CAT 50 Day Streak – Day 9
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
Sheilah Miller is a 39-year-old Black woman who was admitted to the hospital to give birth to her child. But there were complications. Hours later, she had lost a lot of blood and suffered a debilitating stroke. Her physician, Dr Smith, a white man, repeatedly ignored her complaints of pain and discomfort due to his prejudice against her identity. The baby lived, but Ms Miller was paralysed from the neck down. As a patient, she had knowledge to share about her pain, her discomfort, her suffering. But, for more than 10 hours, Dr Smith refused to consider her knowledge due to his bigotry. Ms Miller suffered enormously as a result of Dr Smith’s medical malpractice. She was harmed financially with medical expenses from her hospitalisation, and lost wages due to time away from work. Her physical harm, paralysis, is obvious, and her emotional harm may manifest itself as anxiety or depression. But there is another kind of harm she suffered: epistemic. Epistemic harm, while real, is not widely known.
The term ‘epistemic’ is derived from the Ancient Greek word episteme, meaning knowledge. Knowledge, and especially seeking and giving knowledge, is essential to being human. As profoundly social creatures, humans are givers of knowledge, but according to the philosopher Miranda Fricker in her groundbreaking book Epistemic Injustice, epistemic harm prevents, denies and rejects that. If our ability to give knowledge is rejected, then so is our humanness and our dignity. To be harmed epistemically is to be humiliated and degraded as a human being; it is to be treated not as a someone but as a something. People don’t need to listen to things or regard them with respect or credibility. Suppose, for example, that we deny someone the right to be heard or the right to explain their position on an important issue based on a prejudice that we have regarding the social group that the person belongs to. By denying them that right, we would have, in effect, denied them an essential part of their own humanity. After all, other things being equal, human beings possess rationality and autonomy, and these characteristics are constitutive of what it means to be a human being.
Thus, an injustice of this kind cuts deeply since it affects the very core of what it means to be a human being. A victim of epistemic harm is not regarded as a rational human being but as an infant or an animal, or a piece of furniture. A great injustice of the United States’ legal system is that it will allow Ms Miller to be compensated for her financial, physical and emotional harm, but not her epistemic harm. Ms Miller suffered serious epistemic harm and yet cannot be compensated for it, even though the other harms flowed from her original epistemic harm. Her attempt to give her knowledge was rejected and ignored for 10 hours. Imagine how frustrated and scared she must have felt – hours of pleading and yet being ignored by Dr Smith as one unworthy of care or credibility.
Epistemic harm, as the passage defines it, is having your knowledge rejected because of prejudice against your social group. In B, the employee offers knowledge (a safety warning), it is dismissed because of their gender, and further harm follows, just as in Ms Miller’s case.
A is an accident with no testimony and no prejudice involved. C is carelessness, not identity-based rejection of someone’s knowledge. D is deception of a consumer, not a refusal to hear someone.
The author argues that Ms Miller’s other harms “flowed from her original epistemic harm”. Evidence that epistemic harm generally comes first and makes other harms worse gives that claim general support, which strengthens the case for compensating it.
B gives doctors a reason to discount testimony, which weakens the claim. C says the existing categories are enough, which also weakens it. D questions whether epistemic harm is even a separate category.
The passage says the harm came from Dr Smith’s prejudice and bigotry, which made him ignore her knowledge of her own pain. Blaming her “lack of medical knowledge” contradicts this, so D cannot be inferred.
A follows from the law compensating financial, physical and emotional harm but not epistemic harm. B fits the claim that epistemic harm, though real, is “not widely known” and goes uncompensated. C follows from the author calling its non-recognition “a great injustice”.
The harm in the passage is a doctor rejecting a patient’s testimony because of prejudice about her identity. Training doctors to weigh patient testimony fairly, regardless of identity, goes straight at that cause.
A bypasses the patient’s voice rather than restoring it. B deals with negligence after the event. D sends knowledge from doctor to patient, the opposite direction to the problem.
The passage says logic is the “sturdy backbone” of science and technology but has “a fundamental problem”: it defines truth through abstract categories that words refer to, so it fails to capture the intuition that consequence should depend on the content of propositions. B states exactly this.
A says the foundations “continue to effectively” work, which contradicts the “fundamental problem”. C says modern logic succeeds, the opposite of Prawitz’s point. D misstates Prawitz, who showed that logic fails to capture the content-based intuition.
- His unique blend of humour and creativity has attracted a substantial following on various social media platforms.
- Moffitt began his career by experimenting with different types of content and quickly found success in the niche of interactive video games.
- Logan Moffitt, a 23-year-old content creator from Canada, has gained widespread recognition for his innovative approach to digital storytelling.
- As a result, he has become one of the most influential figures in the online content creation community.
The order runs like this:
- 3: Introduces Logan Moffitt by full name and gives the topic, his recognition.
- 2: “Moffitt began his career…”, the start of his story, uses the surname only.
- 1: “His unique blend of humour and creativity” attracted a large following.
- 4: “As a result”, he became one of the most influential figures, which concludes the paragraph.
The phrase “not only contaminated our rivers” assumes that river pollution has just been mentioned. That happens only in the last sentence (“…and pollute rivers…”). The missing sentence then extends the damage from rivers to the oceans, so it belongs at blank 4.
At blanks 1–3 the paragraph is still discussing the meaning of economics and our drift from nature. Rivers have not yet come up.
- During the first half of 2022, a mere 2% of international trade contracts were denominated or settled in renminbi, pale in comparison to the US dollar's dominance of around 75% of global trade contracts and settlements.
- The Chinese renminbi faces several hurdles in becoming a global reserve currency.
- Also, China's communist government would need to loosen its tight control to allow the open and flexible financial markets necessary to support a currency's reserve status.
- While 70 central banks hold the renminbi in their reserves, it is only the fifth-most held currency globally.
The order runs like this:
- 2: Thesis: the renminbi faces several hurdles to becoming a reserve currency.
- 4: First hurdle: only the fifth-most held currency despite 70 central banks holding it.
- 1: Supporting data: just 2% of trade contracts against the dollar’s 75%.
- 3: “Also” adds a final hurdle, the government’s tight control of financial markets.
The sentence after blank 3 says “Further, it is also held, as a general opinion sometimes derived from the Orientalists…”. Both “also” and “the Orientalists” assume the Orientalists were already linked to an earlier view. The missing sentence gives that link: Orientalists documented classical Indian thought as “systems” (darshanas), which feeds the “unified body of knowledge” view in the previous sentence. So it belongs at blank 3.
Blanks 1 and 2 would break the link between “the commonsense view… is distorted” and “This general distorted understanding”. At blank 4, the Orientalists would be introduced after they had already been referred to as “the Orientalists”.
- When they perceive early signs of winter approaching, these squirrels gain weight and build long burrows in the ground where they courageously descend sometime in October, not to see light again until the following March, at least.
- Remarkably, the body temperature of these animals during hibernation can fall to sub-zero values, and heartbeats and respiration decrease to a tiny fraction of their normal rates.
- The thirteen-lined ground squirrel is one typical example of a seasonal hibernator.
- Not surprisingly, then, hibernation has been described as a state between life and death.
- From clinical applications to space travel, scientists, entrepreneurs, governmental agencies, and even writers and artists turn to hibernation as a possible solution for our problems.
The coherent paragraph is 3 → 1 → 2 → 4:
- 3: Introduces the thirteen-lined ground squirrel as a hibernator.
- 1: “These squirrels” prepare and descend into burrows for the winter.
- 2: “Remarkably”, body temperature, heartbeat and breathing drop sharply.
- 4: “Not surprisingly, then”, hibernation is called a state between life and death.
Sentence 5 moves to human uses of hibernation (medicine, space travel). That is a different topic from the biology of how the squirrel hibernates.
DILR · Data Interpretation & Logical Reasoning
Yash had a trip to Goa, Manali, Agra, Shimla, Delhi, Pune and Jaipur one after another, not necessarily in the given order. He started his trip from one of the given cities. To reach from one city to another city, the modes of transport used were bus, train, aeroplane, truck, ship and car.
- (i) Yash visited Shimla before visiting Delhi and after visiting Pune.
- (ii) He travelled to Goa by truck.
- (iii) He travelled from Agra to the next city by bus.
- (iv) He travelled from Delhi to Jaipur by car.
- (v) He travelled from Manali to the next city by aeroplane.
- (vi) Manali and Agra are not the first cities, and Jaipur is not the last city visited by Yash.
- (vii) He did not travel to Manali by train.
- (viii) He travelled by train before travelling by aeroplane and after travelling by ship.
- (ix) He visited at most one city after visiting Jaipur.
- Jaipur and Delhi. At most one city comes after Jaipur (ix), and Jaipur isn’t last (vi), so Jaipur is 6th. Delhi → Jaipur is a direct car journey (iv), so Delhi is 5th and leg 5 is by car.
- Last city. It can’t be Jaipur, Delhi, Manali (he flies onward from it) or Agra (he takes a bus onward from it). Pune and Shimla both come before Delhi. So Goa is 7th, reached by truck (leg 6).
- First city. Manali and Agra aren’t first, and Shimla comes after Pune, so Pune is 1st.
- Positions 2–4 are Shimla, Agra and Manali. Legs 1–4 use bus, train, aeroplane and ship, with ship → train → aeroplane in that order (viii). So the aeroplane leg (out of Manali) is leg 3 or 4.
- Manali 3rd: ship and train are legs 1 and 2, so he reached Manali by train ✗ (vii).
- Manali 4th, Agra 2nd: bus is leg 2, so ship is leg 1 and train is leg 3, and he again reached Manali by train ✗.
- Manali 4th, Agra 3rd: bus is leg 3, ship leg 1, train leg 2 ✓.
| Order | City | Mode to next city |
|---|---|---|
| 1 | Pune | Ship |
| 2 | Shimla | Train |
| 3 | Agra | Bus |
| 4 | Manali | Aeroplane |
| 5 | Delhi | Car |
| 6 | Jaipur | Truck |
| 7 | Goa | – |
The first city is Pune and the last is Goa: Pune, Goa.
From the table in Q11, Shimla (2nd) → Agra (3rd) is leg 2, which is by train.
Agra is 3rd and Delhi is 5th, so only Manali (4th) lies between them: 1 city.
- A: The city after Pune was Shimla ✗
- B: He reached Delhi from Manali by aeroplane ✗
- C: Shimla was the 2nd city ✗
- D: Agra → Manali (leg 3) was by bus ✓
8 students appeared in an examination and scored marks as given below:
| Amar | Udit | Diya | Isha | Tanvi | Om | Ravi | Seema |
|---|---|---|---|---|---|---|---|
| 59 | 78 | 55 | 34 | 73 | 38 | 87 | 47 |
After the exam, some of them approached the teacher and asked for a re-evaluation. The teacher re-evaluated their papers, and the scores of all students who approached the teacher for re-evaluation increased after the re-evaluation. The following facts are known:
- The scores of no two students were the same.
- The rank of any student after the re-evaluation was not the same as before.
- The total increase in the marks of the students was not more than 50.
Original ranking:
| Rank | Student | Score |
|---|---|---|
| 1 | Ravi | 87 |
| 2 | Udit | 78 |
| 3 | Tanvi | 73 |
| 4 | Amar | 59 |
| 5 | Diya | 55 |
| 6 | Seema | 47 |
| 7 | Om | 38 |
| 8 | Isha | 34 |
- Students who don’t approach keep their marks, so their rank changes only if someone from below overtakes them.
- Isha is last and can’t fall further, so she must rise, which means she must approach.
- Ravi must lose 1st place, so someone must reach at least 88.
If Isha were the only one, she would need 34 → 88 (+54), which is more than 50. With two it works, e.g. Tanvi 73 → 88 and Isha 34 → 60 (total 41). So at least 2 students approached.
One of the two is Isha. She can’t reach 88 within 50, so the other student (Y) must pass Ravi (score ≥ 88). Isha must then pass every non-approacher who was ranked below Y.
| Y | Y → 88 | Isha must pass | Isha’s increase | Total |
|---|---|---|---|---|
| Udit | +10 | Tanvi (73) | +40 | 50 |
| Tanvi | +15 | Amar (59) | +26 | 41 |
| Amar | +29 | Diya (55) | +22 | 51 ✗ |
| Diya | +33 | Seema (47) | +14 | 47 |
| Seema | +41 | Om (38) | +5 | 46 |
| Om | +50 | Seema (47) | +14 | 64 ✗ |
The minimum is Tanvi → 88 and Isha → 60: total increase 41.
Detailed solution coming soon.
Detailed solution coming soon.
The cheapest way to change every rank is to split the ranking into blocks and lift the lowest student in each block just above the top of that block:
- Ravi, Udit, Tanvi: Tanvi 73 → 88 (+15, 20.55%)
- Amar, Diya, Seema: Seema 47 → 60 (+13, 27.66%)
- Om, Isha: Isha 34 → 39 (+5, 14.71%)
New order: Tanvi, Ravi, Udit, Seema, Amar, Diya, Isha, Om. Every rank changes. The highest percentage increase is Seema’s: 13/47 = 27.66%.
All 8 can approach while staying within 50 marks. Example:
- Ravi 87 → 88 (+1), Udit 78 → 79 (+1), Tanvi 73 → 89 (+16)
- Amar 59 → 60 (+1), Diya 55 → 56 (+1), Seema 47 → 61 (+14)
- Om 38 → 39 (+1), Isha 34 → 40 (+6)
Total = 41 ≤ 50, there are no ties, and the new order (Tanvi, Ravi, Udit, Seema, Amar, Diya, Isha, Om) changes every rank. So at most 8 students.
QA · Quantitative Ability
Let the total be T. “One-k-th of the others” means a share of T/(k + 1):
Parvez = T/2, Qadir = T/4, Rashid = T/6, Sarfaraz = T/12 (these add up to T ✓).
Smallest + largest = T/12 + T/2 = 7T/12 = 1750, so T = 3000.
Rashid = 3000/6 = ₹ 500.
Let y = (√3)x. Then 3x = y2 and (√3)x + 4 = 9y.
y2 − 9y + 20 = 0, so y = 4 or y = 5 (both positive, so both are valid).
3x/2 = 4 gives x = 2 log3 4, and 3x/2 = 5 gives x = 2 log3 5.
Sum = 2(log3 4 + log3 5) = 2 log3 20.
The product has 9 terms. The term with n threes = 3 × (111…1 with n ones), which gives 39 from the nine 3s.
A repunit 11…1 (n ones) is divisible by 3 only when its digit sum n is a multiple of 3:
- 111 = 3 × 37 → one factor of 3
- 111111 = 3 × 37037 (digit sum 20, not divisible by 3) → one factor of 3
- 111111111 = 9 × 12345679 (digit sum 37, not divisible by 3) → two factors of 3
Highest power = 9 + 1 + 1 + 2 = 13.
Let the cost price be ₹100 per kg, so the usual selling price is ₹120 per kg.
The customer pays for 1 kg at a 20% discount: 0.8 × 120 = ₹96. The shopkeeper actually hands over 900 g, which cost him ₹90.
Profit % = (96 − 90)/90 × 100 = 6.67%.
The shorter leg is √(252 − 242) = 7. The inradius is r = (7 + 24 − 25)/2 = 3.
At the corner between the hypotenuse and the 7 cm leg, the angle θ has cos θ = 7/25. So sin(θ/2) = √((1 − 7/25)/2) = 3/5.
Both centres lie on the angle bisector. The incentre is r / sin(θ/2) = 5 from the vertex, and the small centre (radius s) is 5s/3 from the vertex. External tangency gives 5 − 5s/3 = 3 + s, so 8s/3 = 2.
s = 0.75 cm.
When Rahul starts, Karan is 6 × 25 = 150 m ahead. Rahul gains at 10 − 6 = 4 m/s, so they first meet after 37.5 s, at 375 m from the start.
After that they meet every 1200/4 = 300 s. In that time Rahul runs 3000 m = 2.5 laps, so the meeting point moves by half a lap each time: 375 m, 975 m, 375 m, …
That gives 2 distinct points. Shortcut: speeds are in the ratio 3 : 5, and for the same direction the number of distinct points is 5 − 3 = 2.
Surface area: 2πr2 + 2πrh = 150π, so rh = 75 − r2.
Volume V = πr2h = πr(75 − r2) = π(75r − r3). Setting dV/dr = 75 − 3r2 = 0 gives r = 5, and then h = (75 − 25)/5 = 10.
h : r = 10 : 5 = 2 : 1.
a/(1 − r) = 22.5 and a(1 + r) = 20.
Dividing the second by the first: (1 − r)(1 + r) = 20/22.5 = 8/9, so r2 = 1/9. Since r is negative, r = −1/3.
a = 22.5 × (4/3) = 30, and the fifth term is ar4 = 30 × 1/81 = 10/27.
Triangle DBE is right-angled at E with ∠B = 60°. So BE = DE / tan 60° = 6√3 / √3 = 6.
x = BC = BE + EC = 6 + 8 = 14.
Water = 43.75% of 300 = 131.25 L and milk = 168.75 L (ratio 9 : 7).
Removing X litres leaves a fraction k = 1 − X/300 of each liquid. Then 3 L of water is added: milk = 168.75k and water = 131.25k + 3.
Milk : water = 5 : 4 gives 4 × 168.75k = 5(131.25k + 3), so 675k = 656.25k + 15 and k = 0.8.
X = 300 × 0.2 = 60 litres.
Correct: 0 · Wrong: 0 · Accuracy: 0%
Keep the streak alive. See you tomorrow for Day 10.
