CAT 50 Day Streak – Day 31
30 questions across VARC, DILR & QA · +3 for a correct answer · −1 for a wrong MCQ · no negative marking for TITA
VARC · Verbal Ability & Reading Comprehension
The optic nerve lies at the back of the human eye, connected to the retina, which is made up of receptors sensitive to incoming light. The nerve’s job is to transmit visual input gathered by those receptors to the brain. But the optic nerve’s location atop a tiny portion of the retina also means there is a blind spot in our vision, a region in the visual field that is literally unseen.
In science, that blind spot is experience. Experience is intimate — a continuous, ongoing background for all that happens. It is the fundamental starting point below all thoughts, concepts, ideas and feelings. The philosopher William James used the term “direct experience.” Others have used words like “presence” or “being.” Philosopher Edmund Husserl spoke of the “Lebenswelt” or life-world to highlight the irreducible totality of our “already being in a living world” before we ask any questions about it.
From this perspective, experience is a holism; it can’t be pulled apart into smaller units. It is also a precondition for science: To even begin to develop a theory of consciousness requires being already embedded in the richness of experience. But dealing with this has been difficult for the philosophies that guide science as it’s currently configured.
In many ways, experience landed in science’s blind spot by design. As the methodologies of modern science were being established from the 16th through the 19th centuries, a central goal was to set aside personal, or subjective, elements. What the early architects of the scientific method, such as Francis Bacon, sought to do was break down the elements of experience into aspects that remain unchanged from person to person, or what the philosopher Michel Bitbol calls the “structural invariants of experience.” Identifying these elements, which became the basis for making measurements, was the first step in our scientific interrogations of nature.
In this way, over time, scientists began to imagine a perspective-less perspective, a supposed God’s-eye view of the universe — free of any human bias. The philosopher Thomas Nagel calls this the “view from nowhere.” And this philosophical position eventually became synonymous with mainstream science itself. The development of the thermometer, and from it the science of thermodynamics, offers a notable example of our scientific culture’s blind spot. In it, we can see how those unchanging elements of experience are extracted and then, in time, misconstrued as a false perspective-less perspective.
The embodied feeling of being hot or cold is a basic example of direct experience. But developing a measurable scale of this experience for future scientific inquiry took centuries of work. Much of this story played out in what we now call laboratories, where those elements of experience could be isolated and probed. First, hot and cold needed to become correlated with something like the level of alcohol or mercury in a graduated tube. This was the invention of thermometry. Once a way to measure degrees was established, those degrees could then be used to investigate other focal points of experience, like the boiling point of water. A mathematically formulated theory of thermodynamics was then slowly developed, describing the relationship between temperature and heat flow.
The author says the thermometer “offers a notable example of our scientific culture’s blind spot”. It shows how unchanging elements of experience “are extracted and then, in time, misconstrued”. The final paragraph traces that process from felt hot and cold, to a measured scale, to an abstract theory.
A: the passage never says the inventors consciously applied Bacon. B: the author contrasts the two ideas rather than reconciling them. C: “most important” is never claimed; hot and cold are only a “basic example”.
Bacon and others “sought to … break down the elements of experience into aspects that remain unchanged from person to person”. These were the structural invariants that became the basis for measurement.
A: they set aside subjective elements; they did not throw out all experience. B: the God’s-eye view is something scientists came to imagine “over time”; it was not the founders’ stated aim. D: nothing says the feeling of hot and cold was unreliable; it was the starting point for thermometry.
The paragraph moves in three steps. First comes the felt experience of hot and cold. That feeling is then correlated with the level of alcohol or mercury in a tube, which gives thermometry. Finally, measured degrees lead to a mathematically formulated theory of thermodynamics.
A: there is no “subjective theory” at the start, and nothing is “proven” universal. C: the paragraph doesn’t begin with a false position or call thermodynamics flawed. D: it reverses the direction, since experience is turned into measurement, not the other way round.
- A scientific ideal that seeks to eliminate personal bias and perspective.
- A philosophical stance that imagines a God-like, perspective-less observation point.
- A principle introduced by Francis Bacon to explain the structure of experience.
The view from nowhere is described as “a perspective-less perspective, a supposed God’s-eye view of the universe — free of any human bias”, and a “philosophical position” that became synonymous with mainstream science. That covers both 1 (an ideal free of bias) and 2 (a God-like, perspective-less stance).
Statement 3 is wrong: the term is Thomas Nagel’s, not Bacon’s. Bacon is linked to breaking experience into invariants, a phrase the passage attributes to Michel Bitbol.
A captures both parts of the passage. SETI keeps searching despite decades of failure, and that perseverance echoes religious beliefs in superior, benevolent beings from the heavens.
B overstates: failure gives “more reason to doubt”; it doesn’t prove there is no alien life. C narrows the passage to the two examples and drops the main point about persisting despite failure. D is neutral and positive, missing the author’s critical “metaphysical superstition” angle.
“This structure” needs a structure as its antecedent. That is the cosmic web, named just before blank 3. The sentence explains when it began forming (the Big Bang), and the next sentence, “It’s still evolving today”, carries the same story forward to the present.
At blank 1 the only antecedent is the Milky Way disk, and a Big Bang origin story would interrupt the zooming-out sequence. At blank 2 the new arrangement hasn’t yet been described as a structure. At blank 4, going back to its origin after “still evolving today” reverses the timeline.
- Consider the relentless choice in online shopping, for example.
- If you don’t have a ‘trusted brand’ in mind to whittle down the literally thousands of options, where should you start?
- If we’re maximizers, we settle for nothing less than the best possible option.
- Is this particular stitching important, or do you prefer that kind of belt loop?
- Say you’re browsing for a new pair of jeans.
The coherent paragraph is 1 → 5 → 2 → 4:
- 1: “Consider … online shopping, for example” opens the illustration.
- 5: “Say you’re browsing for a new pair of jeans” narrows to a specific case.
- 2: Without a trusted brand, where do you start among thousands of options?
- 4: The questions get finer (stitching, belt loops), showing how relentless the choice is.
Sentence 3 introduces a new concept, “maximizers”, with the first-person “we”. The other four stay inside a second-person shopping scenario, and none of them sets up or uses this term.
The passage says exciting events can destabilise people at risk of mania. It still wants them to enjoy those events, while monitoring mood and keeping support, medication, sleep and a doctor in reach. D keeps both halves.
A is addressed to everyone (“people”) and drops mania entirely. B says “avoid” such events, which contradicts “By all means, we want people to experience and enjoy these events”. C sets medication against engagement, but the passage encourages both.
- It’s so prevalent that society has coined a term for mindlessly scrolling past post after post of depressing content: doomscrolling.
- Though social media has long been the bearer of bad news, many people have taken to creating under the hashtag ‘Hopecore’.
- Teenagers between thirteen and eighteen spend an average of eight and a half hours online daily, with the potential to be exposed to the worst kinds of content.
- Teenagers now inhabit echo chambers of doubt and uncertainty, doomscrolling away, and this is a large part of what’s causing us to be increasingly nihilistic.
- In the midst of a technological revolution, our minds are flooded by an abundance of negative stimuli.
The coherent paragraph is 5 → 3 → 1 → 4:
- 5: Our minds are flooded with negative stimuli.
- 3: Teenagers spend 8.5 hours online daily, exposed to the worst content.
- 1: “It’s so prevalent” that it now has a name: doomscrolling.
- 4: Teenagers are “doomscrolling away”, which feeds nihilism.
Sentence 2 turns to a positive counter-trend (“Hopecore”). The other four build a single negative argument about doomscrolling, so it doesn’t belong.
The paragraph lists the author’s selection criteria. After “I’ve focused on toys that will help encourage a baby’s development”, the sentence adds a second category with “I’ve also selected practical products”. Then “I also spoke to parenting experts” moves on to the research method.
Blank 1 comes before the list is introduced (“Compiling this list”). At blank 2 it would split the description of the toys. At blank 4 it would separate “Based on this” from the expert insight it refers to.
DILR · Data Interpretation & Logical Reasoning
The students of an institute enrolled in three different courses: Machine learning, Blockchain and Digital marketing. A student is enrolled in none, one or multiple certifications. The information below is known.
- The number of students enrolled in only machine learning is 3/4th of the number of students enrolled in only digital marketing.
- The number of students enrolled in only blockchain is 40% more than the number of students enrolled in blockchain and machine learning, but not in digital marketing.
- The number of students enrolled in all three courses is twice the number of students enrolled in blockchain and digital marketing, but not in machine learning.
- The number of students who enrolled in both digital marketing and machine learning is 20% more than the number of students enrolled in only machine learning.
- The number of students enrolled in only machine learning is three times the number of students enrolled in blockchain and machine learning, but not in digital marketing.
- The number of students who enrolled in both digital marketing and blockchain is the average of the number of students enrolled only in digital marketing and only in blockchain.
- 21 students did not enroll in any of the certifications.
- 1/4th of the total students enrolled in only digital marketing.
- Base variable. Let ML ∩ BC only (not DM) = x. Then only ML = 3x, only BC = 1.4x and only DM = 3x ÷ ¾ = 4x.
- DM ∩ BC. Its total is the average of only DM and only BC = (4x + 1.4x)/2 = 2.7x. With all three = 2 × (BC ∩ DM only), BC ∩ DM only = 0.9x and all three = 1.8x.
- DM ∩ ML. Its total = 1.2 × 3x = 3.6x, so DM ∩ ML only = 3.6x − 1.8x = 1.8x.
- Total. Enrolled = 3x + 4x + 1.4x + x + 0.9x + 1.8x + 1.8x = 13.9x. Only DM is ¼ of the total: 4 × 4x = 13.9x + 21, so 2.1x = 21 and x = 10.
| Region | Students |
|---|---|
| Only Machine learning | 30 |
| Only Blockchain | 14 |
| Only Digital marketing | 40 |
| ML & BC only | 10 |
| BC & DM only | 9 |
| DM & ML only | 18 |
| All three | 18 |
| None | 21 |
| Total | 160 |
Total students = 139 + 21 = 160.
From the table in Q11, only blockchain = 1.4 × 10 = 14.
From the table in Q11, digital marketing = only DM + BC & DM only + DM & ML only + all three = 40 + 9 + 18 + 18 = 85.
From the table in Q11, ML ∩ BC = ML & BC only + all three = 10 + 18 = 28.
From the table in Q11, exactly two = 10 + 9 + 18 = 37, plus all three = 18. Total = 55.
“At most two” means 0, 1 or 2 certifications, which is everyone except those in all three. From the table in Q11: 160 − 18 = 142.
(Leaving out the 21 students with no certification would give 121, option D. “At most two” includes zero, though.)
Eight students of a class lived in eight different houses on a street numbered from 1-8 from right to left. The roll number of each of these students is different and is the square of the house number in which some other student lives. The roll number of Bina is a multiple of 3, and she lives in an even-numbered house immediately left of the person whose roll number is 16. The person whose roll number is the square of the house number in which Renu lives, lives in the leftmost house. Neeraj lives immediately left of Ishani, and both have a roll number which is a multiple of 4 but not 9. The roll number of Ishani is higher than the roll number of Neeraj. The roll number of Jinu is the square of the house number in which Ishani lives. Three people live between Renu and the person whose roll number is 16. Uday lives to the right of Geeta but to the left of Anuj. The difference between the roll number of the person living in the leftmost house and the person living in the 4th house is 24.
- Setup. House 1 is the rightmost and house 8 the leftmost. Roll numbers are 1, 4, 9, …, 64, and nobody’s roll number is the square of their own house number.
- House 8 and house 4. Squares differing by 24 are (49, 25) and (25, 1), so house 8 holds 49, 25 or 1. House 8’s roll number is Renu’s house squared, so Renu is in house 7, 5 or 1.
- Bina and the 16-holder. Bina is in an even house h with roll number 16 at h − 1. Renu is 4 houses from the 16-holder. That leaves three cases: (16 at 1, Bina 2, Renu 5), (16 at 3, Bina 4, Renu 7) or (16 at 5, Bina 6, Renu 1).
- Case 16 at 3. House 8 = 49, so house 4 = 25. But Bina is in house 4 and her roll number is a multiple of 3 ✗.
- Case 16 at 5. House 8 = 1 and house 4 = 25. No placement of Neeraj and Ishani (rolls from 4, 16, 64) works ✗.
- Case 16 at 1. House 8 = 25. Neeraj and Ishani must take 4 and 64, so Ishani = 64 and Neeraj = 4. The only valid pair of houses is Ishani 6, Neeraj 7. Then Jinu = 36 and must be in house 3, so Bina = 9. Anuj < Uday < Geeta fills houses 1, 4 and 8. The leftover rolls 1 and 49 go to Renu (house 5) and Uday (house 4), in either order ✓.
| House | Student | Roll no. |
|---|---|---|
| 8 (leftmost) | Geeta | 25 |
| 7 | Neeraj | 4 |
| 6 | Ishani | 64 |
| 5 | Renu | 1 or 49 |
| 4 | Uday | 49 or 1 |
| 3 | Jinu | 36 |
| 2 | Bina | 9 |
| 1 (rightmost) | Anuj | 16 |
All roll numbers except Renu’s and Uday’s are fixed, so 6 students can be identified.
From the table in Q17, Anuj lives in house 1 with roll number 16.
- A: Bina (9 = 3²) and Anuj (16 = 4²) are one pair. The second pair is Ishani–Renu (64, 49) or Uday–Jinu (49, 36), depending on the case. Two pairs either way ✓
- B: Houses 4 and 5 hold 1 and 49, sum 50 ✓
- C: Geeta = 25, odd ✓
- D: Jinu is in house 3 (odd), but her roll number is 36 (even) ✗, so this is false.
The lowest two roll numbers are 1 and 4. Roll number 4 is Neeraj in house 7. For two houses to lie between them, roll number 1 must be in house 4 (houses 5 and 6 between). House 4 is Uday’s, so Uday’s roll number is 1.
QA · Quantitative Ability
10a + 7b = 750, 3a + 4c = 360 and 5b + 4c = 490. Subtracting the second from the third: 5b − 3a = 130.
From the first, a = (750 − 7b)/10. Substituting: 50b − 3(750 − 7b) = 1300, so 71b = 3550 and b = 50.
10 articles of B = Rs. 500.
Each remainder is 2 less than its divisor, so N + 2 is divisible by 7 × 11 × 13 = 1001. Hence N = 1001k − 2.
The largest 4-digit value is at k = 9: N = 9007. Digit sum = 9 + 0 + 0 + 7 = 16.
Let N be the number of steps, e the escalator speed and p Paul’s speed. Going up: N = 20 + 20e/p. Going down: N = 60 − 60e/p.
Equating: 80e/p = 40, so e/p = ½ and N = 30.
Qadir walks 24 steps, so the escalator covers 6, and his time = 6/e. Ritesh walks 10, so the escalator covers 20, and his time = 20/e. Ratio = 6 : 20 = 3 : 10.
In a parallelogram, d12 + d22 = 2(a2 + b2), so 576 + 256 = 2(144 + b2).
416 = 144 + b2, so b2 = 272 and b = √272 cm (= 4√17 ≈ 16.5 cm).
Let boys = ak and girls = 4k. Then 25(4k + 18) = 19ak, so k(19a − 100) = 450.
19a − 100 must be a positive divisor of 450 (a ≥ 6). Checking a = 6, 7, 8, … gives 14, 33, 52, 71, 90, … and only 90 (a = 10) divides 450, so k = 5.
Boys = 50 and girls = 20; after 18 join, 38 : 50 = 19 : 25 ✓. n = 70.
[log2 1] + [log2 2] + [log2 3] + [log2 4] + … + [log2 255]
[log2 n] = k for the 2k numbers from 2k to 2k+1 − 1. Since 255 = 28 − 1, every block k = 0 to 7 is complete.
Sum = Σ k·2k (k = 0 to 7) = 0 + 2 + 8 + 24 + 64 + 160 + 384 + 896 = 1538.
Let Q’s initial share be q, so P = 1.2q. After a year, P = 1.2q × 4/3 = 1.6q and Q = 1.2q. R then equals Q = 1.2q.
The shares still total 100%: 1.6q + 1.2q + 1.2q = 4q = 100, so q = 25. Initially P = 30% and Q = 25%, so R = 100 − 55 = 45%.
Side lengths: a = BC = √(362 + 152) = 39, b = CA = 56, c = AB = √(202 + 152) = 25. Perimeter = 120.
x = (39 × 10 + 56 × (−10) + 25 × (−46))/120 = −1320/120 = −11.
y = (39 × 5 + 56 × (−10) + 25 × 5)/120 = −240/120 = −2.
Incenter = (−11, −2).
The set has 8 elements, so it has 28 = 256 subsets. The non-primes are 4, 6, 8 and 9, giving 24 = 16 subsets with no prime (including the empty set).
Subsets with at least one prime = 256 − 16 = 240.
S7 = 7(a + 3d) and S11 = 11(a + 5d). So 7(a + 3d)/[11(a + 5d)] = 6/11, which gives 7a + 21d = 6a + 30d, i.e. a = 9d.
T7 = a + 6d = 15d. For 130 < 15d < 140 with d a natural number, d = 9 (T7 = 135). Common difference = 9.
Correct: 0 · Wrong: 0 · Accuracy: 0%
Keep the streak alive. See you tomorrow for Day 32.
