HPAS Prelims 2018 CSAT (Paper II) with Answers & Explanations

Explanation

A cliche is a phrase, expression, or idea that has been used so frequently that it has lost its original impact and novelty, often representing a commonplace or widely repeated saying. In the passage, the statement managers are naturally born is described as a cliche containing some truth. A truism is a statement or common saying that is so obvious or well-known that it goes without saying, often containing a self-evident truth. In this context, both terms refer to widely accepted, unoriginal, and overused statements, making truism the correct synonym.

Explanation

The passage defines management in its very first sentence as getting things done through people. It further clarifies that management involves pointing the way and ensuring that everyone concerned reaches that destination, which directly translates to achieving organizational goals with the assistance and coordination of others.

Explanation

The passage explicitly states that a person's charisma, inspirational qualities, and ways of handling people combine to produce an individual who is widely regarded as a natural leader. This direct reference from the text confirms that these specific attributes are the components that work together to define a natural leader.

Explanation

Charisma refers to a compelling charm, magnetic appeal, or attractiveness that inspires admiration and draws people in. The opposite of this quality is a force or feeling that drives people away or causes intense distaste. Repulsion represents a feeling of strong dislike or a force that drives away, making it the direct antonym of charisma.

Explanation

The first blank precedes "Orient", which begins with a vowel sound, requiring the indefinite article "an". The second blank precedes "Longman", which begins with a consonant sound, requiring the indefinite article "a".

Explanation

In English grammar, the noun separation is idiomatically followed by the preposition from when expressing the act of parting or being kept apart from a specific person. Therefore, the phrase separation from me correctly conveys the meaning of the children being unable to bear being parted or distanced from their parent.

Explanation

A ruminant is a herbivorous mammal that acquires nutrients from plant-based food by fermenting it in a specialized stomach prior to digestion, principally through microbial actions. This process, known as rumination, involves regurgitating partially digested food, called cud, and chewing it again to break down the tough plant matter further. Examples of ruminant animals include cattle, sheep, goats, buffaloes, deer, and giraffes.

Explanation

The coordinating conjunction or is used to connect two independent clauses where the second clause represents the negative consequence or alternative result of the first clause not happening. In this sentence, the act of dying is the direct consequence of not receiving something to drink, which makes or the correct conjunction to show this relationship.

Explanation

The term gourmet refers to a person with a refined palate and deep appreciation for high-quality, finely prepared food and drink. Derived from the French language, it describes someone who has expert knowledge of culinary arts and is a connoisseur of gastronomy.

Explanation

Amnesty is an official, general pardon granted by a government to a group of individuals, typically political offenders, which restores them to the status of innocent citizens. This term originates from the Greek word amnestia, meaning forgetfulness or oblivion, representing a sovereign state's decision to formally overlook and forgive past political transgressions.

Explanation

The phrasal verb make out means to understand, decipher, or comprehend something that is unclear or difficult. In the given sentence, it correctly expresses the inability to grasp or comprehend the meaning of the passage.

Explanation

The sentence uses a superlative adjective (the most fussy) to describe a person, which is typically followed by a clause in the present perfect tense to express an experience up to the present moment. The structure "subject + is + superlative + that + subject + have/has + ever + past participle" is the standard grammatical construction for such comparative experiences. Therefore, "have ever" correctly completes the sentence to show that Loveleen is the most fussy girl the speaker has encountered in their life up to the current moment.

Explanation

The phrasal verb set aside means to declare a legal decision, judgment, or decree to be invalid, void, or annulled. In legal terminology, when a court cancels or overturns a previous decree, order, or ruling, it is said to set aside the decree. This fits the context of the sentence where the Honourable Court invalidates the decree.

Explanation

The phrasal verb "put down" means to suppress, crush, or stop a rebellion, mutiny, or riot by force. In this context, it perfectly fits the sentence to describe how the French Government crushed the rebellion using a firm hand.

Explanation

The phrasal verb put up with means to tolerate, endure, or accept an unpleasant situation or condition without complaining. In the given sentence, the preposition with is already present immediately after the blank space. Therefore, inserting put up completes the phrasal verb put up with, which perfectly fits the context of institutions having to tolerate a large amount of noise.

Explanation

The word cumbersome is an adjective that describes something large, heavy, difficult to carry, or hard to manage and complete due to its complexity or difficulty. In this context, it appropriately describes a task that is physically demanding, slow, and challenging for the cadets to undertake, such as crossing a mountain.

Explanation

The provided newspaper report explicitly states that the flight I.C.764, which was scheduled to leave Delhi for Calcutta at 4:40 p.m., was cancelled suddenly and inexplicably without a word of explanation or apology. Therefore, no explanation was given by the airlines for the cancellation of this flight.

Explanation

The author explicitly states in the passage that the bungling at the Delhi airport confirmed that its monopoly position had made Indian Airlines as callous as it is inefficient. The text describes a sequence of logistical failures, broken promises by airport officials, the failure of the duty officer to update the computer records despite confirming the tickets, and the rude behavior of the staff, all of which directly attributes the entire chaotic episode to the deep-seated mismanagement and callousness of the airline management.

Explanation

The passage explicitly describes the actions of the Duty Officer, D.S. Jolly, as part of a fraud practiced on the passengers. He readily signed and wrote O.K. on the tickets to pacify the stranded passengers and defuse the immediate confrontation at the departure lounge. However, by omitting the essential step of punching the entry into the computer system, he rendered the physical endorsements completely useless for the next day. This deliberate omission allowed him to temporarily escape the difficult situation while knowing the passengers would not actually be registered for the flight.

Explanation

The passage describes that the stranded passengers of flight I.C.764, who had been transferred to the Wednesday morning flight I.C.401, were finally taken aboard on Wednesday. This boarding was preceded by an acrimonious argument and uproarious confusion, as the passengers vehemently disputed the chain of half-truths, falsehoods, and extreme rudeness exhibited by the airline personnel.

Explanation

The author makes this comment because of the severe mismanagement, lack of accountability, and callous attitude displayed by a monopolistic organization like Indian Airlines. Throughout the passage, the author details a sequence of administrative failures, including sudden flight cancellations without apology, unfulfilled guarantees of alternative seating, and fraudulent ticket endorsements by airport officials. These persistent issues, combined with the rude behavior of the staff, highlight how the absence of competition in a bureaucratic monopoly breeds inefficiency and poor service, making such an institution unworthy of the country and its citizens.

Explanation

In the passage, the author uses the term churlishness to describe the rude, unsympathetic, and ill-mannered behavior of the Indian Airlines staff. This is directly illustrated in the preceding sentence, where stranded passengers, including women and children, were told to rebook their tickets for the next day without receiving any apology for the massive delay and inconvenience, and without the airline offering any responsibility or compensation for their overnight stay and meals in Delhi.

Explanation

The author explicitly expresses all three views in the newspaper report. First, the author asserts in the opening sentence that the monopoly position of Indian Airlines has made it as callous as it is inefficient. Second, the author states that the excuses and explanations from the airlines long ago ceased to command credence. Finally, the author concludes by stating that if the government wishes to serve the flying public better, it must allow some form of competition to save passengers from such harassment. Since all three individual statements are directly supported by the passage, they are all true.

Explanation

The word abundant means existing or available in large quantities, overflowing, or more than sufficient. The word plentiful is a direct synonym that also means existing in great quantity or abundance, making it the most accurate term to describe a large and sufficient quantity of data in this context.

Explanation

The word redundant means exceeding what is necessary or normal, or being no longer needed or useful. Superfluous also refers to being unnecessary, especially through being more than enough. Both words represent something that is excess or extra to requirements, making them direct synonyms in the context of writing and language.

Explanation

The word impending refers to something, particularly an event that is unpleasant or unwelcome, that is about to happen or looming in the near future. Similarly, the word imminent describes an event that is on the verge of taking place, fast-approaching, or occurring very soon. In the context of a disaster, both terms signify that the event is about to happen.

Explanation

The word handy means useful, easy to use, or helpful in a practical way. In the given context, grouping stars by constellation provides an easy and practical method to map the sky, which makes convenient the most appropriate synonym as it refers to something that fits in well with peoples needs, activities, or plans, saving time or effort.

Explanation

The word insolvent describes a financial state where an individual or entity is unable to pay their debts as they fall due. Bankrupt is the precise synonym for this condition, representing the formal or legal status of being insolvent and unable to satisfy outstanding financial obligations to creditors.

Explanation

The word lynch refers to the act of a mob killing someone, especially by hanging, for an alleged offense without any legal trial. Since lynching is essentially a form of extrajudicial execution, the term most nearly synonymous with it in general meaning is kill.

Explanation

A rebate is a portion of a payment or tax that is returned or given back to the payer after the full amount has been paid. Because it represents a repayment of money previously paid, it is most nearly synonymous with a refund.

Explanation

By comparing the letters of the words with their corresponding code symbols in the same positions, the individual letter codes are identified as follows:

From GONE, G is coded as 5, O is coded as %, N is coded as 2, and E is coded as #.

From MEDAL, M is coded as 4, E is coded as #, D is coded as 3, A is coded as , and L is coded as @.

Using these letter-to-symbol mappings for the word GOLD, G becomes 5, O becomes %, L becomes @, and D becomes 3. Combining these in order gives the code 5%@3.

Explanation

The coding follows a pattern where the letters of the word are shifted forward alternately by +3 and +2 positions, with the resulting code written in lowercase.

For the word COMPUTER: C + 3 = f O + 2 = q M + 3 = p P + 2 = r U + 3 = x T + 2 = v E + 3 = h R + 2 = t

Applying this alternating +3, +2 shift pattern to the word LANGUAGE: L + 3 = o A + 2 = c N + 3 = q G + 2 = i U + 3 = x A + 2 = c G + 3 = j E + 2 = g

This yields the coded sequence ocqixcjg.

Explanation

Assume all five friends are facing North, meaning their right and left match our right and left.

The statement that only M is between L and S implies that the sequence must be either L-M-S or S-M-L.

The statement that N is to the immediate right of S dictates that N must be placed directly to the right of S. This requirement is only satisfied by the L-M-S configuration, yielding the sequence L-M-S-N. In the alternative S-M-L configuration, the position immediately to the right of S is already occupied by M.

The statement that R is to the immediate left of L allows us to place R directly to the left of L.

Combining these clues gives the final order of the five friends from left to right as R-L-M-S-N.

In this arrangement of five individuals, the third position represents the middle of the row, which is occupied by M.

Explanation

The starting position of Hemant is designated as the origin (0, 0).

His movements can be mapped on a Cartesian coordinate system as follows: First, he walks 4 meters North to the coordinate (0, 4). Next, he turns 90° right, which is East, and moves 3 meters to (3, 4). Then, he turns 90° right, which is South, and walks 4 meters to (3, 0). From there, he turns 90° left, which is East, and moves 1 meter to (4, 0). Finally, he turns 90° right, which is South, and moves 3 meters to his destination at (4, -3).

The total horizontal displacement from the starting point is 4 meters East, and the total vertical displacement is 3 meters South.

Using the Pythagorean theorem, the straight-line distance d between the starting point (0, 0) and the final destination (4, -3) is calculated as: d = √(4² + (-3)²) d = √(16 + 9) d = √25 d = 5 meters

Explanation

From the given information, A is a male and is married to B, who is a female. C is the brother of A. B is the daughter-in-law of F, which means F is the parent of B's husband, A. Since the husband of F has died, F is a female. Therefore, F is the mother of A.

Explanation

C is the brother of A. D is the son of C. Since E is the sister of D, both D and E are children of the same parent, C. Because E is female, she is the daughter of C.

Explanation

A and B are a married couple, where A is the husband (male) and B is the wife (female). C is the brother of A. Since C is the brother of B's husband, C is the brother-in-law of B.

Explanation

We determine the gender of each of the six family members from the given relations:

First, A and B are a married couple with A being the male member. This means A is male and B is female.

Second, C is the brother of A, which means C is male.

Third, D is the only son of C, which means D is male.

Fourth, E is the sister of D, which means E is female.

Fifth, B is the daughter-in-law of F, whose husband has died. Since B is married to A, F is the mother of A and C. F is female.

The male members in the family are A, C, and D, giving a total of three male members.

Explanation

A and B are a married couple with A being the male member and B being the female member. C is the brother of A, which means A and C are brothers who share the same parents. B is the daughter-in-law of F, meaning F is the parent of B's husband, A. Since the husband of F has died, F is a female, making her the mother of A. Since A and C are brothers, F is also the mother of C.

Explanation

The refresher course spans from 22nd May to 29th May. Since 23rd May is Sunday, we can map the days of the week for each date as follows: 22nd May is Saturday 23rd May is Sunday (Holiday) 24th May is Monday 25th May is Tuesday 26th May is Wednesday 27th May is Thursday 28th May is Friday 29th May is Saturday

By applying the given conditions: Psychology is scheduled on the first day, which is 22nd May (Saturday). Mechanics is scheduled on the last day, which is 29th May (Saturday). Philosophy is scheduled after the holiday on 24th May (Monday). Economics is scheduled after Philosophy. Science is scheduled on the day immediately preceding Engineering. There is a one-day gap between Economics and Engineering, establishing the consecutive sequence of Economics, Science, and Engineering. Placing this sequence in the remaining open days, Economics is scheduled on 25th May (Tuesday), Science on 26th May (Wednesday), and Engineering on 27th May (Thursday). Sociology is scheduled on 28th May (Friday).

Explanation

Based on the given constraints, we can determine the sequence of subjects from 22nd May to 29th May:

Since the course must start with Psychology, 22nd May is Psychology.

23rd May is a Sunday holiday.

Philosophy is scheduled after the holiday, on 24th May.

Economics is scheduled after Philosophy, on 25th May.

Since Science must be on the day before Engineering, and there must be a one-day gap between Economics and Engineering, Science is scheduled on 26th May and Engineering is scheduled on 27th May.

The course ends with Mechanics on 29th May.

Therefore, the only remaining subject, Sociology, must be scheduled on 28th May. Sociology is the subject that precedes Mechanics.

Explanation

By analyzing the given conditions, we can schedule the courses from 22nd May to 29th May as follows:

Psychology must start the course, so it is scheduled on 22nd May. 23rd May is a holiday. Philosophy is scheduled after the holiday, on 24th May. Economics is scheduled after Philosophy, on 25th May. Science must be on the day before Engineering, and there is a 1-day gap between Economics (25th May) and Engineering. Therefore, Science is on 26th May and Engineering is on 27th May. Sociology is scheduled on 28th May. Mechanics ends the course on 29th May.

The complete schedule is: 22nd May: Psychology 23rd May: Holiday 24th May: Philosophy 25th May: Economics 26th May: Science 27th May: Engineering 28th May: Sociology 29th May: Mechanics

Science is scheduled on 26th May and Philosophy is scheduled on 24th May. There is exactly a 1-day gap (25th May) between Science and Philosophy.

Explanation

To determine the schedule of the refresher courses from 22nd May to 29th May, we can map out the 8-day timeline:

May 22: Psychology (Starts with Psychology) May 23: Holiday (Sunday) May 24 to May 28: Slots for Philosophy, Sociology, Economics, Science, and Engineering May 29: Mechanics (Ends with Mechanics)

We are given that Science must be on the day immediately preceding Engineering, creating a consecutive block of Science followed by Engineering.

Additionally, there must be a gap of exactly one day between Economics and Engineering. This placement requires Science to be scheduled between Economics and Engineering, resulting in the sequence: Economics, Science, Engineering.

Since Science is scheduled on the day prior to Engineering, the subject that follows Science is Engineering.

Explanation

According to the given statements, let X represent xivs, T represent trax, and F represent finix.

The first statement, all xivs are trax, establishes that the set of xivs is a subset of trax (X ⊆ T). The second statement, all trax are finix, establishes that the set of trax is a subset of finix (T ⊆ F).

By the transitive property of set inclusion, if X ⊆ T and T ⊆ F, then X ⊆ F. This means that all xivs are finix, which directly validates conclusion II.

Explanation

The statement Some computers are telephones means there is a common intersection between the set of computers and the set of telephones. The second statement All telephones are elephants means the entire set of telephones is a subset of the set of elephants. Since the telephones that intersect with computers are entirely contained within the set of elephants, it logically follows that some computers are also elephants. This makes conclusion I definitely true. Conclusion II, which states that All telephones are computers, does not logically follow because we only know that some computers are telephones, and we cannot assume the reverse holds for all telephones. Therefore, only conclusion I follows.

Explanation

Neither statement establishes any direct link between ears and teeth, so neither conclusion can be independently derived from the given premises. However, Conclusion I ('No tooth is ear') and Conclusion II ('Some ears are teeth') are contradictory propositions forming a complementary pair, so one of them must be true. Therefore, either conclusion I or II follows.

Explanation

The first statement establishes that the set of hives is completely contained within the set of shells. The second statement asserts that there is no overlap between the set of shells and the set of houses. Because hives are entirely inside the set of shells, and shells have absolutely no connection with houses, it is impossible for any hive to be a house. This logically validates Conclusion I, which states that no hive is a house. Conversely, because no shell is a house, there can be no overlap between houses and shells, making Conclusion II false. This confirms that only conclusion I follows.

Explanation

To find the code for the word sweet, compare Statement I cod dex nou representing banana is sweet with Statement IV da ber nou representing oranges are sweet. The only common word between the two English sentences is sweet, and the corresponding common code between the two coded sentences is nou. This directly establishes that nou stands for sweet.

Explanation

By comparing statements I and II, the common code is 'dex' and the common word is 'is'. Thus, 'dex' represents 'is'.

By comparing statements II and III, the common code is 'hux' and the common word is 'furniture'. Thus, 'hux' represents 'furniture'.

In statement II, 'piz dex hux' represents 'furniture is good'. Since 'dex' represents 'is' and 'hux' represents 'furniture', the remaining code 'piz' must represent the remaining word 'good'.

Explanation

The given jumbled letters are E (1), C (2), K (3), P (4), T (5), and O (6). Rearranging these letters forms the meaningful English word POCKET.

Mapping each letter of the word POCKET to its corresponding number: P corresponds to 4 O corresponds to 6 C corresponds to 2 K corresponds to 3 E corresponds to 1 T corresponds to 5

Arranging these numbers in the sequence of the word POCKET yields 462315.

Explanation

Arranging the numbered letters according to the sequence 4152736 forms the meaningful English word STELLAR. In this arrangement, 4 corresponds to S, 1 corresponds to T, 5 corresponds to E, 2 corresponds to L, 7 corresponds to L, 3 corresponds to A, and 6 corresponds to R.

Explanation

The jumbled letters R (1), I (2), T (3), P (4), I (5), O (6), M (7), X (8), Y (9) can be rearranged to form the meaningful English word PROXIMITY.

Using the letter positions from the given options, the number sequence 416827539 maps to the letters as follows: 4 corresponds to P 1 corresponds to R 6 corresponds to O 8 corresponds to X 2 corresponds to I 7 corresponds to M 5 corresponds to I 3 corresponds to T 9 corresponds to Y

This successfully spells out the word PROXIMITY, which means nearness in space, time, or relationship.

Explanation

The letters A, N, C, T, I, B, E correspond to the numbers 1, 2, 3, 4, 5, 6, 7. Arranging these numbers in the order of 3165274 yields:

3 -> C 1 -> A 6 -> B 5 -> I 2 -> N 7 -> E 4 -> T

This forms the meaningful English word CABINET.

Explanation

From Statement I, we have the equation 3p = 2q. By dividing both sides of the equation by 3q, we get p/q = 2/3. This directly gives the unique ratio p:q as 2:3. Therefore, Statement I alone is sufficient to answer the question.

From Statement II, we have the equation 2p + q = 6. This is a single linear equation with two variables, which has infinitely many solutions for p and q. For example, if p = 2, then q = 2, giving a ratio p:q of 1:1. If p = 1, then q = 4, giving a ratio p:q of 1:4. Because different values of p and q yield different ratios, Statement II alone is not sufficient to determine a unique ratio.

Explanation

From Statement I, solving the quadratic equation n² - 10n + 9 = 0 gives (n - 1)(n - 9) = 0. This yields two possible integer values for n, which are n = 1 or n = 9. Statement I alone is not sufficient because it does not provide a single unique value.

From Statement II, the inequality is given as 1/6 > 1/(n - 1) > 1/9. Taking the reciprocals reverses the inequality signs, resulting in 6 < n - 1 < 9. Adding 1 to each term gives 7 < n < 10. The possible integer values for n in this range are n = 8 or n = 9. Statement II alone is not sufficient because it does not provide a single unique value.

Combining both statements, the only integer value of n that satisfies both conditions is n = 9.

Explanation

Analyzing Statement I: We are given that 100n is a four-digit number. The range for a positive four-digit integer is from 1000 to 9999. Thus, we have the inequality 1000 ≤ 100n ≤ 9999. Dividing all parts of the inequality by 100, we obtain 10 ≤ n ≤ 99.99. Since n is an integer, n must lie in the range from 10 to 99. Any integer in this range is a two-digit number. If we consider negative four-digit numbers, the inequality becomes -9999 ≤ 100n ≤ -1000, which yields -99 ≤ n ≤ -10, representing negative two-digit numbers. In either case, Statement I alone is sufficient to answer that n is a two-digit number.

Analyzing Statement II: We are given that n² is a four-digit number. Since squares of real numbers are non-negative, n² must be a positive four-digit number, meaning 1000 ≤ n² ≤ 9999. Taking the square root of all parts of the inequality gives √1000 ≤ |n| ≤ √9999. Since 31² = 961 and 32² = 1024, the minimum integer value for the magnitude of n is 32. Since 99² = 9801 and 100² = 10000, the maximum integer value for the magnitude of n is 99. This gives the range 32 ≤ |n| ≤ 99. Therefore, n must be an integer from 32 to 99 or from -99 to -32. Every integer in these ranges is a two-digit number. Thus, Statement II alone is also sufficient to answer the question.

Explanation

The average of five numbers p, q, r, s, and t is defined as (p + q + r + s + t) / 5.

From statement I, the average of p, q, and r is m, which gives the sum p + q + r = 3m.

From statement II, the average of s and t is n, which gives the sum s + t = 2n.

Combining both statements, the total sum of all five variables is 3m + 2n. The average of all five variables is therefore (3m + 2n) / 5. This shows that both statements I and II together are necessary and sufficient to answer the question.

Explanation

The terms in the sequence follow a pattern where the differences between consecutive terms increase by 2.

72 - 56 = 16 90 - 72 = 18 110 - 90 = 20

Following this pattern, the next difference should be 22: 110 + 22 = 132

The next difference would then be 24: 132 + 24 = 156

Alternatively, each term in the sequence can be expressed in the form n × (n + 1) for consecutive integers: 7 × 8 = 56 8 × 9 = 72 9 × 10 = 90 10 × 11 = 110 11 × 12 = 132 12 × 13 = 156

Thus, the number 130 is incorrect and should be 132.

Explanation

The differences between consecutive terms in the given sequence are: 13 − 8 = 5 21 − 13 = 8 32 − 21 = 11 47 − 32 = 15 63 − 47 = 16 83 − 63 = 20

The first three differences (5, 8, and 11) increase by a constant value of 3. This indicates that the sequence of differences should form an arithmetic progression with a common difference of 3. Following this pattern, the subsequent differences must be 14, 17, and 20.

Applying these correct differences to the terms of the sequence: The term after 32 should be 32 + 14 = 46. The term after 46 should be 46 + 17 = 63. The term after 63 should be 63 + 20 = 83.

This series of calculations perfectly aligns with the rest of the sequence, which proves that the number 47 is incorrect and should be replaced by 46.

Explanation

The sequence is formed by the formula n³ - 1, where n is the position of the term starting from n = 1.

Applying this formula to each term: For n = 1: 1³ - 1 = 0 For n = 2: 2³ - 1 = 7 For n = 3: 3³ - 1 = 26 For n = 4: 4³ - 1 = 63 For n = 5: 5³ - 1 = 124 For n = 6: 6³ - 1 = 215 For n = 7: 7³ - 1 = 342

The sixth term in the sequence is given as 217, but according to the pattern, it must be 215.

Explanation

The sequence follows a systematic mathematical progression where each subsequent term is obtained by multiplying the preceding term by a factor that increases by 0.5 at each step, and then adding that same factor.

The first term is 7. The second term is 7 × 0.5 + 0.5 = 4. The third term is 4 × 1 + 1 = 5. The fourth term is 5 × 1.5 + 1.5 = 9. The fifth term is 9 × 2 + 2 = 20. The sixth term must be 20 × 2.5 + 2.5 = 52.5. The seventh term is 52.5 × 3 + 3 = 160.5.

In the given sequence, the value 51 is written instead of 52.5, which makes it the wrong number in the series.

Explanation

The sequence follows the mathematical pattern where each subsequent number is obtained by multiplying the previous number by 2 and then subtracting 2.

6 × 2 - 2 = 10 10 × 2 - 2 = 18 18 × 2 - 2 = 34 34 × 2 - 2 = 66 66 × 2 - 2 = 130 130 × 2 - 2 = 258

Following this consistent rule, the third term in the sequence should be 18 instead of 14.

Explanation

The given series can be broken down into alternating descending sequences (starting with 9) and ascending sequences (starting with 1). In each successive block, the last digit from either the descending or the ascending part is omitted alternately.

Segment 1: Descending: 9 8 7 6 (length 4) Ascending: 1 2 3 4 5 (length 5)

Segment 2: Descending: 9 8 7 (the last digit 6 from the previous descending sequence is omitted, length 3) Ascending: 1 2 3 4 5 (length 5)

Segment 3: Descending: 9 8 7 (length 3) Ascending: 1 2 3 4 (the last digit 5 from the previous ascending sequence is omitted, length 4)

Segment 4: Descending: 9 8 (the last digit 7 from the previous descending sequence is omitted, length 2) Ascending: starts with 1

Since the descending sequence of Segment 4 (9 8) is complete, the next term must be the start of the subsequent ascending sequence, which is 1.

Explanation

The given sequence is an alternating series made up of two distinct interleaved series.

The first series consists of the letters at the odd positions: 1st term: A (1) 3rd term: B (2) 5th term: C (3) 7th term: D (4) 9th term: E (5)

This sequence consists of consecutive letters of the alphabet.

The second series consists of the letters at the even positions: 2nd term: B (2) 4th term: D (4) 6th term: F (6) 8th term: H (8) 10th term: J (10)

This sequence consists of letters with even alphabetical positions, increasing by 2.

The next term in the series is the 11th term, which belongs to the first series. Following E, the next consecutive letter is F.

Explanation

The given letter series is formed by repeating the reverse alphabetical sequence starting from the letter I, with each subsequent group being shortened by two letters from the end:

First group: I H G F E D C B A (9 letters, ending at A) Second group: I H G F E D C (7 letters, ending at C) Third group: I H G F E (5 letters, ending at E)

Following this pattern, the fourth group must contain 3 letters (I H G). The letter immediately following the end of the third group (E) is the start of this fourth group, which is I.

Explanation

The series is: 9 7 5 3 1 1 8 6 4 2 2 9 7 5 3 1 8 6 4 2 2 9 7 5 3 1 8 6 4 2 9 7 5

The series consists of alternating groups of descending odd numbers (starting from 9) and descending even numbers (starting from 8), with a systematic change in the trailing repetition pattern across successive groups:

Group 1 (odd): 9 7 5 3 1 1 — last digit (1) is repeated Group 2 (even): 8 6 4 2 2 — last digit (2) is repeated Group 3 (odd): 9 7 5 3 1 — no repetition of the last digit Group 4 (even): 8 6 4 2 2 — last digit (2) is repeated Group 5 (odd): 9 7 5 3 1 — no repetition Group 6 (even): 8 6 4 2 — no repetition (last digit 2 is dropped entirely) Group 7 (odd): 9 7 5 ... — continues the descending odd pattern

In Group 7, the sequence follows the descending odd pattern 9, 7, 5, and the next number must be 3.

The answer is 3, which corresponds to option C.

Explanation

The number series is constructed by concatenating groups of sequential integers that always start with 2, with each subsequent group containing one more term than the previous group.

First group: 2 Second group: 2, 3 Third group: 2, 3, 4 Fourth group: 2, 3, 4, 5 Fifth group: 2, 3, 4, 5, 6 Sixth group: 2, 3, 4, 5, 6, 7

The provided sequence lists the terms up to the fifth term of the sixth group (2, 3, 4, 5, 6). Therefore, the next number in this sequence is 7.

Explanation

To find the numeric numbers that satisfy the given conditions, we need to locate digits that are immediately followed by a vowel (A, E, I, O, U) but not immediately preceded by another digit. The pattern we are looking for is: (Non-digit) (Digit) (Vowel).

Analyzing the given arrangement: A 8 B 6 # 7 H U % 3 F V R 2 I @ 4 1 W E 9 © L 5

Let us examine each digit in the sequence: 8 is followed by B (consonant). 6 is followed by # (symbol). 7 is followed by H (consonant). 3 is followed by (symbol). 2 is followed by I (vowel) and preceded by R (non-digit). This satisfies the condition. 4 is followed by 1 (digit). 1 is followed by W (consonant). 9 is followed by © (symbol). 5 is at the end of the sequence and not followed by any element.

Thus, there is only one such numeric number (2) in the arrangement that is immediately followed by a vowel and not immediately preceded by a numeric number.

Explanation

To find the symbols that are immediately followed by a consonant and immediately preceded by a number, we look for the pattern: Number → Symbol → Consonant.

Analyzing the symbols in the given arrangement:

The symbol is preceded by the number 3 and followed by the consonant F, which gives the valid group 3 F.

The symbol © is preceded by the number 9 and followed by the consonant L, which gives the valid group 9 © L.

No other symbols in the arrangement satisfy both conditions simultaneously. Thus, there are exactly two such symbols.

Explanation

The given arrangement is: A 8 B 6 # 7 H U % 3 F V R 2 I @ 4 1 W E 9 © L 5

The symbols present in the arrangement are: #, %, , @, and ©.

After dropping all symbols, the remaining elements in order are: A 8 B 6 7 H U 3 F V R 2 I 4 1 W E 9 L 5

Counting from the left end of the modified sequence: 1st: A 2nd: 8 3rd: B 4th: 6 5th: 7 6th: H 7th: U 8th: 3

The eighth element from the left end is 3, which corresponds to option D.

Explanation

The original number is 7346285.

Arranging the digits of this number in ascending order gives 2345678.

Comparing the positions of the digits in both sequences:

Original: 7 3 4 6 2 8 5 Sorted: 2 3 4 5 6 7 8

The digits 3 and 4 occupy the second and third positions respectively in both the original and sorted arrangements. Since only these two digits remain in their original positions, there are exactly two such digits.

Explanation

To compare numbers with large exponents, we simplify them by finding the greatest common divisor of the exponents. The exponents are 50, 40, 30, and 20, and their greatest common divisor is 10.

By rewriting each expression with a common outer exponent of 10, we get:

3⁵⁰ = (3⁵)¹⁰ = 243¹⁰ 4⁴⁰ = (4⁴)¹⁰ = 256¹⁰ 5³⁰ = (5³)¹⁰ = 125¹⁰ 6²⁰ = (6²)¹⁰ = 36¹⁰

Comparing the simplified bases directly reveals that 256 is the largest base. Since 256 is greater than 243, 125, and 36, raising it to the power of 10 yields the largest overall value. This confirms that 4⁴⁰ is the greatest number.

Explanation

Using the property of square roots, shifting the decimal point inside the square root by 2n places to the left shifts the decimal point of the square root value by n places to the left.

Given that √5329 = 73, the individual terms can be evaluated directly:

√53.29 = 7.3 √0.5329 = 0.73 √0.005329 = 0.073 √0.00005329 = 0.0073

Adding these values together:

73 + 7.3 + 0.73 + 0.073 + 0.0073 = 81.1103

Explanation

Let a = 0.75.

The given expression can be written as: a³ / (1 - a) + (a² + a + 1)

By taking the common denominator (1 - a), the expression becomes: [a³ + (1 - a)(a² + a + 1)] / (1 - a)

Using the algebraic identity (1 - a)(1 + a + a²) = 1 - a³, the numerator simplifies directly: [a³ + 1 - a³] / (1 - a) = 1 / (1 - a)

Substituting a = 0.75 back into the simplified expression: 1 / (1 - 0.75) = 1 / 0.25 = 4

Taking the square root of this value: √4 = 2

Explanation

Rationalizing each term by multiplying and dividing by its conjugate yields:

√a - √b = (√a - √b)(√a + √b) / (√a + √b) = (a - b) / (√a + √b)

Applying this to each of the given numbers, where the difference between the terms inside the square root is consistently 2:

√7 - √5 = 2 / (√7 + √5) √5 - √3 = 2 / (√5 + √3) √9 - √7 = 2 / (√9 + √7) √11 - √9 = 2 / (√11 + √9)

Since the numerator is 2 in all cases, the value of the fraction is largest when the denominator is smallest. Among the denominators, √5 + √3 is the smallest. Thus, the largest value is √5 - √3.

Explanation

Let x = √(7√(7√(7...)))

Squaring both sides of the equation: x² = 7√(7√(7...)) x² = 7x

Since x is greater than 0, we can divide both sides by x to get: x = 7

Thus, the left-hand side value is 7.

Now, equating this to the right-hand side, which is written as 343⁽y - 1): 7 = 343⁽y - 1)

Since 343 is 7³, we can rewrite the equation as: 7¹ = (7³)⁽y - 1) 7¹ = 7⁽3(y - 1))

By equating the exponents of the base 7: 1 = 3(y - 1) 1 = 3y - 3 3y = 4 y = 4/3

Explanation

Evaluating the values of x, y, and z:

For x: x = (0.08)² = 0.0064, which is a small positive number.

For y: y = 1 / (0.08)² = 1 / 0.0064 = 156.25, which is a large positive number.

For z: z = (1 - 0.08)² - 1 = (0.92)² - 1 = 0.8464 - 1 = -0.1536, which is a negative number.

Comparing the three values, since z is negative, x is a small positive number, and y is a large positive number, we get the relation z < x < y.

Explanation

We need to find the value of x⁴ - 17x³ + 17x² - 17x + 17 at x = 16.

Since x = 16, we note that 17 = x + 1. Substituting 17 = (x + 1) into every occurrence of 17 in the expression:

x⁴ - (x+1)x³ + (x+1)x² - (x+1)x + (x+1) = x⁴ - x⁴ - x³ + x³ + x² - x² - x + x + 1 = 1

All terms cancel except the final +1, giving the value 1.

Verification by direct substitution: substituting 17 = (x+1) only in the first three coefficient terms and leaving the constant as 17: x⁴ - (x+1)x³ + (x+1)x² - (x+1)x + 17 = -x + 17 = -16 + 17 = 1

Both approaches confirm the answer is 1, which corresponds to option B.

Explanation

According to the divisibility rule of 11, a number is divisible by 11 if the difference between the sum of the digits at odd positions and the sum of the digits at even positions is either 0 or a multiple of 11.

For the number 738A6A, we compute these sums: Sum of digits at odd positions = 7 + 8 + 6 = 21 Sum of digits at even positions = 3 + A + A = 3 + 2A

The difference between these sums is: 21 - (3 + 2A) = 18 - 2A

For the number to be divisible by 11, this difference must be 0 or a multiple of 11. Since A is a single-digit integer, we set the difference to 0: 18 - 2A = 0 2A = 18 A = 9

Explanation

To find the distance between Pintu's house and his school, we can use the standard relation between speed, distance, and time. Let the distance be d km.

When walking at 3 km per hour, Pintu is 5 minutes late, and when walking at 4 km per hour, he is 5 minutes early. The total difference in time between the two journeys is 5 - (-5) = 10 minutes, which is equal to 10/60 hour, or 1/6 hour.

The formula for the distance d when speeds S₁ and S₂ and the difference in time Δt are known is: d = (S₁ × S₂) ÷ (S₂ - S₁) × Δt

Substituting S₁ = 3 km/h, S₂ = 4 km/h, and Δt = 1/6 hour: d = (3 × 4) ÷ (4 - 3) × 1/6 d = 12 ÷ 1 × 1/6 d = 2 km

Explanation

Let the unknown number replacing both question marks be x.

The given equation is: x / 576 = 256 / x

By cross-multiplying, we obtain: x² = 256 × 576

Taking the square root on both sides: x = √(256 × 576) x = √256 × √576

Since √256 = 16 and √576 = 24, the equation simplifies to: x = 16 × 24 x = 384

Explanation

Express all the terms on the left-hand side with base 2:

8¹.¹ = (2³)¹.¹ = 2³.³ 4².⁷ = (2²)².⁷ = 2⁵.⁴ 2³.³ = 2³.³

Applying the law of exponents where aᵐ × aⁿ = a⁽m+n):

2³.³ × 2⁵.⁴ × 2³.³ = 2⁽3.3 + 5.4 + 3.3) = 2¹²

Equating this to the right-hand side:

2¹² = 2^?

Comparing the exponents on both sides gives ? = 12.

Explanation

Let x = 1.242424...

Multiplying both sides by 100 to shift the decimal point past the first repeating block: 100x = 124.242424...

Subtracting the first equation from the second: 100x - x = 124.242424... - 1.242424... 99x = 123 x = 123/99

To express this fraction in its simplest form where p and q have no common factors, divide both the numerator and denominator by their greatest common divisor, which is 3: p/q = (123 ÷ 3)/(99 ÷ 3) = 41/33

Here, p = 41 and q = 33 are positive integers with no common factors.

The sum of p and q is: p + q = 41 + 33 = 74

Explanation

Let the original fraction be x/y.

When the numerator x is increased by 800%, the new numerator becomes x + 8x = 9x.

When the denominator y is increased by 300%, the new denominator becomes y + 3y = 4y.

The resulting fraction is given as 9/7. Therefore:

9x / 4y = 9/7

Multiplying both sides by 4/9 to isolate x/y:

x/y = (9/7) × (4/9) = 4/7

Explanation

First, calculate ³/₅ of 735: (³/₅) × 735 = 3 × 147 = 441

Next, calculate ²/₃ of 633: (²/₃) × 633 = 2 × 211 = 422

To find how much greater the first value is than the second, subtract the second value from the first: 441 − 422 = 19

Explanation

To find the number of females working in scale II, we calculate the total number of employees in scale II and subtract the number of male employees working in scale II.

Total number of employees in scale II = 15% of 1500 = 225

Number of male employees in scale II = 18% of 800 = 144

Number of female employees in scale II = Total employees in scale II - Male employees in scale II = 225 - 144 = 81

Explanation

From the table provided, we extract the Scale V data:

• Total employees in Scale V = 12% of 1500 = 0.12 x 1500 = 180
• Male employees in Scale V = 12% of 800 = 0.12 x 800 = 96
• Female employees in Scale V = Total - Male = 180 - 96 = 84

Ratio of male to female employees in Scale V: = 96 : 84

Dividing both by their GCD (which is 12): = 8 : 7

The ratio of male to female employees working in Scale V is 8 : 7, which corresponds to option C.

Explanation

To find the total number of female employees working in Scales III and IV together, we subtract the total male employees in these scales from the total employees in these scales.

Total employees in Scales III and IV together: Total = 1500 × (19% + 10%) = 1500 × 29% = 435

Total male employees in Scales III and IV together: Males = 800 × (16% + 11%) = 800 × 27% = 216

Total female employees in Scales III and IV together: Females = 435 - 216 = 219

Explanation

Total number of employees in Scale VI is 14% of 1500, which is equal to 1500 × 0.14 = 210.

Number of male employees in Scale VI is 9% of 800, which is equal to 800 × 0.09 = 72.

The percentage of male employees working in Scale VI relative to the total number of employees in that scale is (72 ÷ 210) × 100 = 34.28%.

Rounding off to the nearest integer gives 34%.

Explanation

The total number of employees in Scale VI is 14% of 1500, which is calculated as: 1500 × 14/100 = 210

The number of male employees in Scale VI is 9% of 800, which is calculated as: 800 × 9/100 = 72

The number of female employees in Scale VI is the difference between the total employees and male employees in Scale VI: 210 - 72 = 138

The number of male employees in Scale I is 24% of 800, which is calculated as: 800 × 24/100 = 192

The ratio of female employees in Scale VI to male employees in Scale I is: 138 : 192

Dividing both terms by their greatest common divisor, which is 6, gives the simplified ratio: 23 : 32