CAT 50 Day Streak Day 29

Day 29 / 50

CAT 50 Day Streak – Day 29

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

What makes a successful popular science book? One could not find a better paradigm than Richard Dawkins’s 1976 best-selling classic The Selfish Gene. This book presented a quite widely, if not universally, accepted interpretation of the so-called “Modern Synthesis,” the set of ideas that has constituted much evolutionary thinking since the mid-20th century. Because the theoretical science that drove the Modern Synthesis was population genetics, the mathematical study of the evolutionary trajectories of genes, it was natural to think of evolution as a theory about genes, and Dawkins took this view to a somewhat extreme conclusion, painting evolution as genes striving to replicate themselves—a.k.a. the gene’s-eye perspective. Individual genes were seen as competing with one another to have the most positive effects on the organisms in which they resided, and thus to become more prevalent in the next generation.

This was an intriguing vision, and Dawkins presented and developed it in elegant and engaging prose, showing an exceptional talent for providing illuminating metaphors and vivid examples. The outcome was a spectacular success: over 48 years and a million copies later, Amazon tells me that it is currently the number three bestseller on the topic of evolution. As Dawkins has often told us, a well-adapted idea will tend to be selected and become more prevalent. The Selfish Gene was as well-adapted as a book can be, and it has illustrated this principle, though by deliberate print reproduction rather than biological reproduction. In the subsequent half-century, Dawkins has written several books that pretty much tell the same story as his first, and they have also been met with great success.

Dawkins’s most recent book, this summer’s The Genetic Book of the Dead: A Darwinian Reverie, is the latest iteration of these ideas. Since individual books are already indefinitely reproducible, a new version requires a new hook—a novel mutation?—and in this case, he provides it through the idea that an organism’s genome is a kind of palimpsest, layers of which can be peeled away to reveal the history of the organism’s lineage through the adaptive challenges that the genes evolved to address. The gene’s-eye view, to put it another way, is backwards-looking. Though this is a pleasant enough conceit, it is in the end a fairly trivial permutation of the original vision from The Selfish Gene.

There are, of course, many new examples, and the illustrations by artist Jana Lenzová are a delightful enhancement. The book could serve well as an introduction to some basic evolutionary ideas such as the difference between homology and analogy. Each of these gets a chapter with many entertaining examples. There are also chapters explicitly reiterating the main messages of The Selfish Gene and The Extended Phenotype; the book is appropriately palimpsest-like. The major problem is that the adaptive landscape has changed substantially since the 1970s, and Dawkins has failed to evolve. Or perhaps more disturbingly, and anticipating some similar reservations about the other new book reviewed here, Sara Imari Walker’s Life as No One Knows It: The Physics of Life’s Emergence, the niche for a popular science book is mainly to provide a good story, even if it is a bit simplistic and occasionally economical with the science.

Q1MCQ
The primary purpose of the passage is to:
AHighlight how Dawkins’s The Selfish Gene revolutionized evolutionary theory through mathematical genetics.
BExplain why Dawkins’s gene-centred view of evolution continues to dominate contemporary biology.
CReview Dawkins’s latest book while suggesting that it reiterates ideas from his earlier works with limited novelty.
DContrast Dawkins’s The Selfish Gene with Sara Imari Walker’s Life as No One Knows It in terms of scientific rigour.
Solution Answer: C

The passage is a review of The Genetic Book of the Dead. It calls the book “the latest iteration of these ideas” and “a fairly trivial permutation of the original vision”. That is a review that finds limited novelty.

A: The Selfish Gene is background only, and the author credits population genetics, not Dawkins, with the mathematics. B: the author says the landscape “has changed substantially”, the opposite of continued dominance. D: Walker’s book is mentioned only in passing at the end.

Q2MCQ
The author’s attitude toward The Genetic Book of the Dead is best described as:
Ascathingly dismissive of its recycled content and poor examples.
Bqualifiedly positive, appreciating its presentation but critical of its scientific relevance.
Cbroadly neutral, viewing it as a competent introduction to basic evolutionary ideas.
Denthusiastic, seeing it as a necessary and brilliant mutation of Dawkins’s original thesis.
Solution Answer: B

The author praises the presentation: “many new examples”, “delightful” illustrations, and a good introduction to basic ideas. But the author faults its science: Dawkins “has failed to evolve” with the field. That mix is qualified praise.

A: the examples are called “entertaining”, not poor, and the tone isn’t scathing. C ignores the clear criticism. D contradicts “a fairly trivial permutation”.

Q3MCQ
Which of the following, if true, would most seriously weaken the author’s “major problem” with Dawkins?
AA recent poll of evolutionary geneticists reveals that the “gene’s-eye perspective” from the 1970s is still the undisputed, dominant model in the field.
BThe Genetic Book of the Dead receives overwhelmingly negative reviews from literary critics for its prose style.
CSara Imari Walker’s book, Life as No One Knows It, is proven to be based on simplistic and outdated physics.
DThe Genetic Book of the Dead becomes a number one bestseller, outselling The Selfish Gene.
Solution Answer: A

The “major problem” is that the field has moved on since the 1970s while Dawkins hasn’t. If the gene’s-eye view is still the undisputed dominant model, the field hasn’t moved on, and the criticism collapses.

B is about prose style, not science. C is about Walker, not Dawkins. D concerns sales, which says nothing about whether the science is outdated; it may even fit the author’s worry about popular books.

Q4MCQ
Which of the following book reviews would be most consistent with the author’s “disturbing” reservation in the final sentence?
A“A failure. The author’s narrative is compelling, but it glosses over the complex, modern science, which many readers will find disappointing.”
B“A dense, rigorous, and challenging read. It will likely only be read by specialists, as it makes no concessions to popular storytelling.”
C“This book’s narrative is convoluted and its science is impenetrable. It has, deservingly, failed to find an audience.”
D“This book is a runaway success, and it’s easy to see why. The author presents a grand, sweeping story of the cosmos that is easy to follow and deeply inspiring, despite its reliance on scientific theories that were largely superseded a decade ago.”
Solution Answer: D

The disturbing thought is that popular science succeeds by telling a good story even when the science is simplistic or dated. D describes exactly that: a runaway success with an easy, inspiring story built on superseded theories.

A calls the book a failure, but the worry is that such books succeed. B describes rigour with no storytelling, the opposite. C describes a book with neither a good story nor success.

Q5MCQ
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 Ghana was the first to become independent, but only in 1957.
Paragraph Most African leaders and scholars are also opposed to the universality of human rights because Africa had no adequate representation in 1948 when the UDHR was drafted, deliberated and subsequently adopted. ___(1)___. Africa was under-represented mainly because, except for Ethiopia, Liberia and South Africa, the whole of Sub-Saharan Africa was still under colonial rule. ___(2)___. For this reason, it is argued that human rights have no moral purchase in societies which “were not adequately represented in the meetings that defined them. ___(3)___. Consequently, it is said that these societies should not be bound by international human rights norms, since doing so amounts to subjugation to Western imperialism, the concept of which led to colonialism. ___(4)___. Furthermore, it is argued that the imposition of Western human rights values is an affront to the sovereignty of these new States because it negates the right of self-determination.
AOption 1
BOption 2
COption 3
DOption 4
Solution Answer: B (Option 2)

The sentence explains how late independence came: even the first state (Ghana) became free only in 1957, nine years after 1948. It belongs right after “the whole of Sub-Saharan Africa was still under colonial rule”, at blank 2.

At blank 1, colonial rule hasn’t been mentioned yet. Blanks 3 and 4 sit inside the moral and political argument that follows, where a historical date would interrupt the reasoning.

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.
  1. The theory typically assumes fixed factor endowments (like labor, capital, technology) and unchanging production functions.
  2. Countries often actively create new comparative advantages through investment in education, infrastructure, research and development, and industrial policy.
  3. This specialization, the theory argues, leads to a more efficient allocation of global resources and mutual gains from trade for all participating countries.
  4. However, economic development is inherently a dynamic process.
  5. One major criticism targets the static nature of comparative advantage.
Solution Answer: 3

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

  • 5: One major criticism is the theory’s static nature.
  • 1: The theory assumes fixed endowments and unchanging production functions.
  • 4: “However”, development is dynamic.
  • 2: Countries actively create new comparative advantages.

Sentence 3 states the theory’s claimed benefits, and “This specialization” has no antecedent here. It belongs to a paragraph explaining the theory, not one criticising it.

Q7TITA
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.
  1. The Himba tribe of Namibia, for instance, exhibits impressive skin repair, aided by natural ointments, a high-protein diet, and specific genetic traits.
  2. While the movie is fictional, real-life cases do exist where individuals exhibit rapid wound healing.
  3. Scientists attribute the Bajau’s ability to genetic adaptations that enhance skin elasticity and repair capabilities, despite their extensive time in water.
  4. Similarly, the Bajau community from Southeast Asia also displays remarkable healing properties.
Solution Answer: 2143

The order runs like this:

  • 2: The movie is fictional, but real-life cases exist.
  • 1: The Himba, “for instance”, are the first example.
  • 4: “Similarly”, the Bajau are the second example.
  • 3: Scientists explain “the Bajau’s ability”.
Q8MCQ
The passage given below is followed by four alternate summaries. Choose the option that best captures the essence of the passage.
Passage Water, in case you are not up to date on the science, is good for you. It helps to regulate your body temperature, lubricates and cushions your joints, and aids your digestive system in getting rid of waste. Not drinking enough can affect your mood and disrupt your physical and cognitive performance, but getting plenty of it might help you safely lose weight, by aiding appetite regulation and increasing your metabolic rate. There is even some evidence that glugging enough might help you perform better in exams – though, of course, there might be a correlation between the sort of people who tote their own water jugs and those who study hard. H2O, in short, is great. But does it matter where you get it?
AWater’s dietary importance is well-established, but the debate continues about whether drinking water from different sources affects health and performance.
BDrinking water is claimed to boost metabolism and mood, improve joint health and digestion, and directly enhance exam performance.
CAdequate hydration supports various physiological and mental processes, and there is definitive proof of water causing improved academic outcomes.
DWater is essential for bodily functions and cognitive performance, with potential benefits for weight loss and exam success, though the source of the water remains a question.
Solution Answer: D

D covers the bodily and cognitive benefits and keeps the hedges (“potential”) on weight loss and exams. It also ends on the passage’s open question about the source.

A invents an ongoing “debate”; the passage only raises the question. B says “directly enhance”, but the passage warns the exam link may be mere correlation. C says “definitive proof”, the opposite of the passage’s caution.

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.
  1. Their success, however, has been uneven due to challenges like ineffective implementation and resistance from landlords.
  2. Post-independence, measures included abolishing exploitative systems and redistributing surplus land to the landless.
  3. Land reforms in India were primarily initiated to address deep-rooted inequalities in land ownership and promote social justice.
  4. These reforms aimed to empower marginalized communities and foster a more inclusive agrarian economy.
Solution Answer: 3241

The order runs like this:

  • 3: Introduces land reforms in India and why they began.
  • 2: The post-independence measures.
  • 4: “These reforms” and their aims.
  • 1: “Their success, however,” has been uneven, which concludes the paragraph.
Q10TITA
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.
  1. Socio-economic factors also play a crucial role; access to high-quality green space is often inequitably distributed, and community engagement is paramount for the long-term success of urban greening initiatives.
  2. Ultimately, urban ecology calls for a holistic, adaptive management approach, where cities are viewed as living laboratories for exploring innovative ways to reconcile human development with ecological integrity.
  3. Habitat fragmentation remains a primary obstacle, alongside the introduction of invasive species that can outcompete native flora and fauna.
  4. However, the path to ecologically vibrant cities is fraught with challenges.
  5. Effective urban ecological design emphasizes connectivity, recognizing that isolated green patches offer limited benefits.
Solution Answer: 5

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

  • 4: The path “is fraught with challenges”.
  • 3: Habitat fragmentation and invasive species are the primary obstacles.
  • 1: Socio-economic factors “also” matter.
  • 2: “Ultimately”, a holistic approach is needed, which concludes the paragraph.

Sentence 5 describes a design principle, not a challenge. It fits a paragraph on what good urban design looks like, not this one about obstacles.

DILR · Data Interpretation & Logical Reasoning

Q11 – Q20 0/10
Set 1 · Q11 – Q15

MBA Karo is the best institute when it comes to MBA preparation for Indian MBA entrance exams. During the last week, it hosted the spectacular “Big Million Days” festival, offering its highly coveted NMAT course and mock tests at a discounted price. The prices of the course and mock tests, which were originally Rs. 8000 and Rs. 1500, respectively, were sold at Rs. 5000 and Rs. 1000, respectively.

The graph below shows the revenue during the seven days of the sale. All figures are in Rs. 1000.

Revenue (in Rs. 1000): Mon 70, Tue 105, Wed 90, Thu 116, Fri 66, Sat 82, Sun 73 REVENUE (IN RS. 1000) 140 120 100 80 60 40 20 0 70 105 90 116 66 82 73 MON TUE WED THU FRI SAT SUN

The table shows the difference between the number of courses and mock tests sold on each of the days. It is known that a total of 100 courses were sold during the week.

DayMonTueWedThuFriSatSun
Difference between Courses and Mocks sold103610627
Q11TITA
What is the total number of mock tests sold during this period?
Solution Answer: 102
  • Equations. With c courses and m mocks, revenue (in Rs. 1000) is R = 5c + m and |c − m| = d. If c > m, then c = (R + d)/6. If m > c, then c = (R − d)/6. Only integer values are valid.
  • Fixed days. Mon: c = 10, m = 20. Thu: c = 21, m = 11. Sat: c = 14, m = 12. Sun: c = 11, m = 18.
  • Two-option days. Tue: 18/15 or 17/20. Wed: 16/10 or 14/20. Fri: 12/6 or 10/16.
  • 100 courses. The fixed days give 56, so Tue + Wed + Fri = 44. Only 18 + 16 + 10 and 18 + 14 + 12 work. Tuesday is always 18.
  • Mocks. Total revenue = 602, and courses earn 100 × 5 = 500. So mocks earn 102, which is 102 mock tests (in either case).
DayRevenueDifferenceCoursesMocks
Mon70101020
Tue10531815
Wed90616 / 1410 / 20
Thu116102111
Fri66610 / 1216 / 6
Sat8221412
Sun7371118
Total602100102

(Wed and Fri go together: either Wed 16/10 with Fri 10/16, or Wed 14/20 with Fri 12/6.) Total mock tests = 102.

Q12TITA
What is the highest number of courses sold in a single day?
Solution Answer: 21

From the table in Q11, Thursday had the most courses sold: 21.

Q13MCQ
On how many days was the number of courses sold greater than the number of mock tests sold?
A3
B4
C5
DCannot be determined
Solution Answer: B

From the table in Q11, courses beat mocks on Tue, Thu and Sat in every case. The fourth day is Wed (16/10) in one case and Fri (12/6) in the other. Either way the answer is 4 days.

Q14MCQ
How many courses were sold on Tuesday?
A17
B18
C17 or 18
D19
Solution Answer: B

From Q11, Tue + Wed + Fri must total 44. With Tuesday = 17, the best possible is 17 + 16 + 12 = 45 or 17 + 16 + 10 = 43, and nothing gives 44. So Tuesday = 18.

Q15MCQ
If at least 10 mock tests were sold each day, what percent of revenue on Wednesday was from the sale of mock tests?
A11.11%
B16.67%
C20%
D22.22%
Solution Answer: A

The case with Friday 12/6 has only 6 mocks on Friday, so it is ruled out. That leaves Wednesday with 16 courses and 10 mocks.

Mock revenue = 10 × 1000 = Rs. 10,000 out of Rs. 90,000, which is 11.11%.

Set 2 · Q16 – Q20

The chief minister of a state has to select 5 ministers in his cabinet out of Jatin, Kunal, Laxman, Mukesh, Raj, Suraj, Tarak and Uday. The age (in years) of each of these ministers is different among 36, 38, 39, 45, 48, 54, 57 and 59 years. From the eight ministers, the CM has to select at least one minister who is in his thirties, at least one minister who is in his forties and at least two ministers who are in their fifties. The CM must ensure the following additional conditions are also met:

  • If Laxman is in the cabinet, Mukesh must not be in the cabinet.
  • Suraj, who is in his fifties, will be in the cabinet only if Mukesh is in the cabinet.
  • Raj is six years older than Laxman and if one of them is in the cabinet, the other must be in the cabinet.
  • Kunal, who is in his thirties, will be in the cabinet only if Uday is not in the cabinet.
  • Suraj is younger than Uday and Uday will be in the cabinet only if Jatin is in the cabinet.
  • Tarak is three years younger than Jatin.
  • If Raj is in the cabinet, Uday must be in the cabinet.
Q16TITA
In how many ways can the cabinet be selected?
Solution Answer: 2
  • Raj = Laxman + 6. The only age pairs 6 apart are (39, 45) and (48, 54).
  • Tarak = Jatin − 3. The pairs are (36, 39), (45, 48) and (54, 57).
  • Suraj < Uday. Suraj is in his fifties, so Uday is too.
  • Laxman = 39 fails. Then Raj = 45 and Jatin/Tarak must be 57/54. That leaves only 59 for both Suraj and Uday ✗.
  • So: Laxman 48 and Raj 54. Suraj and Uday get 57 and 59. Jatin/Tarak = 39/36. Kunal (thirties) = 38 and Mukesh = 45.
  • Laxman in: Raj, Uday and Jatin must be in. Mukesh is out, which forces Suraj out, and Kunal is out because Uday is in. The fifth member is Tarak: {Jatin, Laxman, Raj, Tarak, Uday} ✓.
  • Laxman out: Raj is out, so the only fifties left are Suraj and Uday, and both must be in. Then Mukesh and Jatin are in and Kunal is out: {Jatin, Mukesh, Suraj, Tarak, Uday} ✓.
MinisterAgeCabinet 1Cabinet 2
Tarak36✓✓
Kunal38✗✗
Jatin39✓✓
Mukesh45✗✓
Laxman48✓✗
Raj54✓✗
Suraj57✗✓
Uday59✓✓

The cabinet can be selected in 2 ways.

Q17MCQ
Who among the following will definitely be in the cabinet?
  1. Jatin
  2. Tarak
  3. Uday
AOnly I and II
BOnly I and III
COnly II and III
DAll of them
Solution Answer: D

From the table in Q16, Jatin, Tarak and Uday are in both possible cabinets, so all of them are definitely in.

Q18MCQ
What is Mukesh’s age?
A48 years
B45 years
C39 years
D38 years
Solution Answer: B

From the table in Q16, Mukesh is 45 years old.

Q19MCQ
Who among the following can never be in the cabinet?
AKunal
BLaxman
CSuraj
DTarak
Solution Answer: A

Uday is in both cabinets, and Kunal can join only if Uday is out. So Kunal can never be in the cabinet. Laxman and Suraj each appear in one cabinet, and Tarak is in both.

Q20MCQ
If the second-oldest person is in the cabinet, who among them cannot be in the cabinet?
AJatin
BMukesh
CRaj
DUday
Solution Answer: C

The second-oldest person is Suraj (57). Suraj is only in Cabinet 2, {Jatin, Mukesh, Suraj, Tarak, Uday}, so Raj cannot be in the cabinet.

QA · Quantitative Ability

Q21 – Q30 0/10
Q21TITA
If 2x = 5 and 5y = 64, find xx + 1 + yy + 6.
Solution Answer: 1

2xy = (2x)y = 5y = 64 = 26, so xy = 6 and y = 6/x.

yy + 6 = 6/x6/x + 6 = 11 + x.

Sum = xx + 1 + 1x + 1 = 1.

Q22MCQ
A circus tent is cylindrical up to a height of 4.2 m and conical above it. The common diameter of the base of the cylindrical and conical parts is 6 m. If the total height of the tent from the ground is 8.2 m, find the cost of canvas needed to make the tent at the rate of Rs 160 per m2.
A20214
B20865
C19875
D18456
Solution Answer: A

Radius = 3 m. The cone’s height is 8.2 − 4.2 = 4 m, so its slant height is √(9 + 16) = 5 m.

Canvas = cylinder’s curved surface + cone’s curved surface = 2π(3)(4.2) + π(3)(5) = 25.2π + 15π = 40.2π m2.

Cost = 40.2 × 227 × 160 ≈ 20,214.9, i.e. Rs. 20,214.

Q23TITA
Two runners run a race of 7 km on a circular track of length 500 m in the same direction. The ratio of the speeds of the two athletes is 2:5. If they run in the same direction, how many times do they meet in the entire race?
Solution Answer: 8

When the faster runner finishes 7000 m, the slower one has run 7000 × 2/5 = 2800 m.

The faster runner has gained 7000 − 2800 = 4200 m. They meet once for every 500 m gained: 4200/500 = 8.4, so they meet 8 times.

Q24MCQ
A bookstore owner sells three kinds of books: fiction, non-fiction, and biographies. On a particular day, the owner sold the following number of books: 80 fiction books, 100 non-fiction books, and 130 biographies. If none of the customers bought more than two books of each type, what is the minimum number of buyers who have visited the shop that day?
A55
B60
C65
D70
Solution Answer: C

Each buyer can take at most 2 biographies, so 130 biographies need at least 130/2 = 65 buyers.

65 buyers can also cover the 80 fiction and 100 non-fiction books (up to 130 of each). Minimum = 65.

Q25MCQ
If 28m – 20m2 – 8mn – n2 – 24 ≥ 25, find the product mn.
A49
B-49
C-35
D35
Solution Answer: B

Rearranging: 20m2 + 8mn + n2 − 28m + 49 ≤ 0.

This is (n + 4m)2 + (2m − 7)2 ≤ 0, so both squares must be 0: m = 3.5 and n = −14.

mn = 3.5 × (−14) = −49.

Q26MCQ
Bhanu, Jai, and Parv invested the money in the ratio 4:5:6 in a business at the beginning of the year, where Bhanu works as an active partner and receives 20% of the profit as a salary at the end of the year, and the remaining is distributed in their investment ratios. Find the total money earned by Bhanu if the difference between the money earned by Parv and that by Jai is Rs. 160000 at the end of the year.
ARs. 1200000
BRs. 1360000
CRs. 1150000
DRs. 1240000
Solution Answer: D

Let the profit be P. The distributed share is 0.8P, split 4:5:6. Parv − Jai = (1/15) × 0.8P = 1,60,000, so 0.8P = 24,00,000 and P = 30,00,000.

Bhanu = salary 0.2P + (4/15) × 0.8P = 6,00,000 + 6,40,000 = Rs. 12,40,000.

Q27MCQ
A four-digit number is such that the first digit is half the fourth digit. The second digit is equal to the third digit. Also, the number formed by the first and the second digit is half the number formed by the third and the fourth digit. What is the remainder when the number is divided by 23?
A1
B5
C7
D12
Solution Answer: C

Let the number be abbd with d = 2a. Then 2(10a + b) = 10b + d, so 20a + 2b = 10b + 2a, i.e. 18a = 8b, or 9a = 4b.

Since a and b are digits, a = 4, b = 9 and d = 8. The number is 4998.

4998 = 23 × 217 + 7, so the remainder is 7.

Q28TITA
Find the number of real values of ‘x’, for which log5 (log5 (log2 (x2 – 8x – 208))) = 0
Solution Answer: 2

Working outwards: log5(log2(…)) = 1, so log2(…) = 5, so x2 − 8x − 208 = 32.

x2 − 8x − 240 = 0 gives (x − 20)(x + 12) = 0, so x = 20 or −12. Both keep every log argument positive, so there are 2 values.

Q29MCQ
An elevator can carry a maximum load of 810 kg. It is carrying a group of people whose weights are all distinct integers (in kg). The lightest person weighs 48 kg and the heaviest person weighs 75 kg. If the median weight of the five heaviest people is 68 kg, what is the maximum possible number of people that can be in the group?
A12
B13
C14
D15
Solution Answer: C

To fit the most people, keep every weight as low as possible. The three heaviest are 75, 69 (the lowest possible above 68) and 68, totalling 212 kg.

Everyone else weighs at most 67, with distinct weights starting from 48. They have at most 810 − 212 = 598 kg between them.

48 + 49 + … + 58 (11 people) = 583 ≤ 598, but adding 59 gives 642 > 598. So the maximum is 11 + 3 = 14 people.

Q30MCQ
In the given figure, find y-x.
Two intersecting circles meeting at F and C. From external point A: tangent AB = x to the upper circle; secant A–C–F with AC = 3 and CF = 9; secant A–D–E through the lower circle with AD = 2 and DE = y
A10
B12
C9
D8
Solution Answer: A

C and F lie on both circles, so AC × AF = 3 × 12 = 36 is A’s power with respect to each circle.

Upper circle (tangent-secant): x2 = 36, so x = 6.

Lower circle (secant-secant): AD × AE = 36, so 2(2 + y) = 36 and y = 16.

y − x = 16 − 6 = 10.

Day 29 complete! 🔥
0 / 90

Correct: 0 · Wrong: 0 · Accuracy: 0%

Keep the streak alive. See you tomorrow for Day 30.

Get Question PDF And Video Solution on: MBA KARO WhatsApp Community