IBPS Clerk Prelims 2020 Question Paper with Answers & Explanations

Explanation

The passage explicitly mentions that sleep allows us to consolidate and store memories, clear cognitive-disrupting waste products, and process emotional experiences. By enabling memory consolidation and supporting optimal brain function, sleep directly enhances cognitive activity, thereby improving the ability to acquire knowledge while processing emotional experiences effectively.

Explanation

According to the passage, regeneration of neurons occurs in the cerebral cortex during normal sleep. In a sleep-deprived individual, this neural regrowth and repair is impaired, causing the brain to fail to function optimally. Statement (i) describes a benefit of normal sleep rather than a cause of brain malfunction, while statement (ii) refers to general physical symptoms rather than the physiological cause of brain dysfunction. Therefore, only statement (iii) accurately identifies the cause of brain incompetency in a sleep-deprived person.

Explanation

The phrasal verb "bounce back" means to recover quickly from a difficulty, fatigue, or illness. In the context of the passage, getting a quality good night's sleep helps an individual recover effectively from the physical and mental strain caused by acute or chronic sleep deprivation.

Explanation

The passage establishes that an adult requires 7 to 8 hours of peaceful, quality sleep per day and explicitly defines sleep deprivation as the inability to complete the sufficient sleep time required by a person. Furthermore, it notes that various factors can interfere with the quality of sleep an individual receives. Therefore, sleep deprivation refers to a state caused by inadequate quantity or quality of sleep.

Explanation

According to the passage, safeguarding oneself from sleep deprivation involves adopting several healthy habits to promote better sleep quality. The text explicitly highlights that regular physical activity such as walking, jogging, or swimming helps one sleep better. It also advises avoiding electronic devices right before bedtime because they interfere with sleep, and lists avoiding or limiting alcohol consumption among the key habits for securing a good night's sleep. Therefore, all three measures—getting regular daytime exercise, refraining from electronic gadgets before bed, and limiting alcohol intake—are directly supported by the passage as effective ways to prevent sleep deprivation.

Explanation

The word sufficient means enough to meet a specific requirement or purpose. Adequate shares the exact same meaning of being enough or satisfactory in quantity or degree to satisfy a particular need.

Explanation

The word "induce" means to persuade, influence, or prompt someone to do something, or to bring about a specific action, feeling, or state. Similarly, "encourage" means to persuade, motivate, or give stimulus to someone to act in a certain way. Both terms convey the idea of influencing or giving an impetus to bring about a desired response or outcome.

Explanation

Replenish means to fill something up again, restore stock, or replace consumed supplies. In contrast, exhaust means to completely drain, empty, or use up a resource or supply. Therefore, exhaust serves as the direct antonym of replenish.

Explanation

Part A contains a grammatical error in the use of the preposition. The correct phrase is "slicing a cake into pieces" rather than "between pieces." The preposition "into" is used to indicate division or transformation into parts, whereas "between" refers to a position or relationship involving two or more distinct entities. Replacing "between" with "into" makes the sentence grammatically correct and contextually meaningful.

Explanation

Of two related past actions, the earlier one takes the past perfect and the later one the simple past. Receiving the bad news happened first ('she had received'), and staying up followed it, so part (A) should read 'She stayed up' rather than 'She had stayed up'. The error is in part (A).

Explanation

When two subjects are connected using phrases such as 'as well as', 'along with', or 'together with', the verb agrees in number with the first subject. Here, the first subject is 'He', which is singular. Therefore, the singular verb 'was going' must be used instead of the plural verb 'were going'.

Explanation

The sentence is grammatically correct and contextually meaningful in all its parts. The singular subject "The coaching industry" correctly agrees with the verb "plays", and the pronoun "it" takes the singular verb "contributes". The adjective "significant" appropriately modifies the uncountable noun "revenue", and the prepositions "in" and "to" are used accurately in their respective phrases. Since there are no errors in syntax, subject-verb agreement, or word usage, the sentence requires no correction.

Explanation

The sentence begins with a present simple conditional clause, "If I don't turn on my air conditioner", which establishes a general habit or conditional situation in the present. To maintain proper tense consistency, the main clause must also be in the present tense ("is hot" or "gets hot"). Using the past tense verb "was" creates a grammatically incorrect tense mismatch with the present tense condition.

Explanation

The sentence contains an error in the use of the preposition. The word "too" is an adverb meaning "also" or "excessively," whereas the preposition "to" is required after the verb "happening" to indicate the person affected. Since the sentence expresses a general truth or aphorism, the present continuous tense "is happening" is correctly retained alongside the correct preposition "to".

Explanation

The plural subject pronoun "they" requires the corresponding plural intensive pronoun "themselves" to maintain proper grammatical agreement. Using "himself" creates an agreement error in both number and gender. Additionally, the past perfect auxiliary verb "had" is required to maintain proper verb agreement and tense structure within the clause. Thus, "they themselves had" correctly resolves the pronoun agreement error while maintaining grammatical accuracy.

Explanation

In relative clauses, the relative pronoun "that" replaces the noun "house" and serves as the direct object of the verb "built". Adding the object pronoun "it" creates grammatical redundancy, as the target noun is already represented by the relative pronoun. Omitting the redundant pronoun "it" yields the grammatically correct clause "that Jack built".

Explanation

When a sentence begins with a negative or limiting adverbial phrase such as "In no way", subject-auxiliary inversion is mandatory. The correct structure requires the auxiliary verb to precede the subject: Negative Phrase + Auxiliary Verb + Subject + Main Verb. In this sentence, the auxiliary verb "do" correctly precedes the subject "I" immediately following "In no way". Because subject-auxiliary inversion is properly applied, the sentence is grammatically correct as written.

Explanation

The blank modifies the verb phrase "came about", requiring an adverb to describe how early musical instruments originated. Contextually, the passage explains that instruments arose spontaneously depending on whatever materials happened to be available or from situational triggers like the clamor of battle. This indicates an unplanned, chance-based origin rather than a structured or intentional process, making "randomly" the contextually and grammatically correct adverb.

Explanation

The passage discusses the definition and evolution of musical instruments. The phrase "created or adapted to make musical sounds" refers to objects that were either purpose-built as instruments or modified from existing tools to produce music. The verb adapted accurately expresses the concept of altering or adjusting something to serve a new function, fitting seamlessly with the surrounding context of using available resources for sound production.

Explanation

The sentence requires a verb in the past participle form following the present perfect auxiliary verb "have" ("have also _____"). Contextually, the passage discusses how musical instruments adapted, transformed, and developed over time alongside changing human needs and uses. The word "evolved" correctly fits both the grammatical requirement of a past participle and the contextual meaning of developing or adapting gradually over time in response to ever-changing applications.

Explanation

In blank (21), "depended" is the grammatically and contextually appropriate choice because it forms the standard phrasal combination "depend on" to indicate reliance. The context explains that musical devices relied entirely on the natural resources available to each civilization, which is directly reiterated by the following sentence, "In other words, people worked with what they had." Combined with the auxiliary "have always," the past participle "depended" correctly completes the present perfect construction "have always depended on."

Explanation

Poetry is meant to be spoken aloud or performed orally. In the context of the passage, "recited" accurately describes how traditional poetry was spoken aloud or delivered from memory alongside human noise-makers (early musical instruments) to give it rhythm. Grammatically, "recited" functions correctly as a past participle in the passive voice construction "was recited", fitting both the theme of oral tradition and the sentence structure smoothly.

Explanation

The singular subject "The U.P. ordinance" requires the third-person singular verb "violates" in the first position to form the parallel structure "not only violates guaranteed fundamental rights". In the second position, the prepositional phrase requires the noun "conflict" to form the standard idiom "in conflict with". The adjective "existing" is correctly placed in the third position modifying "personal laws". Swapping the first two words yields the grammatically sound sequence B-A-C.

Explanation

The adjective "abrupt" appropriately modifies the noun "changes" to describe sudden policy decisions. The verb "aggravated" correctly indicates that these changes worsened the situation. The noun "deficit" pairs naturally with "trust" to form the standard political expression "trust deficit." Replacing A with C (abrupt), keeping B (aggravated), and replacing C with A (deficit) gives the correct sequence CBA, producing the meaningful sentence: "The abrupt changes in the sector brought in through the three laws have aggravated the trust deficit of the government."

Explanation

Replacing the bold words in the sequence BCA places "embraced" in position A, "strategy" in position B, and "aftermath" in position C. This yields a grammatically and contextually correct sentence: "The Chinese Communist Party initially embraced nationalism as a co-option strategy in the aftermath of the Tiananmen Square massacre."

The verb "embraced" acts as the main predicate following the adverb "initially," "strategy" correctly forms the noun compound "co-option strategy," and "aftermath" properly completes the prepositional phrase "in the aftermath of."

Explanation

To make the sentence grammatically and contextually correct, the words must be rearranged in the sequence CBA. The infinitive marker "to" after "asking States" requires the base verb "produce" (C) to form "to produce quantifiable data". The verb "justify" (B) is correctly placed to show the purpose ("to justify"). Finally, the noun "reservation" (A) appropriately completes the phrase "levels of reservation". The reordered sentence reads: "The Supreme Court has been asking States to produce quantifiable data to justify their levels of reservation."

Explanation

The sequence CEDAB forms a grammatically correct and logically coherent sentence. "Discontent over the" (C) combines with "new farm laws" (E) to form the subject phrase, followed by the verb phrase "is a result of" (D). This is completed by the clause "sidestepping debate" (A) and "and discussion in Parliament" (B). Together, they form the complete meaningful sentence: "Discontent over the new farm laws is a result of sidestepping debate and discussion in Parliament."

Explanation

The introductory clause "It is crucial to define" naturally takes "the outcomes we are" as its object complement. This connects smoothly to "expecting from", which identifies what is being expected. The preposition "from" takes "population-level vaccination plans" as its object, followed by the qualifying prepositional phrase "for COVID-19". Combining these segments forms the clear and grammatically complete sentence: "It is crucial to define the outcomes we are expecting from population-level vaccination plans for COVID-19."

Explanation

The sequence ABCED forms a grammatically correct and meaningful sentence: "WHO must work alongside China in quickly uncovering the origins of the virus." In this order, phrase A ("WHO must") introduces the subject and modal verb, which requires the base verb phrase in B ("work alongside"). Phrase C ("China in quickly") completes the prepositional object for "alongside" and sets up the preposition "in" with an adverb. Phrase E ("uncovering the") provides the gerund following "in quickly", which directly governs the noun phrase object in D ("origins of the virus") to complete the thought logically.

Explanation

The sequence DEABC constructs a grammatically complete and meaningful sentence: "Only information bearing a nexus to public activity should be available to the public." In this structure, the subject "Only information" (D) is qualified by the adjectival phrase "bearing a nexus to" (E), which naturally links to the object "public activity should" (A). This leads into the predicate verb phrase "be available" (B) and completes the thought with the prepositional phrase "to the public" (C).

Explanation

When two trains move in opposite directions, their relative speed is the sum of their individual speeds.

Total distance to be covered = Sum of lengths of Train A and Train B = 600 meters Time taken to cross = 20 seconds

Relative speed = Total Distance / Time = 600 / 20 = 30 m/s

Converting the relative speed to km/hr: Relative speed = 30 × (18 / 5) = 108 km/hr

Since Relative Speed = Speed of Train A + Speed of Train B: 108 = 36 + Speed of Train B Speed of Train B = 108 - 36 = 72 km/hr

Explanation

Profit share ratio equals the ratio of the product of investment and time duration for each partner.

For A: First 4 months = X × 4 = 4X Next 8 months = 2X × 8 = 16X Total equivalent investment for A = 4X + 16X = 20X

For B: Joined for 8 months = 2X × 8 = 16X

Ratio of profit share of A to B = 20X : 16X = 5 : 4

Total profit ratio units = 5 + 4 = 9 units = Rs. 13950 1 unit = 13950 ÷ 9 = Rs. 1550

A's share of profit = 5 × 1550 = Rs. 7750

Explanation

Let the investments in the two schemes be 200x and 300x, making the total amount invested 500x.

Using the net effective rate formula for compound interest over 2 years, rₑff = r₁ + r₂ + (r₁ × r₂)/100: Effective CI rate for Scheme 1 at 20% p.a. = 20 + 20 + (20 × 20)/100 = 44% Effective CI rate for Scheme 2 at 10% p.a. = 10 + 10 + (10 × 10)/100 = 21%

Interest from Scheme 1 = 44% of 200x = 88x Interest from Scheme 2 = 21% of 300x = 63x Total interest = 88x + 63x = 151x

Given total interest = Rs. 1208: 151x = 1208 x = 8

Total amount invested = 500x = 500 × 8 = Rs. 4000

Explanation

Perimeter of a rectangle is 2 × (Length + Breadth). Given that the perimeter is 84 meters and the breadth is 18 meters:

2 × (Length + 18) = 84 Length + 18 = 42 Length = 24 meters

The sum of the length of the rectangle and the side of the square is given as 72 meters:

Length + Side of square = 72 24 + Side of square = 72 Side of square = 72 - 24 = 48 meters

Explanation

Let the time taken by A, B, and C to complete the full work alone be 4x, 6x, and 3x days respectively.

Their individual 1-day work rates are 1/(4x), 1/(6x), and 1/(3x).

Combined 1-day work rate = 1/(4x) + 1/(6x) + 1/(3x) = (3 + 2 + 4)/(12x) = 9/(12x) = 3/(4x).

Given that all three together complete the work in 8 days, their combined 1-day work rate is 1/8.

3/(4x) = 1/8 4x = 24

Thus, A alone takes 4x = 24 days to finish the full work.

The time required for A to complete ¾ of the work is 24 × (3/4) = 18 days.

Explanation

For Equation I: 2x² - 3x + 1 = 0 2x² - 2x - x + 1 = 0 (2x - 1)(x - 1) = 0 x = ½, 1 (or 0.5, 1)

For Equation II: 2y² - 5y + 3 = 0 2y² - 2y - 3y + 3 = 0 (2y - 3)(y - 1) = 0 y = 1, 1.5

Comparing the values: When x = 0.5 and y = 1, x < y. When x = 0.5 and y = 1.5, x < y. When x = 1 and y = 1, x = y. When x = 1 and y = 1.5, x < y.

Since x is either smaller than or equal to y across all combinations, x ≤ y.

Explanation

For equation I, x² + 21x + 110 = 0 factors as (x + 10)(x + 11) = 0, giving x = -10 and -11.

For equation II, y² + 17y + 72 = 0 factors as (y + 8)(y + 9) = 0, giving y = -8 and -9.

Comparing the roots, both values of x (-10 and -11) are strictly smaller than both values of y (-8 and -9), establishing that x < y.

Explanation

From Equation I: x² = 4 x = ±2 (x = 2, -2)

From Equation II: y² - 6y + 8 = 0 (y - 2)(y - 4) = 0 y = 2, 4

Comparing the values of x and y: When x = 2 and y = 2, x = y When x = 2 and y = 4, x < y When x = -2 and y = 2, x < y When x = -2 and y = 4, x < y

Combining all comparisons, x ≤ y.

Explanation

Solving Equation I: x² + 9x - 22 = 0 (x + 11)(x - 2) = 0 x = -11, 2

Solving Equation II: 2y² - 7y + 6 = 0 2y² - 4y - 3y + 6 = 0 (2y - 3)(y - 2) = 0 y = 1.5, 2

Comparing the roots: For x = -11 and y = 1.5: x < y For x = -11 and y = 2: x < y For x = 2 and y = 1.5: x > y For x = 2 and y = 2: x = y

Since x is both greater than y and less than y depending on the combination of roots, no relation can be established between x and y.

Explanation

Solving Equation I: 6x² + 5x + 1 = 0 6x² + 3x + 2x + 1 = 0 (3x + 1)(2x + 1) = 0 x = -1/3, -1/2 (or -0.333, -0.5)

Solving Equation II: 15y² + 11y + 2 = 0 15y² + 6y + 5y + 2 = 0 (3y + 1)(5y + 2) = 0 y = -1/3, -2/5 (or -0.333, -0.4)

Comparing the roots: For x = -1/3 and y = -2/5, x > y (-0.333 > -0.4). For x = -1/2 and y = -1/3, x < y (-0.5 < -0.333).

Since both x > y and x < y are obtained depending on the values chosen, no definite relation can be established between x and y.

Explanation

Using the successive percentage change formula, the final population after a 10% decrease followed by a 20% increase is calculated as:

Final Population = Initial Population × (1 - d/100) × (1 + i/100)

Substituting the given values: Final Population = 15000 × (1 - 10/100) × (1 + 20/100) = 15000 × 0.9 × 1.2 = 15000 × 1.08 = 16200

Alternatively, the effective net change = -10 + 20 + (-10 × 20)/100 = 8% increase. Final Population = 15000 × 1.08 = 16200.

Explanation

Let Cost Price (CP) = 100x. Since the markup is 50%, Marked Price (MP) = 150x.

The successive discounts of 11 1/9% (which equals 1/9) and 10% (which equals 1/10) give: Selling Price (SP) = MP × (1 - 1/9) × (1 - 1/10) SP = 150x × (8/9) × (9/10) = 120x

Total Discount = MP - SP = 150x - 120x = 30x Profit = SP - CP = 120x - 100x = 20x

Difference between discount given and profit earned = 30x - 20x = 10x

Given that 10x = 200, we get x = 20.

Marked Price (MP) = 150x = 150 × 20 = Rs. 3000.

Explanation

Let the speed of the boat in still water be v and the speed of the stream be s.

The difference between downstream speed and upstream speed is (v + s) - (v - s) = 2s = 5 km/hr, which gives s = 2.5 km/hr.

Given the ratio v : s = 19 : 5, 5 units correspond to 2.5 km/hr, so 1 unit corresponds to 0.5 km/hr. Therefore, v = 19 × 0.5 = 9.5 km/hr.

Downstream speed = v + s = 9.5 + 2.5 = 12 km/hr Upstream speed = v - s = 9.5 - 2.5 = 7 km/hr

Time taken downstream = 42 / 12 = 3.5 hours Time taken upstream = 31.5 / 7 = 4.5 hours

Total time = 3.5 + 4.5 = 8 hours.

Explanation

Let the initial quantity of the mixture be V liters.

Since P and Q are in the ratio 5:3, taking out 16 liters of the mixture removes: Quantity of P removed = (5 ÷ 8) × 16 = 10 liters Quantity of Q removed = (3 ÷ 8) × 16 = 6 liters

After replacing 16 liters of mixture with liquid Q: Final quantity of P = (5/8)V - 10 Final quantity of Q = (3/8)V - 6 + 16 = (3/8)V + 10

Given that the new ratio of P to Q is 1:1, set both quantities equal: (5/8)V - 10 = (3/8)V + 10 (5/8 - 3/8)V = 20 (2/8)V = 20 V = 80 liters

Explanation

Sum of present ages of A and B = 55 + (2 × 5) = 65 years.

Given the ratio of present ages of A to B is 8 : 5, total ratio units = 13. 1 unit = 65 / 13 = 5 years.

Present age of A = 8 × 5 = 40 years. Present age of B = 5 × 5 = 25 years.

Since the average of present ages of B and C is 35 years, B + C = 35 × 2 = 70 years. Present age of C = 70 - 25 = 45 years.

Difference between the present age of A and C = 45 - 40 = 5 years.

Explanation

Let the missing value be x.

(x ÷ 5 ÷ 7) × 14 + 112 = 420

(x ÷ 35) × 14 = 420 - 112

(x × 14) / 35 = 308

2x / 5 = 308

2x = 308 × 5

2x = 1540

x = 770

Explanation

First, simplify the exponent using the order of operations (BODMAS): 4 × 16 ÷ 32 + 1 = 4 × (1/2) + 1 = 2 + 1 = 3

Let the missing value be x. Substituting the simplified exponent into the original equation: x³ + 12² = 360 x³ + 144 = 360 x³ = 360 - 144 x³ = 216 x = ∛216 = 6

Explanation

Evaluate the left-hand side step by step using BODMAS:

50% of 128 = ½ × 128 = 64

Since √16 = 4, (√16 / 2) × 4 = (4 / 2) × 4 = 2 × 4 = 8

Adding these values gives the left-hand side: 64 + 8 = 72

Equating the left-hand side with the right-hand side: 72 = ? + 10 ? = 72 - 10 = 62

Explanation

Simplify each component of the given mathematical expression individually:

First, evaluate the cube root term: ³√1331 = 11, which gives (³√1331) ÷ 11 = 11 ÷ 11 = 1. Second, evaluate the square root term: √81 = 9.

Now, substitute these evaluated values back into the original equation: 1 + 9 + ? = 27 10 + ? = 27

Solving for the missing value: ? = 27 − 10 ? = 17

Explanation

Substitute the values of the squares into the given expression:

14² = 196 5² = 25

Now, add the terms on the left-hand side: 196 + 179 + 25 = (?)² 400 = (?)²

Taking the square root on both sides: ? = √400 = 20

Explanation

Evaluate the expression step-by-step using the standard order of operations:

28.5 × 34 = 969 2320 ÷ 8 = 290

Summing the left-hand side gives: 969 + 290 = 1259

For the right-hand side, 36² = 1296.

Equating both sides: 1259 = 1296 - ? ? = 1296 - 1259 = 37

Explanation

Applying the BODMAS rule, perform multiplication and division first:

47 × 27 = 1269 15600 ÷ 8 = 1950

Now add all the terms together: 1269 + 1950 + 181 = 1269 + 181 + 1950 = 1450 + 1950 = 3400

Explanation

Applying the BODMAS rule, division and multiplication are performed first, followed by addition and subtraction:

112.5 × 5 = 562.5 4560 ÷ 6 = 760 175 × 7 = 1225

Substituting these values back into the expression:

562.5 + 760 − 1225 = 1322.5 − 1225 = 97.5

Explanation

Simplify the terms inside the square root: 250 × 44 = 11000 40% of 8500 = 0.40 × 8500 = 3400

Adding both terms gives 11000 + 3400 = 14400. Taking the square root gives √14400 = 120.

Now solve the linear equation for the unknown value: 80% of ? = 120 0.80 × ? = 120 ? = 120 ÷ 0.80 = 150

Explanation

RHS: (594/264) x (2300/115) = (9/4) x 20 = 45. LHS: ? x 40 / 24 x 27 = ? x 45. Equating, 45 x ? = 45, so ? = 1, i.e. option (a).

Explanation

Let the unknown value in place of the question mark be x.

The given equation is x + 13 × 50 = 420 + 45% of 800 + 220.

First, evaluate the multiplication on the left-hand side: 13 × 50 = 650 This gives LHS = x + 650.

Next, evaluate the percentage on the right-hand side: 45% of 800 = (45 / 100) × 800 = 360

Summing all the terms on the right-hand side: RHS = 420 + 360 + 220 = 1000

Equating the left and right sides: x + 650 = 1000 x = 1000 - 650 x = 350

Explanation

Convert 12.5% to the standard fraction ⅛.

12.5% of 960 = 960 ÷ 8 = 120 16 × 12 = 192

Substituting these values into the given equation: 12% of ? + 120 = 192 12% of ? = 192 - 120 12% of ? = 72

Solving for the missing value: ? = (72 × 100) ÷ 12 ? = 600

Explanation

Let the unknown number in place of the question mark be x.

The given equation is: 15 × x + 20% of 450 = 360

First, evaluate the percentage term: 20% of 450 = (20 / 100) × 450 = 90

Substitute 90 back into the original equation: 15 × x + 90 = 360

Subtract 90 from both sides: 15 × x = 360 - 90 15 × x = 270

Divide both sides by 15: x = 270 / 15 = 18

Explanation

Convert 75% into its fraction equivalent ¾.

Substituting ¾ into the equation: (¾) × (¾) × (8/9) × 1800 = ? + 600

Simplify the left-hand side: (9/16) × (8/9) × 1800 = ? + 600 (1/2) × 1800 = ? + 600 900 = ? + 600

Solving for the unknown: ? = 900 - 600 = 300

Explanation

Let the missing number be x.

x% of 900 + 500 = 4 × 197 (x / 100) × 900 + 500 = 788 9x + 500 = 788 9x = 288 x = 288 / 9 = 32

Explanation

Based on the given conditions, the eight boxes from top to bottom (positions 8 to 1) are arranged as follows:

Position 8: S Position 7: P Position 6: U Position 5: R Position 4: Q Position 3: T Position 2: V Position 1: W

In this arrangement: Both S (position 8) and Q (position 4) are above T (position 3) with three boxes (P, U, R) between them. Box P is adjacent to S, satisfying the condition that not more than one box is between S and P. There are two boxes (R, Q) between U and T, one box (Q) between T and R, two boxes (Q, T) between R and V, and box W is placed below V.

The boxes located between T (position 3) and S (position 8) are Q, R, U, and P, which totals 4 boxes. Therefore, there are more than three boxes between box T and box S.

Explanation

Arranging the eight boxes vertically from top (8) to bottom (1):

Since both S and Q are placed above box T with three boxes between them, S and Q occupy positions 8 and 4, while box T is at position 3.

With one box between T and R, box R is placed at position 5. Two boxes lie between R and V with V below R, placing box V at position 2, which leaves box W at position 1 below V.

Two boxes are placed between U and T, so box U is at position 6. The remaining box P is at position 7. Since no more than one box can be between S and P, box S must be at position 8, which places box Q at position 4.

The complete order from top to bottom is S, P, U, R, Q, T, V, W. Box R is located at position 5, directly above box Q at position 4.

Explanation

By arranging the eight boxes from top (position 8) to bottom (position 1):

Since S and Q have three boxes between them and both are placed above T, S and Q occupy positions 8 and 4, which places T at position 3.

Two boxes between U and T places U at position 6. One box between T and R places R at position 5. Two boxes between R and V with V below R places V at position 2. Box W is below box V, so W must be at position 1. Placing P at position 7 leaves zero boxes between S and P, satisfying the condition.

The vertical arrangement from top to bottom is S (8), P (7), U (6), R (5), Q (4), T (3), V (2), and W (1). Therefore, box W is at the bottommost position.

Explanation

Based on the given conditions, S and Q are both placed above T with three boxes between them. Assigning S to the 8th (topmost) position and Q to the 4th position places T at the 3rd position. Two boxes between T and U places U at the 6th position. One box between T and R places R at the 5th position. Two boxes between R and V with V below R places V at the 2nd position. As W is below V, W takes the 1st position at the bottom. P takes the remaining 7th position, which satisfies the condition of having no more than one box between S and P.

The final arrangement from top to bottom is S, P, U, R, Q, T, V, W. Box U is located directly below box P.

Explanation

Based on the given conditions, the top-to-bottom arrangement of the eight boxes from position 8 (top) to position 1 (bottom) is determined as follows. Since both S and Q are placed above box T with three boxes between them, S and Q occupy position 8 and position 4, placing T at position 3. With two boxes between T and U, U is placed at position 6. With one box between T and R, R is placed at position 5. Box V is placed two boxes below R at position 2, and box W is placed below V at position 1. Box P occupies position 7, which satisfies having not more than one box between S and P. The final order from top to bottom is S/Q (8), P (7), U (6), R (5), Q/S (4), T (3), V (2), and W (1). The boxes located between box W (position 1) and box R (position 5) are V, T, and Q/S, making a total of three boxes.

Explanation

Applying the specified rules to each letter of BACKGROUND gives: B (consonant - 1) = A A (vowel + 1) = B C (consonant - 1) = B K (consonant - 1) = J G (consonant - 1) = F R (consonant - 1) = Q O (vowel + 1) = P U (vowel + 1) = V N (consonant - 1) = M D (consonant - 1) = C

The resulting arrangement of letters is A, B, B, J, F, Q, P, V, M, C. Looking at this new set, only the letter B appears more than once. Thus, exactly one letter is repeated.

Explanation

Arranging the six persons from heaviest to lightest in positions 1 to 6: Since both A and E are heavier than F, and F is heavier than B, C, and D, with C placed immediately after F, F occupies the 3rd position and C occupies the 4th. Neither B nor C is the lightest, making D the 6th person and B the 5th. Since E cannot be the heaviest, A is 1st and E is 2nd. The complete arrangement from 1st to 6th is A > E > F > C > B > D.

The weight of the 2nd lightest person (5th position, B) is given as 17 kg. The weight of the 2nd heaviest person (2nd position, E) is 2 × 17 = 34 kg. Since B + C = 44 kg, the weight of C (4th position) is 44 - 17 = 27 kg.

Because F lies between E (34 kg) and C (27 kg), the weight of F must satisfy 27 kg < F < 34 kg. Therefore, 30 kg is a valid possible weight for F.

Explanation

Arranging the six persons in descending order of weight from 1 (heaviest) to 6 (lightest):

Since C is just lighter than F, and F is heavier than B and D, the order of these four must be F > C > B > D, with D being the lightest (6th) as neither B nor C is the lightest. Thus, F is 3rd, C is 4th, B is 5th, and D is 6th. Since E is not the heaviest, A is 1st and E is 2nd.

The complete arrangement from heaviest to lightest is: A > E > F > C > B > D.

There are 2 persons heavier than F (A and E). Similarly, there are 2 persons lighter than C (B and D). Therefore, the number of persons heavier than F is the same as the number of persons lighter than C.

Explanation

The 2nd lightest person is at position 5 with a weight of 17 kg, making the 2nd heaviest person (position 2) weigh 2 × 17 = 34 kg. Since F is heavier than B and D, A and E are heavier than F, and neither B nor C is the lightest, D must be the lightest person (position 6). This makes B the 2nd lightest person (position 5), so weight of B = 17 kg.

D is 10 kg lighter than B, so weight of D = 17 - 10 = 7 kg. Total weight of B and C is 44 kg, so weight of C = 44 - 17 = 27 kg. F is 5 kg heavier than C, so weight of F = 27 + 5 = 32 kg.

Since E is not the heaviest, E must be the 2nd heaviest person weighing 34 kg, which leaves A as the heaviest person (position 1). The descending order of persons is A > E (34 kg) > F (32 kg) > C (27 kg) > B (17 kg) > D (7 kg).

Summing all weights to the total of 150 kg: A + 34 + 32 + 27 + 17 + 7 = 150 A + 117 = 150 A = 33 kg

Explanation

Arranging the six persons in descending order of weight based on the given conditions gives: A > E > F > C > B > D.

Since E is not the heaviest and all other persons are lighter than A or E, A is 1st. E is heavier than F, placing E at 2nd. C is just lighter than F, placing F at 3rd and C at 4th. B is not the lightest, placing B at 5th and D at 6th.

In this ranking, B and D are immediately adjacent with no person between them, whereas all the other pairs have exactly one person between them. Therefore, B-D does not belong to the group.

Explanation

Arranging the six persons in descending order of weight from 1st (heaviest) to 6th (lightest): Since E is not the heaviest and A is heavier than E, F, and C, A occupies the 1st position. E is the 2nd heaviest with a weight of 2 × 17 = 34 kg. Since C is just lighter than F and is not the 3rd heaviest, F is in the 3rd position and C is in the 4th position. B is the 2nd lightest person in the 5th position weighing 17 kg (giving C = 44 - 17 = 27 kg). Since neither B nor C can be the lightest, D must occupy the 6th position, making D the lightest among all.

Explanation

From the given statement F > R ≥ T = E > W ≤ Q:

For Conclusion I (E < F): The relationship between F and E from the statement is F > R ≥ T = E, which simplifies directly to F > E, or E < F. Hence, Conclusion I holds true.

For Conclusion II (Q ≥ T): The chain of relationship between T and Q is T = E > W ≤ Q. The presence of opposing inequality symbols (> and ≤) between T and Q means no definite relationship can be established, making Conclusion II false.

Explanation

From the given statement chain, relating element G with elements T and C gives G ≥ H ≥ T = C, which simplifies directly to G ≥ T and G ≥ C.

The inequality G ≥ C means that either G > C or G = C must be true. Since T = C, the condition G > C is identical to G > T (or T < G).

Thus, the relation reduces to either T < G or C = G. Since these two conclusions complement each other to cover the complete relationship G ≥ C, either Conclusion I or Conclusion II is true.

Explanation

For Conclusion I, the path between K and T is K > I ≥ G > F ≤ T. Due to the presence of opposite inequality signs (> and ≤) in the sequence, no definite relationship can be established between K and T.

For Conclusion II, the path between F and R is F ≤ T < R, which translates to R > T ≥ F. Since the strict inequality symbol (>) is present in the path between R and F, R > F is definitely true.

Explanation

From the given statement K < G ≤ D < C > R ≤ Y:

To check Conclusion I (C > G): Combining G ≤ D and D < C gives G < C, which means C > G. Thus, Conclusion I is true.

To check Conclusion II (K < D): Combining K < G and G ≤ D directly yields K < D. Thus, Conclusion II is true.

Both conclusions I and II are true.

Explanation

Arranging the digits of the given number 843576529 in ascending order yields the sequence 234556789.

Comparing the original sequence with the sorted sequence position by position:

Original: 8 4 3 5 7 6 5 2 9 Sorted: 2 3 4 5 5 6 7 8 9

The digits at position 4 (digit 5), position 6 (digit 6), and position 9 (digit 9) remain unchanged. Thus, exactly three numerals remain at the same position.

Explanation

Arranging the 8 persons chronologically by year and date:

Dec 14, 1956: D Dec 23, 1956: H Dec 14, 1957: C Dec 23, 1957: A Dec 14, 1958: E Dec 23, 1958: G Dec 14, 1959: B Dec 23, 1959: F

E is born in an even year (1958) on Dec 14, and D is on Dec 14, 1956, leaving three persons between them. H immediately follows D. The number of persons before H (one) matches the number after B. A, G, and F are all born on the 23rd in chronological order.

Placing C in the remaining slot (Dec 14, 1957) reveals that exactly two persons (D and H) were born before C.

Explanation

The chronological order of the eight birth dates is: 14 December 1956 23 December 1956 14 December 1957 23 December 1957 14 December 1958 23 December 1958 14 December 1959 23 December 1959

E is born in an even year but is not the eldest ( slot 1 ). Three persons, A, G, and F, are born on the same date in that order, requiring three vacant slots on either the 14th or 23rd.

Placing E on 14 December 1958 (slot 5) leaves D on 14 December 1956 (slot 1), satisfying the condition that more than two persons are between E and D.

Since H is born immediately after D, H is placed on 23 December 1956 (slot 2). Exactly one person is born before H, which means exactly one person must be born after B. Therefore, B is placed on 14 December 1959 (slot 7). A, G, and F occupy the 23rd December dates of 1957, 1958, and 1959 respectively, while C occupies 14 December 1957.

Consequently, B was born on 14 December 1959, which falls in the year 1959.

Explanation

Arranging the eight birth dates chronologically from position 1 to 8:

14 Dec 1956: D 23 Dec 1956: H 14 Dec 1957: C 23 Dec 1957: A 14 Dec 1958: E 23 Dec 1958: G 14 Dec 1959: B 23 Dec 1959: F

E is born in an even year (1958) at position 5. Since more than two persons are between E and D, D must be at position 1, which puts H at position 2 immediately after D. Equal number of persons before H (1 person) and after B implies B is at position 7. Since A, G, and F were born on the same date in that order, they occupy the remaining 23rd Dec slots at positions 4, 6, and 8 respectively, leaving C for position 3.

Between A (position 4) and F (position 8), there are exactly three persons: E, G, and B.

Explanation

Solving the birth puzzle gives the order (eldest to youngest) D, H, C, A, E, G, B, F across 1956-1959 on the 14th/23rd. D, C, E and B were all born on the 14th while H was born on the 23rd, so H is the odd one out.

Explanation

The eight birth dates in chronological order from 1 to 8 are: 14 Dec 1956 (1st), 23 Dec 1956 (2nd), 14 Dec 1957 (3rd), 23 Dec 1957 (4th), 14 Dec 1958 (5th), 23 Dec 1958 (6th), 14 Dec 1959 (7th), and 23 Dec 1959 (8th).

Since E was born in an even-numbered year but is not the eldest, E is placed on 14 Dec 1958 (5th slot). Having more than two persons between E and D places D on 14 Dec 1956 (1st slot). Since H was born just after D, H is on 23 Dec 1956 (2nd slot). With one person born before H, one person must be born after B, placing B on 14 Dec 1959 (7th slot).

A, G, and F were born on the same date in chronological order, filling 23 Dec 1957 (4th slot), 23 Dec 1958 (6th slot), and 23 Dec 1959 (8th slot) respectively. The remaining slot on 14 Dec 1957 (3rd slot) is occupied by C.

The final chronological order from 1st to 8th slot is: D, H, C, A, E, G, B, F.

The number of persons born between G (6th slot) and H (2nd slot) is 3 (C, A, and E). Similarly, the number of persons born between C (3rd slot) and B (7th slot) is also 3 (A, E, and G).

Explanation

The statement "Only a few Photo are Video" means that some Photo are Video and some Photo are not Video. This condition restricts only the relation between Photo and Video. It allows for the possibility of all Photo being contained within Frame without violating any given statements, so Conclusion I is a valid possibility.

For Conclusion II, there is no negative or restrictive relation established between Photo and Camera, meaning all Photo could potentially be Camera. Therefore, "Some Photo are not Camera" does not definitely follow. Only Conclusion I logically follows.

Explanation

Statement 1 implies that some Cities are Towns. Statement 2 specifies that No Town is a Village, meaning the portion of Cities that are Towns can never be Villages. Hence, All City can never be Village, so conclusion I does not follow.

Statement 3 states that All Villages are Blocks, and Statement 2 states that No Village is a Town. This means that the portion of Blocks containing Villages can never be Towns. Therefore, Some Block are not Town is logically valid, and conclusion II follows.

Explanation

In syllogism, two conclusions form a complementary pair requiring an either-or relation when three conditions are satisfied:

Neither conclusion logically follows individually from the given statements. Both conclusions share the same subject and predicate elements (Parrot and Bird). The conclusions form a standard complementary pair of the type Some + No (a particular affirmative statement and a universal negative statement).

Since no direct relationship is established between Bird and Parrot from the given statements, neither conclusion I nor conclusion II can be definitely concluded on its own. However, between any two sets, either some elements are common or no elements are common. Therefore, either conclusion I or conclusion II must hold true.

Explanation

"Only Banana is Apple" gives All Apple are Banana, so Apple lies inside Banana; "Some Banana are Papaya" makes Banana overlap Papaya. Conclusion I: Apple can be placed inside the Banana-Papaya overlap without contradicting either statement, so 'Some Apple being Papaya' is a valid possibility and I follows. Conclusion II: plain "Only" carries no definite negative, so the diagram in which Apple and Banana coincide exactly is permitted, and that instantiates 'All Banana can be Apple', so II follows too. Both conclusions follow.

Explanation

Arranging the eight persons sequentially from 1st to 8th based on the given conditions:

Since at most two persons purchase before F, F is placed at position 3. With one person between D and F, D is placed at position 5. P purchases just before S, and one person is between P and D, placing P at position 7 and S at position 8. M purchases just before E, occupying positions 1 and 2. The remaining positions 4 and 6 are filled by O and G respectively, satisfying the condition that O purchases after E and before G.

The final order from 1st to 8th is M, E, F, O, D, G, P, S. Since D is in the 5th position, exactly 3 persons (G, P, and S) purchase after D.

Explanation

Solving the purchase-order puzzle gives M, E, F, O, D, G, P, S. G is sixth and the person immediately after G is P.

Explanation

Based on the given conditions, the order of purchasing from top to bottom (1 to 8) is: Position 1: M Position 2: E Position 3: F Position 4: O Position 5: D Position 6: G Position 7: P Position 8: S

When all eight persons are arranged in alphabetical order from top to bottom starting from D, the new sequence becomes: D (1), E (2), F (3), G (4), M (5), O (6), P (7), and S (8).

Comparing the positions between the original and alphabetical arrangements: Position 2 is occupied by E in both. Position 3 is occupied by F in both. Position 7 is occupied by P in both. Position 8 is occupied by S in both.

Excluding D, exactly four persons (E, F, P, and S) remain in the same position.

Explanation

By evaluating the given conditions, the step-by-step arrangement from 1st to 8th purchase is determined:

M purchases 1st and E purchases 2nd, as M purchases just before E. F purchases 3rd, satisfying the condition that at most two persons purchase before F. O purchases 4th. D purchases 5th, ensuring exactly one person is between D and F. G purchases 6th, as O purchases before G and after E. P purchases 7th, keeping one person between P and D. S purchases 8th, directly after P.

The complete purchasing sequence from 1st to 8th is M, E, F, O, D, G, P, S. The person purchasing at position 4, directly between F (3rd) and D (5th), is O.

Explanation

Placing F at position 3 satisfies the condition that at most two persons purchase before F. Placing D at position 5 ensures one person is between D and F.

Since one person purchases between P and D, and P purchases just before S, P takes position 7 and S takes position 8.

M purchases just before E, placing them at positions 1 and 2 respectively. The remaining condition that O purchases after E and before G places O at position 4 and G at position 6.

The final purchasing order from first to last is M, E, F, O, D, G, P, S.

E is at position 2 and P is at position 7. The four persons between E and P are F, O, D, and G.

Explanation

In CHRISTMAS (C1 H2 R3 I4 S5 T6 M7 A8 S9) two pairs have as many letters between them in the word as in the alphabet: H-M (4 and 4) and S-T (0 and 0). So the answer is Two.

Explanation

In the given arrangement, locate all occurrences of the digit 2 and check their immediately preceding digits:

The first 2 (in 12) is preceded by 1. The second 2 (in 42) is preceded by 4. The third 2 (in 52) is preceded by 5. The fourth 2 (in 52) is preceded by 5. The fifth 2 (in 32) is preceded by 3. The sixth 2 (in 72) is preceded by 7.

To have a numerical value of more than 5, the preceding digit must be 6, 7, 8, or 9. Only the sixth occurrence (72) satisfies this condition because 7 > 5. Thus, there is only one such 2 in the arrangement.

Explanation

To find the element that is seventh to the left of the twentieth from the left end, subtract the positions: 20 - 7 = 13th position from the left end.

Counting the digits from the left in the given sequence: 1st to 5th: 3, 9, 1, 8, 1 6th to 10th: 2, 5, 8, 6, 3 11th to 13th: 6, 4, 2

The 13th digit from the left end is 2.

Explanation

To find the tenth digit from the right end after removing all even digits, count only the odd digits starting from the rightmost position of the given sequence.

Scanning the arrangement from right to left and ignoring the even digits (2, 4, 6, 8), the sequence of odd digits obtained from the right end is: 9 (1st), 5 (2nd), 7 (3rd), 3 (4th), 7 (5th), 9 (6th), 1 (7th), 5 (8th), 5 (9th), and 5 (10th).

Therefore, the tenth digit from the right end in the modified arrangement is 5.

Explanation

To find the number of 1's followed by a perfect square, check the digit immediately following each 1 in the given arrangement. The single-digit perfect squares are 1, 4, and 9.

In the given sequence: The first 1 (in 3918) is followed by 8, which is not a perfect square. The second 1 (in 8125) is followed by 2, which is not a perfect square. The third 1 (in 5149) is followed by 4, which is a perfect square (2² = 4).

Thus, there is only one such 1 that is immediately followed by a perfect square.