CAT 50 Day Streak Day 13

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CAT 50 Day Streak – Day 13

30 questions across VARC, DILR & QA · +3 for a correct answer · −1 for a wrong MCQ · no negative marking for TITA

0/30Attempted

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VARC · Verbal Ability & Reading Comprehension

Q1 – Q10 0/10

Passage · Q1 – Q4

In principle, a cohesive group—one whose members generally agree with one another and support one another’s judgments—can do a much better job at decision making than it could if it were noncohesive. When cohesiveness is low or lacking entirely, compliance out of fear of recrimination is likely to be strongest. To overcome this fear, participants in the group’s deliberations need to be confident that they are members in good standing and that the others will continue to value their role in the group, whether or not they agree about a particular issue under discussion. As members of a group feel more accepted by the others, they acquire greater freedom to say what they really think, becoming less likely to use deceitful arguments or to play it safe by dancing around the issues with vapid or conventional comments. Typically, then, the more cohesive a group becomes, the less its members will deliberately censor what they say out of fear of being punished socially for antagonizing their fellow members.

But group cohesiveness can have pitfalls as well: while the members of a highly cohesive group can feel much freer to deviate from the majority, their desire for genuine concurrence on every important issue often inclines them not to use this freedom. In a highly cohesive group of decision makers, the danger is not that individuals will conceal objections they harbor regarding a proposal favored by the majority, but that they will think the proposal is a good one without attempting to carry out a critical scrutiny that could reveal grounds for strong objections. Members may then decide that any misgivings they feel are not worth pursuing—that the benefit of any doubt should be given to the group consensus. In this way, they may fall victim to a syndrome known as “groupthink,” which one psychologist concerned with collective decision making has defined as “a deterioration of mental efficiency, reality testing, and moral judgment that results from in-group pressures.”

Based on analyses of major fiascoes of international diplomacy and military decision making, researchers have identified groupthink behavior as a recurring pattern that involves several factors: overestimation of the group’s power and morality, manifested, for example, in an illusion of invulnerability, which creates excessive optimism; closed-mindedness to warnings of problems and to alternative viewpoints; and unwarranted pressures toward uniformity, including self-censorship with respect to doubts about the group’s reasoning and a concomitant shared illusion of unanimity concerning group decisions. Cohesiveness of the decision-making group is an essential antecedent condition for this syndrome but not a sufficient one, so it is important to work toward identifying the additional factors that determine whether group cohesiveness will deteriorate into groupthink or allow for effective decision making.

Q1MCQ

Which one of the following most accurately expresses the main point of the passage?

ADespite its value in encouraging frank discussion, high cohesion can lead to a debilitating type of group decision making called groupthink.

BGroup members can guard against groupthink if they have a good understanding of the critical role played by cohesion.

CGroupthink is a dysfunctional collective decision-making pattern that can occur in diplomacy and military affairs.

DFuture efforts to guard against groupthink will depend on the results of ongoing research into the psychology of collective decision making.

Solution Answer: A

The first paragraph praises cohesion for freeing members to speak frankly. The second turns with “But group cohesiveness can have pitfalls”, i.e. groupthink. The third describes groupthink and notes that cohesion is necessary for it. A captures both halves.

B: the passage never says that understanding cohesion prevents groupthink. C: diplomacy and military affairs are only where the evidence comes from. D covers only the final sentence.

Q2MCQ

Which one of the following, if true, would most support the author’s contentions concerning the conditions under which groupthink takes place?

AA study of several groups, each made up of members of various professions, found that most fell victim to groupthink.

BThere is strong evidence that respectful dissent is more likely to occur in cohesive groups than in groups in which there is little internal support.

CExtensive analyses of decisions made by a large number of groups found no cases of groupthink in groups whose members generally distrust one another’s judgments.

DThere is substantial evidence that groupthink is especially likely to take place when members of a group develop factions whose intransigence prolongs the group’s deliberations.

Solution Answer: C

The author says cohesiveness is “an essential antecedent condition” for groupthink. If groups whose members distrust one another (i.e. non-cohesive groups) never show groupthink, that directly supports the claim.

A says nothing about the conditions. B supports the first paragraph’s point about frank discussion, not the conditions for groupthink. D links groupthink to factions, which points to low cohesion and cuts against the author.

Q3MCQ

The passage mentions which one of the following as a component of groupthink?

Aunjustified suspicions among group members regarding an adversary’s intentions

Bstrong belief that the group’s decisions are right

Cgroup members working under unusually high stress, leading to illusions of invulnerability

Dcareful consideration of objections to majority positions

Solution Answer: B

The listed factors include “overestimation of the group’s power and morality”, “excessive optimism” and “a shared illusion of unanimity”. All of these amount to a strong belief that the group’s decisions are right.

A: suspicion of adversaries is never mentioned. C: stress is not mentioned; the illusion of invulnerability comes from overestimating the group. D is the opposite of groupthink.

Q4MCQ

It can be inferred from the passage that both the author of the passage and the researchers mentioned in the passage would be most likely to agree with which one of the following statements about groupthink?

AGroupthink occurs in all strongly cohesive groups, but its contribution to collective decision making is not fully understood.

BThe causal factors that transform group cohesion into groupthink are unique to each case.

CThe continued study of cohesiveness of groups is probably fruitless for determining what factors elicit groupthink.

DOn balance, groupthink cannot be expected to have a beneficial effect in a group’s decision making.

Solution Answer: D

The author defines groupthink as “a deterioration of mental efficiency, reality testing, and moral judgment”. The researchers found it behind “major fiascoes”. Both treat it as harmful, which is D.

A contradicts “not a sufficient one”: cohesion doesn’t always lead to groupthink. B contradicts the idea of a “recurring pattern” with identifiable factors. C contradicts the call to keep looking for those factors.

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 Typophilic publishers tend to pay minute attention to a typeface’s nuances, things that the average reader couldn’t care less about.

Paragraph Lest we take our type too seriously, here’s a short story. ___(1)___. You may have noticed how some books carry a colophon at the end—a device of rich and varied history—that conveys the details of their production. ___(2)___. Since we’re no longer so medievally lavish with our curses, it’s often just a logo or a note that describes the chosen typeface, its history, and the circumstances of its choosing within the overall design. ___(3)___. And admittedly, some take it too far. ___(4)___.

AOption 1

BOption 2

COption 3

DOption 4

Solution Answer: C (Option 3)

Blank 3 follows a note describing “the chosen typeface, its history, and the circumstances of its choosing”. The missing sentence explains that typophilic publishers care about such nuances. The next line, “And admittedly, some take it too far”, needs “some” to refer to those publishers. So the sentence belongs at blank 3.

At blanks 1 and 2 typefaces haven’t come up yet. At blank 4, “some” would have no antecedent.

Q6TITA

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.

They found and publicized patterns of ethical lapses and improperly vetted research, even in the face of insults and lawsuits.
It also highlights the dogged work of outside scientists, teachers, and journalists who questioned the institute’s research history.
As a result, the research institute was investigated and the research director barred from practicing medicine.
This Science investigation unravels the systematic problems at the research hospital where the hydroxychloroquine study took place.

Solution Answer: 4213

The order runs like this:

4: Introduces “This Science investigation”.
2: “It also highlights” the outside scientists, teachers and journalists.
1: “They” (those outsiders) exposed the lapses despite lawsuits.
3: “As a result”, the institute was investigated.

Q7MCQ

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

Passage Historians generally agree that, of the great modern innovations, the railroad had the most far-reaching impact on major events in the United States in the nineteenth and early twentieth centuries, particularly on the Industrial Revolution. There is, however, considerable disagreement among cultural historians regarding public attitudes toward the railroad, both at its inception in the 1830s and during the half century between 1880 and 1930, when the national rail system was completed and reached the zenith of its popularity in the United States. In a recent book, John Stilgoe has addressed this issue by arguing that the “romantic-era distrust” of the railroad that he claims was present during the 1830s vanished in the decades after 1880. But the argument he provides in support of this position is unconvincing.

AWhile historians agree that the railroad profoundly shaped America’s industrial development, they differ sharply on how the public viewed it, and one recent attempt to resolve this debate fails to persuade.

BDespite the railroad’s undisputed influence on American history, cultural historians have largely dismissed debates about how it was perceived by the public in different periods.

CJohn Stilgoe’s claim that early skepticism toward the railroad faded after 1880 has been widely accepted as the most comprehensive account of nineteenth-century public opinion.

DThe railroad’s role in the Industrial Revolution is unquestioned, but its influence on American culture and public imagination has received little scholarly attention.

Solution Answer: A

A covers all three parts: historians agree on the railroad’s impact, they disagree about public attitudes, and Stilgoe’s attempt to settle this is unconvincing.

B: historians actively debate the issue rather than dismissing it. C: the author finds Stilgoe unconvincing, not widely accepted. D: there is “considerable disagreement”, so the topic has had plenty of attention.

Q8TITA

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.

If you encounter a snake while out on a hike, fear will lead you to back away and exercise caution.
By contrast, the fears that dominate political discourse are less concrete.
In ordinary life, fear is often a fitting response to danger.
If the snake is poisonous, fear will have saved your life.
Citizens face real dangers from failed political leadership, as lethal to our livelihood as snake bites.

Solution Answer: 5

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

3: Fear is often a fitting response to danger.
1: Example: a snake on a hike.
4: If it is poisonous, fear saved your life.
2: “By contrast”, political fears are less concrete.

Sentence 5 says political dangers are as real and lethal as snake bites. That contradicts the contrast in sentence 2.

Q9TITA

This seems like just atheism repackaged.
There are pantheists, who think that ‘God’ and ‘the universe’ are simply different words for the same thing.
However, there are versions of the God hypothesis that don’t see things in such binary terms.
There is a fit with the conviction of many mystics, as well as the English Romantic poets, that the Divine is present in all things.
The idea of God I received as a child was of something completely separate from the universe.

Solution Answer: 4

The coherent paragraph is 5 → 3 → 2 → 1:

5: The childhood idea of a God separate from the universe.
3: “However”, some versions are less binary.
2: Example: pantheists, for whom God and the universe are the same.
1: “This seems like just atheism repackaged”, an objection to pantheism.

Sentence 4 praises the idea’s fit with mystics and poets. Placed after 2 it would break the link between pantheism and “This” in sentence 1, and placed after 1 it has nothing to attach to.

Q10MCQ

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 The flesh is low in fibre, making it exceptionally succulent.

Paragraph Yumemizuki peaches are notable for their large size and sweetness. ___(1)___. Developed by a prefectural facility that experiments with fruit trees, Yumemizuki peaches have milky-white flesh that contrasts beautifully with their vibrant, deep pink skin. ___(2)___. While delicious eaten fresh, this variety is also used as an ingredient in desserts and other dishes. ___(3)___. “You can simply freeze the mashed flesh to enjoy as an exquisite sherbet,” said Rina Suzuki, a Yamanashi Prefectural Government Marketing and Export Support Division staffer. ___(4)___.

AOption 1

BOption 2

COption 3

DOption 4

Solution Answer: B (Option 2)

“The flesh” needs the flesh to have been mentioned. It is introduced just before blank 2 (“milky-white flesh”), and the missing sentence adds another quality of it.

At blank 1 the flesh hasn’t been mentioned. At blanks 3 and 4 the paragraph has moved on to uses in desserts and sherbet.

DILR · Data Interpretation & Logical Reasoning

Q11 – Q20 0/10

Set 1 · Q11 – Q15

Four friends, A, B, C and D, played a game of Poker. Initially, they had chips in the 60s, 40s, 50s, and 70s, respectively, such that each one of them had a prime number of chips. They played 6 rounds of the game such that the chips were transferred among them. It is also known that:

A lost 10 chips in each round.
The number of chips with B after every round formed an increasing arithmetic progression.
The chips with D were all numbers between 71 and 77 (both inclusive) but not in any specific order.
B ended up with as many chips as A had at the start of the game.
The number of chips with D was even after rounds 1, 3 and 5.
The number of chips with C was a perfect square after rounds 1 and 4.
Both C and D had 74 chips at the end of round 3.
All except D ended up with a prime number of chips.

Q11TITA

What was the total number of chips used in the game?

Solution Answer: 240

A. A starts with 61 or 67 and ends with 60 fewer, which must be prime. 61 − 60 = 1 isn’t prime, so A starts at 67 and ends at 7. B therefore ends at 67.
D. D’s seven counts (start plus six rounds) are exactly 71 to 77. The counts after rounds 1, 3 and 5 are the three even ones: 72, 74 and 76, with 74 after round 3. The start and rounds 2, 4 and 6 are odd. D starts on a prime, 71 or 73.
B. B gains the same d chips every round, so B starts at 67 − 6d, which must be a prime in the 40s. Only d = 4 works, giving 43.
Total. After round 3: A 37 + B 55 + C 74 + D 74 = 240. Then C + D at the start = 240 − 67 − 43 = 130, which gives C = 59 and D = 71.
Round 1. A 57, B 47, so C + D = 136. D is 72 or 76, and C must be a perfect square, so C = 64 and D = 72.
Round 4. A 27, B 59, so C + D = 154. D is odd and C a perfect square, so C = 81 and D = 73. Round 5 then has D = 76 and C = 84.
Round 6. A 7, B 67, so C + D = 166, with D 75 or 77 and C prime. So C = 89 and D = 77, which leaves D = 75 and C = 67 in round 2.

After	A	B	C	D	Total
Start	67	43	59	71	240
Round 1	57	47	64	72	240
Round 2	47	51	67	75	240
Round 3	37	55	74	74	240
Round 4	27	59	81	73	240
Round 5	17	63	84	76	240
Round 6	7	67	89	77	240

A total of 240 chips were used in the game.

Q12MCQ

At the end of how many rounds did C have more chips than anyone else?

DC never had the highest number of chips

Solution Answer: A

From the table in Q11, D leads after rounds 1 and 2, and C and D tie after round 3. C leads alone after rounds 4, 5 and 6 (81, 84, 89): 3 rounds.

Q13MCQ

After which round was the difference in the number of chips between A and B the least?

ARound 4

BRound 3

CRound 2

DRound 1

Solution Answer: C

|A − B| after each round: Round 1 = 10, Round 2 = 4, Round 3 = 18, Round 4 = 32. The least is after Round 2.

Q14MCQ

At the end of which round did D have 75 chips?

ARound 4

BRound 3

CRound 6

DRound 2

Solution Answer: D

From the table in Q11, D had 75 chips at the end of Round 2.

Q15MCQ

At the end of which round was the range of chips held by the four players the smallest?

ARound 4

BRound 3

CRound 2

DRound 1

Solution Answer: C

Detailed solution coming soon.

Set 2 · Q16 – Q20

100 people each were surveyed by Apple in three months: Jan, Feb and Mar, to find out the likelihood of people buying a MacBook or an iPhone. The results of the survey are given in the following table.

Response	MacBook Jan	MacBook Feb	MacBook Mar	iPhone Jan	iPhone Feb	iPhone Mar
Very unlikely	50	46	22	17	18	21
Somewhat unlikely	24	26	29	14	13	8
Undecided	10	12	15	4	5	7
Somewhat Likely	5	6	11	46	36	34
Very Likely	2	4	7	16	21	25
No Response	9	6	16	3	7	5

Note: No. of persons likely to buy = somewhat likely to buy + very likely to buy. No. of persons unlikely to buy = somewhat unlikely to buy + very unlikely to buy.

Q16MCQ

In Jan, at least how many of the persons surveyed are unlikely to buy a MacBook and also unlikely to buy an iPhone?

C10

D13

Solution Answer: A

In Jan, 50 + 24 = 74 are unlikely to buy a MacBook and 17 + 14 = 31 are unlikely to buy an iPhone.

Out of 100 people, the overlap is at least 74 + 31 − 100 = 5.

Q17TITA

In Mar, what is the least number of persons surveyed who are likely to buy at least one of the MacBook and iPhone?

Solution Answer: 59

In Mar, 11 + 7 = 18 are likely to buy a MacBook and 34 + 25 = 59 are likely to buy an iPhone.

The union is smallest when all 18 MacBook buyers are among the 59, so at least 59.

Q18MCQ

In Feb, if among the persons surveyed, 14 persons said they were undecided to buy either MacBook or iPhone, what percentage of the total people surveyed were undecided to buy both MacBook and iPhone?

A2%

B3%

C4%

D5%

Solution Answer: B

In Feb, 12 were undecided about the MacBook and 5 about the iPhone, and 14 were undecided about at least one.

Undecided about both = 12 + 5 − 14 = 3, i.e. 3% of 100.

Q19TITA

The same set of 100 persons was surveyed in each of the three given months. The number of persons who responded in the same manner regarding their likelihood of buying an iPhone in Feb and Mar is at most

Solution Answer: 91

For each response, at most the smaller of the Feb and Mar counts could have answered the same way in both months:

Very unlikely: min(18, 21) = 18
Somewhat unlikely: min(13, 8) = 8
Undecided: min(5, 7) = 5
Somewhat likely: min(36, 34) = 34
Very likely: min(21, 25) = 21
No response: min(7, 5) = 5

Maximum = 18 + 8 + 5 + 34 + 21 + 5 = 91.

Q20MCQ

The same set of 100 persons was surveyed in each of the three given months. The number of persons who were very unlikely to buy a MacBook in two or more of the three months is at least

A26

B23

C21

D18

Solution Answer: D

Detailed solution coming soon.

QA · Quantitative Ability

Q21 – Q30 0/10

Q21TITA

The average weight of boxers in a tournament is 72 kg. If 10 boxers having an average weight of 78 kg leave and in their place 4 boxers having an average weight of 80 kg join the tournament, the average weight of the group is reduced by 0.7 kg. What was the initial number of boxers in the tournament?

Solution Answer: 46

Let n be the initial number of boxers. The new total is 72n − 780 + 320 = 72n − 460, shared among n − 6 boxers at an average of 71.3:

72n − 460 = 71.3(n − 6) = 71.3n − 427.8, so 0.7n = 32.2 and n = 46.

Q22MCQ

A natural number N has 4 factors. The sum of the factors excluding 1 and the number itself is 132. How many values of N are possible?

B10

C12

D15

Solution Answer: B

A number with exactly 4 factors is either pq (two distinct primes) or p³.

N = pq: we need p + q = 132. The prime pairs are (5, 127), (19, 113), (23, 109), (29, 103), (31, 101), (43, 89), (53, 79), (59, 73) and (61, 71): 9 values.
N = p³: we need p + p² = 132, so p = 11 and N = 1331: 1 value.

Total = 10 values.

Q23MCQ

If a quadratic equation f(x) = 0 has two distinct real roots opposite in sign, the roots of the equation f(x) + f(−x) = 0 are:

AReal, equal in magnitude but opposite in sign

BReal, unequal in magnitude and opposite in sign

CReal, unequal in magnitude and same in sign

DImaginary

Solution Answer: A

Let f(x) = ax² + bx + c. Roots of opposite sign mean their product c/a < 0.

f(x) + f(−x) = 2ax² + 2c = 0, so x² = −c/a > 0. The roots are x = ±√(−c/a): real, equal in magnitude, opposite in sign.

Q24MCQ

England and Australia play a test series until one team wins 5 matches. No match ends in a draw. In how many ways can the series be won?

A126

B144

C231

D252

Solution Answer: D

If a team wins its 5th match in match n (n = 5 to 9), it won 4 of the first n − 1 matches. That gives C(4,4) + C(5,4) + C(6,4) + C(7,4) + C(8,4) = 1 + 5 + 15 + 35 + 70 = 126 ways.

Either team can win: 2 × 126 = 252.

Q25TITA

A library had a certain number of shelves, and each shelf had an equal number of books. One day, ten shelves were removed from the library, and so each of the remaining shelves needed to hold one more book. A week later, 15 more shelves were removed from the library, and now there were three more books in each shelf than there were in the beginning. How many books are there in the library?

Solution Answer: 900

Let there be s shelves with b books each. Removing 10 shelves: (s − 10)(b + 1) = sb, so s = 10b + 10.

Removing 25 shelves in total: (s − 25)(b + 3) = sb, so 3s = 25b + 75. Substituting: 30b + 30 = 25b + 75, so b = 9 and s = 100.

Books = 100 × 9 = 900.

Q26MCQ

In the following figure, ABC and DEF are right-angled triangles. AB = 12 and DE = 8. BF = FC = CE = 3. What is the area of triangle CFG?

Right triangles ABC (right angle at B, AB = 12) and DEF (right angle at E, DE = 8) on base line BE with BF = FC = CE = 3; AC and DF intersect at G

A3.6 sq units

B4.8 sq units

C7.2 sq units

D9.6 sq units

Solution Answer: A

Place B at (0, 0). Then A = (0, 12), F = (3, 0), C = (6, 0), E = (9, 0) and D = (9, 8).

Line AC: y = 12 − 2x. Line FD: y = (4/3)(x − 3). Solving these gives G = (4.8, 2.4).

Area of CFG = ½ × FC × height of G = ½ × 3 × 2.4 = 3.6 sq units.

Q27TITA

x and y are real numbers that satisfy the inequality: 10x² + y² – 6xy + 17 ≤ 8x + 1. Find the value of y² – x².

Solution Answer: 128

Rearrange: 10x² + y² − 6xy − 8x + 16 ≤ 0, which is (y − 3x)² + (x − 4)² ≤ 0.

A sum of squares can’t be negative, so both are 0: x = 4 and y = 12. Then y² − x² = 144 − 16 = 128.

Q28MCQ

A shopkeeper bought three varieties of mangoes at Rs 100, Rs 80 and Rs 60 per kg and mixed them in the ratio 3:4:5. 1/6th of the mangoes were rotten and hence could not be sold. At what price per kg (approx.) should he sell the remaining mangoes so that he gains 35%?

ARs 103

BRs 86

CRs 124

DRs 112

Solution Answer: C

Take 12 kg: cost = 3 × 100 + 4 × 80 + 5 × 60 = Rs 920. A sixth is rotten, so 10 kg can be sold.

Required revenue = 1.35 × 920 = Rs 1242, so the price is 1242 ÷ 10 = Rs 124.2 ≈ Rs 124 per kg.

Q29MCQ

In the given fig., there are two circles of unit radius and centres P and Q, respectively. What is the area of trapezium PRST?

Two unit circles centred at Q and P, each passing through the other's centre; trapezium PRST with RP a diameter of the circle centred at Q and T a point where the circles intersect

A3√38

B3√32

C4√33

D3√34

Solution Answer: D

Each circle passes through the other’s centre, so QP = 1. Place Q at (0, 0): then R = (−1, 0) and P = (1, 0), and RP = 2 is a diameter.

The circles meet at T = (½, √3/2). S is its mirror image on the circle centred at Q: (−½, √3/2). So ST = 1 and the height is √3/2.

Area = ½ × (2 + 1) × √3/2 = 3√3/4.

Q30MCQ

A family consists of a couple and their daughter. The ratio of the present ages of the father and the daughter is 5:1, while that of the present ages of the mother and the daughter is 4:1. When the daughter was born, the average age of her parents was 28 years. How many years from now will the daughter be half as old as her mother?

A12 years

B14 years

C16 years

D18 years

Solution Answer: C

Let the daughter be d. The father is 5d and the mother 4d. At her birth they were 4d and 3d, with average 3.5d = 28, so d = 8 and the mother is 32.

8 + t = (32 + t)/2 gives t = 16 years.

Day 13 complete! 🔥

0 / 90

Correct: 0 · Wrong: 0 · Accuracy: 0%

Keep the streak alive. See you tomorrow for Day 14.

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