CAT 50 Day Streak – Day 22
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
Before he became a science fiction writer, Frank Herbert worked several odd jobs. In 1957, while earning a living as a journalist, Herbert travelled to the state of Oregon to write an article on how the state government was using poverty grasses to stabilize the sand dunes that stretched along the coastline. Impressed by the size and scope of the Pacific Northwest, whose natural landscape seemed to dwarf even the largest cities to which he had been, Herbert never finished the writing assignment. Instead, parts of his mind began working on what would become the most influential science fiction novel in the history of the genre.
Today, we know this novel as Dune. It was originally published in 1965 and serves as the foundation for Denis Villeneuve’s epic film, which was just released in cinemas around the world to both critical and commercial acclaim. It is set in a fictional and very distant future, one in which mankind has managed to colonize even the remotest corners of the galaxy. Its protagonist is Paul Atreides, the prepubescent heir to an ancient, aristocratic family that was granted stewardship of the desert planet Arrakis. Their job is to oversee the mining and export of a spacetime warping, life-extending drug known as spice melange, which can be found only on Arrakis.
When readers were first introduced to the world of Dune back in the 1960s, they quickly discovered that it was unlike any fictional universe they had yet come across. George Lucas was years away from writing the first draft of Star Wars. Science fiction was still in its infancy and usually appeared in the form of short stories that were published in pulp magazines like Amazing Stories. Generally, these stories were far more concerned with crafting a suspenseful plot or exploring an interesting idea about human nature than they were with establishing a living, breathing alternate reality. Herbert’s Dune accomplished the latter without losing sight of the former.
Of course, Herbert was not the first to try his hand at constructing such a reality. More than a decade before he published his magnum opus, the British linguist and fantasy writer J.R.R. Tolkien had already beaten him to it. Tolkien’s The Lord of the Rings trilogy expanded the borders of Middle-earth as they had been outlined in his earlier work, The Hobbit. But where Tolkien drew inspiration from English and Gaelic folklore, Herbert’s academic interests lay elsewhere. The source material he transformed into Dune was found not in myth but in history. Those familiar with Dune can pinpoint numerous connections between Herbert’s imagination and the real world that stimulated it. Since the story takes place in a future version of our actual universe, it only makes sense that the societies portrayed in Dune should bear traces of their present-day counterparts. In Dune, the planets colonized by humanity are organized into a feudal system called the Landsraad — a word borrowed from Danish meaning “land council.” Herbert’s choice to use a foreign term as opposed to an English one hints at the possibility that the book’s galactic empire is Scandinavian in origin, or at the very least based on European feudalism.
Herbert went to report on dune-stabilising grasses, never finished the article, and “instead” began working mentally on what became Dune. The trip turned a narrow assignment into a much larger creative idea.
A: he didn’t abandon journalism because of failure; he was inspired. C: the passage never says it was his first visit. D: the trip was a journalism assignment, not novel research.
“Where Tolkien drew inspiration from English and Gaelic folklore, Herbert’s academic interests lay elsewhere … not in myth but in history.” The difference is the source discipline.
A is a fact about Tolkien alone, not a contrast. B and D are never compared.
The passage only says the term “Landsraad” hints at the possibility that the empire is based on European feudalism. That is a remark about the setting, not a claim that the whole narrative is an allegory.
A: the family oversees spice, a unique, life-extending resource found only on Arrakis. B: the dune-grass assignment was ecological. C: “Dune accomplished the latter without losing sight of the former.”
The passage says sci-fi of the era usually appeared as short stories in pulp magazines. It never says Dune was serialised that way, so A is not supported.
B: Lucas was “years away” from Star Wars. C: the Oregon landscape impressed him. D: humanity has colonised “the remotest corners of the galaxy”.
After the teaser about “literally driving in circles”, the sentence defines roundabouts. The next sentence, “Instead of coming to a complete stop…”, picks up the comparison with traffic lights and stop signs.
At 1 and 2 the definition would come before the hook. At 4 the mechanics have already been described without the term being introduced.
- Most of the running injuries are absent in cultures where shoes are not customarily worn at all.
- Normally, runners with fancy shoes can these days expect a 30–80% chance of an injury.
- Over the past several years, the importance of our feet has been overlooked for the comfort and luxury of wearing shoes.
- Through the reappearance of walking and running as healthy activities, the significance of strong feet is again becoming a matter of concern.
The order runs like this:
- 3: Feet have been overlooked in favour of shoes.
- 4: With walking and running back in fashion, strong feet matter “again”.
- 2: Runners in fancy shoes face a 30–80% injury chance.
- 1: Such injuries are absent where shoes aren’t worn.
- The Maldives has a distinctive culture that it works hard to protect.
- The Maldives is a tiny nation of some 500,000 people, next door to the most populous country in the world.
- In some ways, the importance of the India factor in Maldives politics should be seen as inevitable.
- A strong adherence to Islam should be seen as an expression of the country’s unique identity as much as a declaration of faith.
- But even among informed Maldivians, there is also disquiet that Indian officials went beyond normal diplomatic protocols in their dealings with the former government.
The coherent paragraph is 2 → 3 → 1 → 4:
- 2: A tiny nation next to the world’s most populous country.
- 3: So the India factor is, in some ways, inevitable.
- 1: Yet the Maldives has a distinctive culture it works to protect.
- 4: Islam as an expression of that unique identity.
Sentence 5 brings in a specific diplomatic episode (Indian officials and “the former government”) that nothing introduces. It breaks the paragraph’s focus on size, geography and identity.
The next sentence speaks of “that finite number of rooms”, which needs an earlier mention of a fixed supply. The new sentence provides it, so it goes at blank 1.
At 2–4 the price spike and the tourists’ choices are already under way.
The core claim is that the find “disputes the notion that eastern Asia remained stagnant during the Middle Paleolithic.” C says this.
A: nothing is confirmed about Neanderthals in Asia. B contradicts the passage (the Quina system was known from the Middle East and Europe). D: “proves … identical” is far too strong.
- In Vedantic thought, Krishn lifting the mountain is not an external miracle but an inner revelation.
- The villagers bowed not just to Krishn, but to the very mountain that had protected them – a living symbol of divine refuge.
- When Indra’s pride collapsed, the thunder ceased, and sunlight returned.
- For seven days and nights, the rain fell without pause, yet no one was harmed.
- Under that mountain, time seemed to stand still – fear melted into faith.
The coherent paragraph is 4 → 5 → 3 → 2, telling the story in order:
- 4: Rain for seven days, yet no one harmed.
- 5: Under the mountain, fear melted into faith.
- 3: Indra’s pride collapsed and the storm ended.
- 2: The villagers bowed to Krishn and the mountain.
Sentence 1 steps out of the story into a philosophical (Vedantic) interpretation, which doesn’t fit the narrative sequence.
DILR · Data Interpretation & Logical Reasoning
In a country called Primistan, the currency is called Abhajya (@) and is available in exactly five denominations — @ 2, @ 3, @ 5, @ 7 and @ 11. Each of the five persons, Pranav, Reena, Ian, Mushtaq and Emily had notes of exactly one denomination with them, and no two persons among the five had notes of the same denomination. On a particular day, the five people visited a bookstore and each of them purchased a different book. The amounts that Pranav, Reena, Ian, Mushtaq and Emily paid the shopkeeper were @ 42, @ 105, @ 165, @ 70 and @ 75, respectively. Further, the number of notes that each person gave the shopkeeper was distinct. However, the amount that each person paid the shopkeeper was more than the price of the book that they purchased. Therefore, the shopkeeper returned the excess amounts to each in the form of three notes each, of three different denominations, which were different from those in which the person had paid the shopkeeper.
- Ian. Only 165 is divisible by 11, so Ian paid in @11 (15 notes).
- Emily. 75 can be paid in @3 (25 notes) or @5 (15 notes). 15 is taken by Ian, so Emily paid in @3.
- Reena. 105 can be paid in @3, @5 or @7. @3 is Emily’s, and @7 would be 15 notes (taken), so Reena paid in @5 (21 notes).
- Pranav and Mushtaq. @2 and @7 remain. Pranav with @2 would need 21 notes (taken), so Pranav paid in @7 (6 notes) and Mushtaq in @2 (35 notes).
- Change. Each person’s change is the sum of three different denominations other than their own, which gives the possible book prices below.
| Person | Paid | Denomination | Notes | Possible book prices |
|---|---|---|---|---|
| Pranav | 42 | @7 | 6 | 32, 26, 24, 23 |
| Reena | 105 | @5 | 21 | 93, 89, 85, 84 |
| Ian | 165 | @11 | 15 | 155, 153, 151, 150 |
| Mushtaq | 70 | @2 | 35 | 55, 51, 49, 47 |
| Emily | 75 | @3 | 25 | 61, 57, 55, 52 |
Total notes = 6 + 21 + 15 + 35 + 25 = 102.
Mushtaq paid 35 notes of @2, the most of anyone.
Ian’s change uses three of @2, @3, @5, @7, so it is 10, 12, 14 or 15. His book costs 155, 153, 151 or 150, so 149 is impossible.
Emily’s change uses three of @2, @5, @7, @11. The smallest is 2 + 5 + 7 = 14, so the highest book price is 75 − 14 = 61.
Pranav’s possible prices are 32, 26, 24 and 23. These include a multiple of 3 (24), multiples of 8 (32, 24) and a prime (23), but no multiple of 5.
Reena’s possible prices are 93, 89, 85 and 84. Only 84 is a multiple of 4, so A fixes the price. B leaves 93, 89, 85, and C leaves 89, 85, 84.
A, B, C, D and E are five boys who live in a 10-storey building (excluding the ground floor). Each boy lives on a different floor, and none of them lives on the ground floor. All of them enter the lift on the ground floor, and each one presses the buttons for exactly 2 floors, such that all 10 buttons (floors 1-10) are pressed. None of them presses the button for his own floor. The following information is also known:
- C lives above A but below D, and E lives below D but above B.
- There are exactly 2 floors between the floors of B and A, and exactly one floor between the floors of C and E, where none of the five stay.
- The floor numbers pressed by B are perfect square numbers.
- A pressed the button for C’s floor, B pressed the button for D’s floor, C pressed the button for E’s floor, D pressed the button for A’s floor, and E pressed the button for B’s floor.
- The difference between the floor numbers pressed by E is the floor number of C.
- The difference between the floor numbers pressed by D is a perfect square number.
- A pressed consecutive floor numbers.
- B pressed the buttons for the floors that are above his floor.
- D’s floor. D lives highest (clue 1), and B pressed D’s floor, which must be a perfect square. D = 4 is impossible (four boys can’t fit below it), so D = 9. B pressed squares above his floor, so B pressed 4 and 9, and B ≤ 3.
- B and A. With |A − B| = 3 and empty floors in between: B = 1 gives A = 4. But D presses A’s floor and B already pressed 4, so ✗. B = 3 gives A = 6, which leaves no room for C and E 2 apart above it ✗. So B = 2 and A = 5.
- C and E. They are on 6 and 8 with 7 empty. If C = 6, E would need to press floors 6 apart including floor 2, which is impossible. So C = 8 and E = 6.
- Buttons. A presses 7, 8 (consecutive, including C’s floor). E presses 2 and 10 (difference 8 = C). D presses 5 and 1 (difference 4, a square). C presses 6 and the last floor left, 3.
| Boy | Lives on | Pressed |
|---|---|---|
| A | 5 | 7, 8 |
| B | 2 | 4, 9 |
| C | 8 | 3, 6 |
| D | 9 | 1, 5 |
| E | 6 | 2, 10 |
Vacant floors: 1, 3, 4, 7, 10. Only E (floor 6) lives between the floors he pressed (2 and 10).
From the table in Q17, C lives on floor 8.
D pressed floors 5 and 1.
Floor 2 is B’s. Floors 10, 4 and 7 are vacant.
QA · Quantitative Ability
A 125% profit means the mixture costs 1/2.25 = 4/9 of pure chemical, so the chemical fraction left is 4/9.
(1 − 15/V)2 = 4/9, so 1 − 15/V = 2/3 and V = 45 litres.
(√3 + √2)(√3 − √2) = 1. Let t = (√3 + √2)x; then t + 1/t = 10, so t = 5 ± 2√6.
5 + 2√6 = (√3 + √2)2 and 5 − 2√6 = (√3 + √2)−2, so x = 2 or −2. That gives 2 real values.
c is smallest when a and b take every factor of 3 and 5. In 25!: the power of 3 is 8 + 2 = 10, and the power of 5 is 5 + 1 = 6.
Raising to 5! = 120: a = 1200 and b = 720, so a + b = 1920.
Unfold two adjacent faces into a 4 × 8 rectangle. The shortest path is its diagonal: √(82 + 42) = √80 = 4√5 m. (4√3 is the space diagonal, which a non-flying insect can’t use.)
With an even number of terms, the even-position terms add up to r × (sum of odd-position terms). So total = (1 + r) × odd sum = 8 × odd sum, which gives r = 7.
T15/T12 = r3 = 343.
Starting with N workers, the shortfall each day from day 3 to day 20 is 4, 1, 5, 2, 6, 3, …, 12, 9.
Odd days (3–19): 4 + 5 + … + 12 = 72. Even days (4–20): 1 + 2 + … + 9 = 45. Total shortfall = 117 worker-days.
20N − 117 = 11N, so N = 13.
x2 − 6x + 90 is always positive, and |x + 1| ≥ 0 (equal to 0 at x = −1, where the expression is 0, not negative).
So we need (x − 5)(x + 2) < 0, i.e. −2 < x < 5 with x ≠ −1. The integers are 0, 1, 2, 3, 4: 5 in total.
3080 = 23 × 5 × 7 × 11. The odd factors come from 5 × 7 × 11: 2 × 2 × 2 = 8.
ED = 22 − 7 = 15. Intersecting chords: AE × EB = 7 × 15 = 105, and AE + EB = 20.5.
(BE − AE)2 = 20.52 − 4 × 105 = 420.25 − 420 = 0.25, so the difference is 0.5 cm.
2.5% of the common salary = 800, so Ram and Laxman each earn 32000. Ram gives 3200 and Laxman gives 4000.
Bharat gives 7200 − 3000 = 4200, which is 1/6 of his salary, so he earns 25200.
Total gifts = 11400. Total salary = 89200. 11400/89200 ≈ 12.78%.
Correct: 0 · Wrong: 0 · Accuracy: 0%
Keep the streak alive. See you tomorrow for Day 23.
