 of the red pens are gel and have an opaque body.

Q11TITA

What can be the minimum number of pens in the box?

Solution Answer: 280

Body. Transparent = 3N/5, opaque = 2N/5.
Red. Opaque red = 2/7 × 2N/5 = 4N/35. That is 4/7 of all red pens, so red = N/5 and transparent red = 3N/35.
Gel. Opaque gel = 3/8 × 2N/5 = 3N/20, which is 2/5 of all gel pens, so gel = 3N/8.
Red gel. Opaque red gel = N/40. Let red gel = r. Blue ball = (4N/5 − 3N/8) + r = 17N/40 + r = 8r, so r = 17N/280.

Writing everything in units of u = N/280:

Category	Transparent	Opaque
Red gel	10u	7u
Red ball	14u	25u
Blue gel	53u	35u
Blue ball	91u	45u
Total	168u	112u

Every count is a whole number only if u is a whole number, so the minimum is N = 280.

Q12MCQ

What is the ratio of red transparent gel pens to red opaque ball pens?

A5:7

B2:5

C2:3

DCan’t be determined

Solution Answer: B

From the table in Q11: 10u : 25u = 2 : 5.

Q13MCQ

Which of the following is the largest in number?

Atransparent blue ball pens

Btransparent red gel pens

Copaque red ball pens

Dopaque blue ball pens

Solution Answer: A

The four options are 91u, 10u, 25u and 45u, so transparent blue ball pens (91u) are the largest.

Q14MCQ

Which of the following is definitely a multiple of 5?

opaque red ball pens
opaque blue ball pens
opaque blue gel pens

AOnly I

BOnly I and III

COnly II and III

DAll of them

Solution Answer: D

Opaque red ball = 25u, opaque blue ball = 45u, opaque blue gel = 35u. All three are multiples of 5 for any whole u, so the answer is all of them.

Q15MCQ

If there are a total of 840 pens, how many of them are transparent blue gel pens?

A147

B153

C159

D165

Solution Answer: C

u = 840/280 = 3, so transparent blue gel = 53 × 3 = 159.

Set 2 · Q16 – Q20

A math teacher invited five students to participate in a calculation game.

60 seconds were given to answer every question.

The first, second, third, fourth and fifth students to answer the question correctly were awarded 50, 40, 30, 20 and 10 points, respectively.

In addition to the above, 1 extra point was awarded for each second saved. For example, if a person answered in 42 seconds, they would be awarded 18 bonus points.

The table below gives the time taken by students to answer these questions:

	Q1	Q2	Q3	Q4	Q5
Pushkar	30	52	58		46
Qadir	28	35	48	42
Riya		45	42	39	52
Sakshi	52	31		57	33
Tejas	45		57	56	58

The total number of points scored in the quiz was 1126.
Qadir came 1st with a score of 286, and Tejas was 5th with 178 points.
254 points were scored for question 1 and 193 points for question 3.

Q16MCQ

What is the least time taken by a student to answer a question?

A25 seconds

B26 seconds

C27 seconds

D28 seconds

Solution Answer: B

Each question pays 50 + 40 + 30 + 20 + 10 = 150 in rank points, plus 300 − (sum of times) in bonus. So the points for a question = 450 − (sum of the five times).

Q1. 450 − (155 + Riya) = 254, so Riya = 41.
Q3. 450 − (205 + Sakshi) = 193, so Sakshi = 52.
Total. 2250 − (all times) = 1126, so all times = 1124. This leaves Tejas (Q2) + Pushkar (Q4) + Qadir (Q5) = 125.
Qadir (286). Q1 (82) + Q3 (52) leave 152 for Q2 + Q4 + Q5. Checking his possible ranks, the only fit is Qadir taking 51 s on Q5 (3rd, 39 points), so Tejas (Q2) + Pushkar (Q4) = 74.
Tejas (178). Q1 (35), Q3 (23) and Q5 (12) leave 108 for Q2 + Q4. The only consistent case is Tejas fastest on Q2 in 26 s (84 points) and 4th on Q4 (24 points). That makes Pushkar’s Q4 time 48.

Points (time)	Q1	Q2	Q3	Q4	Q5	Total
Pushkar	70 (30)	18 (52)	12 (58)	42 (48)	54 (46)	196
Qadir	82 (28)	55 (35)	52 (48)	58 (42)	39 (51)	286
Riya	49 (41)	35 (45)	68 (42)	71 (39)	28 (52)	251
Sakshi	18 (52)	69 (31)	38 (52)	13 (57)	77 (33)	215
Tejas	35 (45)	84 (26)	23 (57)	24 (56)	12 (58)	178
Total	254	261	193	208	210	1126

The least time is Tejas’s 26 seconds on Q2.

Q17TITA

How many points did Sakshi score by answering the 3rd question?

Solution Answer: 38

Sakshi took 52 s on Q3 and was 3rd (after Riya 42 and Qadir 48). Points = 30 + 8 = 38.

Q18MCQ

How many total points were scored in the 4th question?

A199

B205

C208

D210

Solution Answer: C

Q4 times are 48, 42, 39, 57 and 56 (sum 242), so the points are 450 − 242 = 208.

Q19TITA

What was the total score of Pushkar?

Solution Answer: 196

70 + 18 + 12 + 42 + 54 = 196.

Q20MCQ

Find the median of the points Riya scored in her five questions.

A49

B50

C52

D55

Solution Answer: A

Riya’s points in order are 28, 35, 49, 68, 71, so the median is 49.

QA · Quantitative Ability

Q21 – Q30 0/10

Q21MCQ

ABC is a right-angled triangle with angle A being the right angle. Angle B is trisected. If AK = 3, KL = 4, find the length of CL.

Right triangle ABC with right angle at A; angle B trisected by BK and BL meeting AC at K and L; AK = 3, KL = 4, LC = x

B10

D12

Solution Answer: A

Let AB = h and each part of angle B = α. Then tan α = 3/h and tan 2α = 7/h.

tan 2α = 2 tan α1 − tan²α gives 6hh² − 9 = 7h, so h² = 63 and tan α = 1/√7.

tan 3α = 3t − t³1 − 3t² with t = 1/√7 gives 5/√7. So AC = h tan 3α = 3√7 × 5/√7 = 15.

CL = 15 − 7 = 8.

Q22MCQ

There are 10 children in a group. 4 tickets were bought for the theatre. The tickets are identical. A child can take at most 2 tickets. In how many ways can the tickets be distributed?

A360

B570

C615

D445

Solution Answer: C

1, 1, 1, 1: ¹⁰C₄ = 210
2, 1, 1: 10 × ⁹C₂ = 360
2, 2: ¹⁰C₂ = 45

Total = 615.

Q23TITA

M is the smallest integer such that 4a + 2 = 5b + 3 = 7c + 5 = M, where a, b, c are natural numbers. If M:(a+b+c) in reduced form is expressed as x:y, what is the value of x+y?

Solution Answer: 109

M ≡ 2 (mod 4) and M ≡ 3 (mod 5) give M ≡ 18 (mod 20). Checking 18, 38, 58, … for M ≡ 5 (mod 7), the first fit is M = 138.

a = 34, b = 27, c = 19, so a + b + c = 80. 138 : 80 = 69 : 40, and x + y = 109.

Q24MCQ

In an ice cream shop, the seller has fixed the prices of three popular flavours of ice cream: A, B, and C in the ratio of 6:4:1. However, in order to attract more customers, the seller reduced the price of flavour A ice cream by 1/5 and that of flavour B ice cream by 1/15. In a year, the ratio of the number of customers who bought flavour A, B, and C ice creams was 10:15:24, respectively, and the money collected by the seller was Rs. 150240. Find the amount paid by the customers who bought flavour A ice creams.

A56340

B64580

C48730

D65420

Solution Answer: A

New prices: A = 6k × 4/5 = 4.8k, B = 4k × 14/15 = 56k/15, C = k.

Revenue ratio: 10 × 4.8 : 15 × 56/15 : 24 × 1 = 48 : 56 : 24 (total 128).

A’s share = 150240 × 48/128 = Rs. 56340.

Q25MCQ

Find the product of all real values of x and y for the given set of equations: 2^x+2 = y² + 16 and 2^x−1 ≤ y

B12

C24

D36

Solution Answer: B

From the second condition, 2^x+2 = 8 × 2^x−1 ≤ 8y. So y² + 16 ≤ 8y, which means (y − 4)² ≤ 0 and y = 4.

Then 2^x+2 = 32, so x = 3. Product = 3 × 4 = 12.

Q26TITA

Find the difference between the largest and smallest integers in the domain of the function f(x) = √(log_x−1(13 − 2x) − 1)

Solution Answer: 1

Base: x − 1 > 0 and x − 1 ≠ 1, so x > 1 and x ≠ 2. Argument: 13 − 2x > 0, so x < 6.5.

The square root needs log_x−1(13 − 2x) ≥ 1. For x > 2 (base > 1), this means 13 − 2x ≥ x − 1, so x ≤ 14/3. There are no integers between 1 and 2.

Integers in the domain: 3 and 4 (check: log₂7 ≥ 1 ✓, log₃5 ≥ 1 ✓, log₄3 < 1 ✗). Difference = 1.

Q27MCQ

20% of employees from Department X are transferred to another department, Department Y; 25% of the remaining employees are transferred to Department Z, and 10% of the remaining employees are transferred to Department W. If the number of male employees left in Department X is 3780, then find the total number of employees in Department X before the transfer. The number of female employees is thrice the number of males, and this ratio remains the same even after the transfer.

A25500

B28000

C32500

D34000

Solution Answer: B

Remaining = N × 0.8 × 0.75 × 0.9 = 0.54N. Males are 1/4 of this: 0.135N = 3780.

N = 28000.

Q28TITA

The length of the common chord of two intersecting circles is 24 cm. If the diameters of the circles are 30 cm and 26 cm, then the distance between the centres (in cm) is

Solution Answer: 14

Half-chord = 12. Distance from each centre to the chord: √(15² − 12²) = 9 and √(13² − 12²) = 5.

With the centres on opposite sides of the chord, the distance = 9 + 5 = 14 cm.

Q29MCQ

What is the difference between the Compound Interest and the Simple Interest for three years, given that the CI for two years is Rs. 24300 and the SI for two years is Rs. 21600 on the same principal and at the same annual rate of interest?

ARs. 8250

BRs. 8525

CRs. 8775

DRs. 8900

Solution Answer: C

SI per year = 10800. CI − SI over 2 years = 2700, which is interest on the first year’s interest: 10800r = 2700, so r = 25% and P = 43200.

3-year CI = 43200 × (1.25³ − 1) = 41175. 3-year SI = 32400. Difference = Rs. 8775.

Q30MCQ

The cost of a samosa, a kachori, and a burger is Rs. 90. Jyoti has Rs. 170, with which she can buy one samosa, two kachoris, and three burgers. How much extra money must she borrow from her friend if she wants to buy 3 samosas, 2 kachoris, and 1 burger?

A40

B30

C25

D20

Solution Answer: D

s + k + b = 90 and s + 2k + 3b = 170.

3s + 2k + b = 4(s + k + b) − (s + 2k + 3b) = 360 − 170 = 190. She has 170, so she must borrow Rs. 20.

Day 20 complete! 🔥

0 / 90

Correct: 0 · Wrong: 0 · Accuracy: 0%

Keep the streak alive. See you tomorrow for Day 21.

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