CAT 50 Day Streak Day 36

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CAT 50 Day Streak – Day 36

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

Physics is in crisis. For the past century or so, we have explained the universe with two wildly successful physical theories: general relativity and quantum mechanics. Quantum mechanics describes how things work in the incredibly tiny world of particles and particle interactions. General relativity describes the big picture of gravity and how objects move. Physicists want to produce a theory of “quantum gravity” that replaces general relativity and quantum mechanics, while capturing the extraordinary success of both.

One of the most prominent mathematical approaches to quantum gravity is loop quantum gravity, which proposes that the fabric of space and time is made of a network of extremely small discrete chunks, or 'loops.' A remarkable aspect of loop quantum gravity is that it appears to eliminate time entirely. A number of other approaches also seem to remove time as a fundamental aspect of reality.

So, we know we need a new physical theory to explain the universe, and that this theory might not feature time. Suppose such a theory turns out to be correct. Would it follow that time does not exist? It’s complicated, and it depends on what we mean by exist. Theories of physics don’t include any tables, chairs, or people, and yet we still accept that tables, chairs, and people exist. Why? Because we assume that such things exist at a higher level than the level described by physics. We say that tables, for example, 'emerge' from an underlying physics of particles whizzing around the universe.

But while we have a pretty good sense of how a table might be made out of fundamental particles, we have no idea how time might be 'made out of' something more fundamental. So, unless we can come up with a good account of how time emerges, it is not clear we can simply assume time exists. Time might not exist at any level.

Saying that time does not exist at any level is like saying that there are no tables at all. Trying to get by in a world without tables might be tough, but managing in a world without time seems positively disastrous. Our entire lives are built around time. We plan for the future, in light of what we know about the past. We hold people morally accountable for their past actions, with an eye to reprimanding them later on. We believe ourselves to be agents (entities that can do things) in part because we can plan to act in a way that will bring about changes in the future.

The discovery that time does not exist would seem to bring the entire world to a grinding halt. We would have no reason to get out of bed.

There is a way out of the mess. While physics might eliminate time, it seems to leave causation intact: the sense in which one thing can bring about another. Perhaps what physics is telling us, then, is that causation and not time is the basic feature of our universe. If that’s right, then the agency can still survive. For it is possible to reconstruct a sense of agency entirely in causal terms. This suggests that time does not exist and may have no direct impact on our lives, even while it propels physics into a new era.

Q1MCQ

None of the following statements can be inferred from the passage EXCEPT that:

ALoop quantum gravity theory is the first theory that eliminates time entirely.

BThe theories that reject time as a basic feature of our universe substitute it with causation as a basic feature.

CScience does not accept that time may have no direct impact on our lives.

DPhysics has established theories that give clarity on how time emerges and exists.

Solution Answer: B

The last paragraph says that while physics might eliminate time, “it seems to leave causation intact”, and that “causation and not time is the basic feature of our universe”. That is the inference in B.

A: loop quantum gravity is called “one of the most prominent” approaches, never the first. C: the passage says nothing about science rejecting this idea. D is the opposite: “we have no idea how time might be ‘made out of’ something more fundamental”.

Q2MCQ

‘We say that tables, for example, emerge from an underlying physics of particles whizzing around the universe.’ What is the purpose of this example?

AWe can imagine how a table might be made out of more fundamental particles, but we cannot imagine the concept of emergent time.

BJust like tables, we can explain how time is made out of fundamental particles.

CThe entire underlying physics of particles whizzing around the universe is unscientific.

DTime and tables are different yet alike in that both ‘emerge’ from more fundamental particles.

Solution Answer: A

The table example sets up a contrast: “while we have a pretty good sense of how a table might be made out of fundamental particles, we have no idea how time might be ‘made out of’ something more fundamental.”

B and D treat time as emerging the same way tables do, which is exactly what the author says we can’t explain. C: the author never calls particle physics unscientific.

Q3MCQ

Which one of the following sets of words and phrases serves best as keywords of the passage?

ALoops, time, universe

BLoops, fundamental, time

CEmergent time, time and agency, causation

DCausation, quantum physics, approaches

Solution Answer: C

The argument moves through three ideas: whether time can “emerge” like tables, what losing time would mean for agency and our lives, and causation as the way out. C names all three.

A and B focus on “loops”, which are mentioned only in passing. D’s “approaches” is generic and leaves out the central questions of emergence and agency.

Q4MCQ

The author makes all of the following arguments in the passage EXCEPT that:

AAccording to the loop quantum gravity theory, space and time are made of a network of extremely small discrete loops.

BPhysics in the new era may explain how time may not actually exist.

CSome new physical theories to explain the universe do not feature time.

DWhat new theories of physics call causation is nothing but another name for time.

Solution Answer: D

The author contrasts causation with time: physics may eliminate time while leaving causation intact. Causation is offered as a replacement for time, not another name for it.

A is stated in paragraph 2. B matches the closing line about physics entering a new era. C matches “this theory might not feature time”.

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.

Researchers worked with 20 patients who were undergoing intracranial recording of brain activity to guide surgery for the treatment of their drug-resistant epilepsy.
They looked at how the patients' brain activity was affected when shown film clips containing different types of cognitive boundary transitions thought to trigger changes in how a memory is stored and that mark the beginning and end of memory files in the brain.
Researchers have identified two types of cells in our brains that are involved in organizing discrete memories based on when they occurred.
This finding improves our understanding of how the human brain forms memories and could have implications for memory disorders such as Alzheimer's disease.

Solution Answer: 3412

The order runs like this:

3: The headline finding: two types of memory-organising cells.
4: “This finding” and why it matters (memory disorders).
1: The method: 20 epilepsy patients with intracranial recording.
2: “They looked at” brain activity during film clips.

Q6MCQ

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 Including under-studied populations in genetic resources enhances scientists’ ability to discover and precisely map variants that are potentially responsible for health traits and diseases.

Paragraph Discovering genetic variants that are involved in health-related traits relies on analysing genetic and health information from large cohorts of people. ___(1)___. However, there has long been an imbalance of genetic ancestries represented in this kind of research, which has excluded large groups of humanity from the downstream benefits. ___(2)___. Millions of genetic variants differ in frequency around the world owing to complex demographic processes, such as migration, that depend on geographic proximity and shared histories. ___(3)___. Therefore, variants found to be associated with a trait in one population could be less frequent or completely absent in another. ___(4)___.

AOption 1

BOption 2

COption 3

DOption 4

Solution Answer: D (Option 4)

The paragraph builds a case: research is ancestrally imbalanced, variant frequencies differ across populations, and so a variant found in one group may be absent in another. The sentence is the conclusion that follows: including under-studied groups improves discovery. It belongs at the end.

At blank 1 the imbalance hasn’t been raised yet. At blanks 2 and 3 the sentence would interrupt the explanation before the “Therefore” step it depends on.

Q7TITA

UNESCO has had time to plan for the agenda that Guterres wants to implement.
The agency must also ensure it can continue to do important work across its three big portfolios: education, science and culture.
UNESCO is the main UN agency advocating for open science.
It has established guidelines for using artificial intelligence in education.

Solution Answer: 1234

The order runs like this:

1: UNESCO has had time to plan for Guterres’s agenda.
2: “The agency must also” keep its three portfolios (education, science and culture) running.
3: An example of that work: it is the main UN advocate for open science.
4: “It has” also issued AI guidelines for education.

Q8MCQ

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 Zinc is light-colored and, as such, reflects a lot of solar energy.

Paragraph ___(1)___. While zinc does heat up enormously in the sun, it’s not a material that’s necessarily climate-unfriendly, Ménard says. ___(2)___. With ventilation and proper insulation underneath the sheets, it can be climate-proofed, he says. ___(3)___. However, since adding insulation to zinc roofs often means slightly changing their slopes, some state-appointed heritage architects block requests on the basis that it would alter Parisian aesthetics. ___(4)___. According to some critics, the new UNESCO designation could make such hurdles worse.

AOption 1

BOption 2

COption 3

DOption 4

Solution Answer: B (Option 2)

Ménard claims zinc is “not necessarily climate-unfriendly”. The sentence gives the first reason: it is light-coloured and reflects solar energy. The next sentence adds the second (ventilation and insulation can climate-proof it).

At blank 1 the sentence would come before the claim it supports. Blanks 3 and 4 sit in the discussion of heritage architects and the UNESCO designation, where reflectivity is out of place.

Q9TITA

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 process of mental health requires its own set of specific skills.
People may visualize mental health as a place one arrives at or a treasure one possesses.
Life, goes the saying, is like a diamond—hard and beautiful.
Many are experiencing the hardness of it quite acutely these days, in the form of stress, dread, and fatigue.
Much of our success in navigating these difficult times depends on our mental health.

Solution Answer: 1

The coherent paragraph is 3 → 4 → 5 → 2:

3: Life is like a diamond, hard and beautiful.
4: Many feel “the hardness of it” acutely now.
5: Navigating “these difficult times” depends on mental health.
2: People picture mental health as a place or a treasure.

Sentence 1 jumps to mental health as a process needing specific skills. Nothing in the paragraph prepares that shift; it would need a contrast such as “But in fact…” to follow sentence 2.

Q10MCQ

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

Passage As we look to greater distances, we also wind up looking back in time. The nearest galaxy, some 2.5 million light-years away, appears to us as it was 2.5 million years ago, because the light requires that much time to journey to our eyes from when it was emitted. More distant galaxies appear as if they were tens of millions, hundreds of millions or even billions of years ago. As we look ever farther away in space, the light we see from the Universe comes from its progressively younger days. Therefore, as we look back in terms of distance, we can also measure how the Universe evolved over its history.

AThe light from distant galaxies travels instantaneously, so observing them reveals the present state of the Universe.

BThe nearest galaxies are seen as they are today, while the light from more distant ones is always from their distant future.

CLooking at galaxies at various distances does not provide any information about the Universe’s history or age.

DObserving distant galaxies allows us to look back in time, as their light shows the Universe’s earlier stages and helps us understand its evolution.

Solution Answer: D

Light takes time to reach us, so farther galaxies show the Universe at earlier stages, which lets us measure how it evolved. D captures this.

A contradicts the travel time of light. B gets both halves wrong: even the nearest galaxy is seen as it was 2.5 million years ago, and light never comes from the future. C contradicts the conclusion that we “can also measure how the Universe evolved”.

DILR · Data Interpretation & Logical Reasoning

Q11 – Q20 0/10

Set 1 · Q11 – Q14

Bluemi is an electronics company operating out of six showrooms S1, S2, S3, S4, S5 and S6. It deals in five major varieties of electronic goods – Mobiles, Tablets, Laptops, Smartwatches and Speakers. The table depicts the sales by showroom (in Rs. Crores).

Showroom	S1	S2	S3	S4	S5	S6
Sales (In Rs. Cr)	27	49	19	31	102	72

The pie chart depicts the category-wise breakdown of sales for Bluemi products.

Pie chart of Bluemi sales by category: Laptops 30%, Mobiles 27%, Tablets 17%, Speakers 16%, Smartwatches 10%

Q11MCQ

If S1, S3 and S5 are the only showrooms dealing in mobiles, and exactly 2 of the 3 dealt only in Mobiles, what approximate % of sales incurred by the other showroom is accounted for by products not in the ‘Mobiles’ category?

A33%

B42%

C66%

D56%

Solution Answer: C

Total sales = 27 + 49 + 19 + 31 + 102 + 72 = 300 Cr. Category sales:

Category	Share	Sales (Rs. Cr)
Laptops	30%	90
Mobiles	27%	81
Tablets	17%	51
Speakers	16%	48
Smartwatches	10%	30

The two mobile-only showrooms together must sell less than 81 Cr. Only S1 + S3 = 46 qualifies, since any pair including S5 exceeds 81. So S5 sells 81 − 46 = 35 Cr of mobiles.

Non-mobile share of S5 = (102 − 35)/102 ≈ 66%.

Q12MCQ

If it is known that two particular categories of Bluemi electronic goods are sold in exactly four of the six showrooms, and in those four showrooms, no other category of products is sold, which of the following must be one of those two particular categories?

ASmartwatches

BTablets

CSpeakers

DLaptops

Solution Answer: D

Those four showrooms sell only the two categories, so the two categories’ totals must equal the four showrooms’ combined sales.

Using the category values in Q11, the possible pair sums are 171, 141, 138, 132, 129, 120, 111, 99, 81 and 78. A four-showroom total is 300 minus the two excluded showrooms. The only match is Laptops + Mobiles = 171 = S2 + S3 + S4 + S6 (49 + 19 + 31 + 72).

As a check, the other three categories total 30 + 48 + 51 = 129 = S1 + S5 ✓. One of the two categories must be Laptops.

Q13MCQ

Considering the information provided in Q12, which of the following are not amongst the four showrooms selling those two particular categories exclusively?

AS1

BS2

CS4

DS6

Solution Answer: A

From Q12, the four showrooms are S2, S3, S4 and S6. S1 (with S5) is not among them.

Q14TITA

What is the maximum possible number of categories that can be sold equally across the six showrooms?

Solution Answer: 2

A category sold equally puts one-sixth of its total in every showroom. Per-showroom shares: Smartwatches 5, Speakers 8, Tablets 8.5, Mobiles 13.5, Laptops 15 Cr.

S3 sells only 19 Cr, so the shares of all equally sold categories must fit within 19. Even the three smallest add to 5 + 8 + 8.5 = 21.5 > 19. Two fit, for example Smartwatches + Speakers = 13. The maximum is 2.

Set 2 · Q15 – Q18

The country of Mekrane contains four areas for radar detection: R, S, T, and U. Each detection area is circular and falls completely within Mekrane.

Part of R intersects T; part of S also intersects T; R does not intersect S. U is completely within R and also completely within T.

Four planes, J, K, L, M, are over Mekrane, such that each plane is in at least one of the four areas.

J is in area S.
K is not in any detection area that J is in.
L is not in any detection area that M is in.
M is in exactly one of the areas.

Q15MCQ

If K is within exactly two of the four areas, then which one of the following CANNOT be true?

AJ is within area T.

BK is within area R.

CM is within area T.

DL is within area R.

Solution Answer: A

Possible regions. R only, S only, T only, R∩T (outside U), U (which means R, T and U together), and S∩T. S never meets R or U.
K in exactly two areas. That means R∩T or S∩T. K can’t be in S (J is in S), so K is in R∩T.
Consequence. K is in T, so J can’t be in T. J is within area T cannot be true. B, C and D are all possible.

Q16MCQ

Which one of the following statements CANNOT be true about the planes?

AM is within area R.

BK is within area U.

CM is within area U.

DL is within area R.

Solution Answer: C

U lies inside both R and T, so any plane in U is in three areas at once. M is in exactly one area, so M cannot be within U.

A: M can be in R only. B: K can be in U if J is in S only. D: L can be in R only (with M elsewhere).

Q17MCQ

If M is within area T, then which one of the following statements CANNOT be true?

AJ is within area T.

BL is within area R.

CK is within exactly two areas.

DL is within exactly two areas.

Solution Answer: D

M is in T only, so L can’t be in T. The only two-area regions are R∩T and S∩T, and both include T. So L cannot be within exactly two areas.

A: J in S∩T with K in R only works. B: L in R only works. C: K in R∩T with J in S only works.

Q18MCQ

If plane L is within exactly three of the areas, which one of the following could be true?

AJ is within exactly three areas.

BJ is within exactly two areas.

CK is within area S.

DM is within area R.

Solution Answer: B

Three areas means L is in U (so also in R and T). M then avoids R, T and U, leaving S only.

A: J is in S, which overlaps at most T, so J can be in two areas at most ✗. B: J in S∩T, with K in R only, works ✓. C: K can’t share S with J ✗. D: M can’t be in R ✗.

Set 3 · Q19 – Q20

Three different faces of a cube are painted in three different colours — crimson, olive and azure. This cube is then cut into 1331 smaller cubes.

Q19MCQ

What is the maximum number of cubes that have exactly one face painted?

A330

B319

C308

D300

Solution Answer: B

1331 = 11³, so each face is 11 × 11. There are two ways to arrange three painted faces:

All three meet at a corner. Each face loses two edges to the other painted faces: 3 × 10 × 10 = 300.
Two opposite faces plus one between them. Each opposite face loses one edge: 2 × 11 × 10 = 220. The middle face loses two opposite edges: 11 × 9 = 99. Total 319.

The maximum is 319.

Q20TITA

N denotes the number of small cubes that have one face painted azure and one face painted olive and no other face painted. How many values are possible for N?

Solution Answer: 3

Azure–olive cubes lie along the edge shared by the azure and olive faces.

Azure and olive are opposite faces. They share no edge, so N = 0.
All three faces meet at a corner. The shared edge has 11 cubes, but the one at the corner also has crimson, so N = 10.
Azure and olive are adjacent, with crimson opposite one of them. Crimson doesn’t touch their shared edge, so N = 11.

N can be 0, 10 or 11: 3 values.

QA · Quantitative Ability

Q21 – Q30 0/10

Q21MCQ

Tank A consists of chemicals P and Q in the ratio of 4:5 and Tank B consists of chemicals Q and R in the ratio of 3:7. 36 litres of mixture from Tank A is mixed with 40 litres of mixture from Tank B in Tank C. Find the ratio of chemicals Q and R left in Tank C after 38 litres of the mixture is replaced by Chemical R.

A3:13

B4:13

C4:11

D3:14

Solution Answer: B

From A (36 L): P = 16, Q = 20. From B (40 L): Q = 12, R = 28. Tank C (76 L): P = 16, Q = 32, R = 28.

Removing 38 L (half) leaves P = 8, Q = 16, R = 14. Adding 38 L of R gives R = 52.

Q : R = 16 : 52 = 4 : 13.

Q22MCQ

Let x, y > 0. If x³y² = 2¹⁵, find the least value of 3x + 2y.

A30

B32

C40

D45

Solution Answer: C

Write 3x + 2y = x + x + x + y + y. By AM ≥ GM, (x + x + x + y + y)/5 ≥ (x³y²)^1/5 = (2¹⁵)^1/5 = 8.

So 3x + 2y ≥ 40, with equality when x = y = 8. The least value is 40.

Q23TITA

A boat went down the river for a distance of 20 km. It then turned back and returned to its starting point, having travelled a total of 7 hours. On its return trip, at a distance of 12 km from the starting point, it encountered a log, which had passed the starting point at the moment at which the boat had started downstream. The downstream speed of the boat (in kmph) is

Solution Answer: 10

Let the downstream speed be D and the upstream speed U, so the stream speed is s = (D − U)/2. Then 20/D + 20/U = 7, and the log drifts 12 km in the time the boat goes 20 km down and 8 km back: 20/D + 8/U = 12/s.

D = 10 and U = 4 satisfy both: 2 + 5 = 7 ✓, and with s = 3, 2 + 2 = 4 = 12/3 ✓.

Downstream speed = 10 km/h.

Q24MCQ

An equilateral triangle ABC is inscribed in a circle C1. A smaller circle C2 is inscribed inside the triangle ABC, touching all its three sides. If P is any point on the circumference of the larger circle C1, what is the value of the expression (PA² + PB² + PC²) / r², where r is the radius of the smaller circle C2?

A24

B18

C12

Solution Answer: A

Let the circumradius be R. The centroid O is also the circumcentre, so PA² + PB² + PC² = 3(PO² + R²) = 3(R² + R²) = 6R².

For an equilateral triangle, r = R/2, so r² = R²/4. The ratio is 6R² ÷ (R²/4) = 24.

Q25MCQ

What is the sum of the smallest three prime factors of 6²² − 1?

A31

B35

C37

D41

Solution Answer: B

6²² − 1 is odd and leaves remainder 2 when divided by 3, so 2 and 3 are not factors.

6² − 1 = 35 divides 6²² − 1, so 5 and 7 are factors. Checking the next primes: 6²² leaves 3 mod 11, 4 mod 13, 8 mod 17 and 4 mod 19, so none of those divide it. By Fermat’s little theorem, 6²² ≡ 1 (mod 23), so 23 is a factor.

Sum = 5 + 7 + 23 = 35.

Q26MCQ

While buying, a shopkeeper uses a faulty balance and receives 1200 grams of tea powder instead of 1000 grams. He gains ‘a’ percentage profit by selling it at Rs. X per kg. If he sells it for Rs. X + 80 per kg and gains (a + 10)% profit, then find the value of a% of X.

A600

B700

C800

DCannot be determined

Solution Answer: D

Let C be the price he pays per marked kg. He actually receives 1.2 kg, so his true cost is C/1.2 per kg and profit % = 1.2X/C − 1.

Raising the price by 80 adds 10 percentage points: 1.2 × 80/C = 0.10, so C = 960. But a = 1.2X/960 − 1 still depends on X, and nothing else fixes X. So a% of X cannot be determined.

Q27MCQ

What is the value of 7^{(3 + log₇ 5)}?

A1575

B3140

C1715

D3460

Solution Answer: C

7^{3 + log₇ 5} = 7³ × 7^{log₇ 5} = 343 × 5 = 1715.

Q28TITA

Amal, Bimal, and Kamal worked on a project in such a way that Amal and Bimal worked on the 1st day, Bimal and Kamal worked on the 2nd day, Amal and Kamal worked on the 3rd day, and the cycle repeated till the work was completed. When Amal works alone, he can complete the work in 30 days. Bimal is two times as efficient as Amal, while Kamal is 1.5 times as efficient as Amal. What is the percentage of extra time needed if they work in this manner compared to when they work together?

Solution Answer: 50

Take the work as 60 units: Amal 2, Bimal 4 and Kamal 3 units per day. Working together (9 per day) takes 60/9 = 20/3 days.

In pairs, one 3-day cycle is 6 + 7 + 5 = 18 units. Three cycles (9 days) give 54, and day 10 (Amal + Bimal, 6 units) finishes the work exactly. Time = 10 days.

Extra time = (10 − 20/3) ÷ (20/3) × 100 = 50%.

Q29MCQ

A golf ball has a diameter equal to 4.2 cm. Its surface has 200 hemispherical dimples, each of a radius of 2 mm. Calculate the total surface area that is exposed to the surroundings.

A74.6 sq cm

B77.9 sq cm

C85.2 sq cm

D80.5 sq cm

Solution Answer: D

Ball surface = 4π(2.1)² = 4 × 22/7 × 4.41 = 55.44 sq cm.

Each dimple (r = 0.2 cm) removes a flat circle of πr² and adds a hemisphere of 2πr², a net gain of πr² = 22/7 × 0.04 ≈ 0.1257. For 200 dimples: ≈ 25.14 sq cm.

Exposed area ≈ 55.44 + 25.14 ≈ 80.5 sq cm.

Q30MCQ

If the sum of the roots of the given quadratic equation 1x − a − 1x − b = 1c is zero, then find the product of the roots.

Aab + 2bc

Bbc + 2ac

Cac + 2bc

Dbc + 2ab

Solution Answer: A

Combining the fractions: (a − b)/[(x − a)(x − b)] = 1/c, so x² − (a + b)x + ab − c(a − b) = 0.

The sum of the roots is a + b = 0, so a = −b. Product = ab − c(a − b) = ab − c(−2b) = ab + 2bc.

Day 36 complete! 🔥

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