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1
Arrange the following words in a meaningful sequence related to a natural phenomenon and its effect: 1. Rainbow, 2. Rain, 3. Sun, 4. Happy, 5. Child.
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Solution: Step 1: Analyze the causal and sequential relationships among the given words. Step 2: 'Rain' (2) is a weather event. Step 3: After or during rain, if the 'Sun' (3) appears, a rainbow can form. Step 4: The 'Rainbow' (1) is then visible. Step 5: A 'Child' (5) is typically delighted by the sight of a rainbow. Step 6: The child becomes 'Happy' (4). Step 7: The correct meaningful sequence is: Rain -> Sun -> Rainbow -> Child -> Happy. Step 8: The corresponding numerical order is 2, 3, 1, 5, 4.
2
In which of the schools (B, C, D, E, and F) does T study? Determine if the given statements are sufficient.
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Solution: Step 1: Identify the set of possible schools for T: {B, C, D, E, F}. Step 2: Analyze Statement I: 'T does not study in the same school as either R or J'. This means T's school is not R's school and not J's school. Step 3: Analyze Statement II: 'R and J study in schools D and F respectively'. So, R studies in D and J studies in F. Step 4: Combine Statement I and Statement II: T does not study in school D and T does not study in school F. Step 5: The remaining possible schools for T are {B, C, E}. Since T could study in B, C, or E, the exact school cannot be determined. Step 6: Therefore, neither Statement I nor Statement II alone or together is sufficient to determine T's school.
3
A committee of 5 members is to be formed from a group of 4 men and 5 women. How many distinct ways are there to form this committee such that it includes at least 1 man?
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Solution: Step 1: Identify the total number of men (4) and women (5). The committee size is 5. Step 2: The condition 'at least 1 man' implies several mutually exclusive cases: - Case 1: 1 man and 4 women (4C1 * 5C4) - Case 2: 2 men and 3 women (4C2 * 5C3) - Case 3: 3 men and 2 women (4C3 * 5C2) - Case 4: 4 men and 1 woman (4C4 * 5C1) Step 3: Calculate the combinations for each case: - Case 1: 4C1 = 4. 5C4 = 5C(5-4) = 5C1 = 5. Product = 4 * 5 = 20. - Case 2: 4C2 = (4 * 3) / (2 * 1) = 6. 5C3 = 5C(5-3) = 5C2 = (5 * 4) / (2 * 1) = 10. Product = 6 * 10 = 60. - Case 3: 4C3 = 4C(4-3) = 4C1 = 4. 5C2 = 10. Product = 4 * 10 = 40. - Case 4: 4C4 = 1. 5C1 = 5. Product = 1 * 5 = 5. Step 4: Sum the results of all these possible cases to find the total number of ways. Step 5: Total number of ways = 20 + 60 + 40 + 5 = 125. (Alternatively, calculate total ways to select 5 persons from 9 (9C5 = 126) and subtract ways to select 5 persons with no men (i.e., all women) (5C5 = 1): 126 - 1 = 125.)
4
Order these water formations from their origin or smallest size to largest: 1. Sea, 2. Rivulet, 3. Ocean, 4. River, 5. Glacier.
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Solution: Step 1: Identify the source of fresh water and its journey through increasingly larger bodies. Step 2: A 'Glacier' (5) is often the source of fresh water, melting into small streams. Step 3: A 'Rivulet' (2) is a very small stream. Step 4: Multiple rivulets merge to form a larger 'River' (4). Step 5: Rivers flow into the 'Sea' (1), a large body of saltwater. Step 6: The 'Ocean' (3) is the largest body of saltwater, encompassing multiple seas. Step 7: The correct sequence is 5, 2, 4, 1, 3.
5
Arrange the following geographical/administrative units in a meaningful hierarchical sequence from smallest to largest: 1. Nation, 2. Village, 3. City, 4. District, 5. State.
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Solution: Step 1: Identify the hierarchy of geographical and administrative divisions, from smallest to largest. Step 2: The smallest unit among the options is a 'Village' (2). Step 3: A 'City' (3) is typically larger than a village. Step 4: Multiple cities and villages comprise a 'District' (4). Step 5: Several districts form a 'State' (5). Step 6: Multiple states collectively form a 'Nation' (1). Step 7: The correct meaningful sequence is: Village -> City -> District -> State -> Nation. Step 8: The corresponding numerical order is 2, 3, 4, 5, 1.
6
Arrange the given words in a meaningful sequence representing human age groups from youngest to oldest: 1. Adult, 2. Child, 3. Infant, 4. Boy, 5. Adolescent.
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Solution: Step 1: Identify the standard chronological progression of human age stages. Step 2: The earliest stage among the options is 'Infant' (3). Step 3: An infant grows into a 'Child' (2). Step 4: A child, specifically a male, is often called a 'Boy' (4). Step 5: A boy/girl then becomes an 'Adolescent' (5). Step 6: Finally, an adolescent becomes an 'Adult' (1). Step 7: The correct meaningful sequence is: Infant -> Child -> Boy -> Adolescent -> Adult. Step 8: The corresponding numerical order is 3, 2, 4, 5, 1.
7
Order the following words to describe the process of tailoring clothes: 1. Cut, 2. Put on, 3. Mark, 4. Measure, 5. Tailor.
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Solution: Step 1: Identify the logical steps involved in creating and wearing tailored clothing. Step 2: The first step is to 'Measure' (4) the fabric/person. Step 3: Based on measurements, the fabric is 'Mark'ed (3). Step 4: The marked fabric is then 'Cut' (1). Step 5: The cut pieces are assembled by a 'Tailor' (5). Step 6: Finally, the finished garment is 'Put on' (2). Step 7: The correct meaningful sequence is: Measure -> Mark -> Cut -> Tailor -> Put on. Step 8: The corresponding numerical order is 4, 3, 1, 5, 2.
8
Sequence these terms related to a natural disaster and its aftermath: 1. Rain, 2. Monsoon, 3. Rescue, 4. Flood, 5. Shelter, 6. Relief.
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Solution: Step 1: Identify the initiating event and its consequences, followed by responses. Step 2: A 'Monsoon' (2) is a season that brings heavy 'Rain' (1). Step 3: Heavy rain can lead to a 'Flood' (4). Step 4: During a flood, 'Rescue' (3) operations are initiated. Step 5: People need 'Shelter' (5) after being rescued or displaced. Step 6: Long-term 'Relief' (6) efforts follow to help recovery. Step 7: The correct sequence is 2, 1, 4, 3, 5, 6.
9
How many distinct arrangements are possible for the letters in the word RIDDLED?
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Solution: Step 1: Count the total number of letters in the word RIDDLED, which is 7. Step 2: Identify any repeated letters. The letter 'D' appears 3 times. Step 3: Use the permutation formula for repeated letters: n! / (p1! * p2! * ...). Step 4: Calculate the number of ways: 7! / 3!. Step 5: Compute the factorials: 7! = 5040; 3! = 6. Step 6: Perform the division: 5040 / 6 = 840.
10
Arrange the following in a logical order: 1. Financial Earnings 2. Social Esteem 3. Learning 4. Overall Happiness 5. Employment
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Solution: Step 1: Understand the terms - Education (3), Job (5), Income (1), Respect (2), Well-being (4) Step 2: Determine logical sequence Step 3: A person first acquires education (3), then gets a job (5), followed by income (1), then respect (2), and finally overall well-being (4) Step 4: Therefore, the sequence is 3, 5, 1, 2, 4
11
Put the following human developmental stages in the correct chronological order: 1. Foetus, 2. Child, 3. Baby, 4. Adult, 5. Youth.
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Solution: Step 1: Arrange the human life stages from conception to maturity. Step 2: 'Foetus' (1) is the earliest stage in the womb. Step 3: After birth, an infant is a 'Baby' (3). Step 4: A baby grows into a 'Child' (2). Step 5: A child then progresses to 'Youth' (5) (adolescence/early adulthood). Step 6: Finally, 'Adult' (4) represents full maturity. Step 7: The correct sequence is 1, 3, 2, 5, 4.
12
Order the given words to represent the process of making a saree from its raw material: 1. Yarn, 2. Plant, 3. Saree, 4. Cotton, 5. Cloth.
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Solution: Step 1: Identify the steps involved in textile production, from the raw material to the finished product. Step 2: The process starts with a 'Plant' (2) (e.g., cotton plant). Step 3: The plant yields 'Cotton' (4). Step 4: Cotton is spun into 'Yarn' (1). Step 5: Yarn is woven into 'Cloth' (5). Step 6: Finally, cloth is fashioned into a 'Saree' (3). Step 7: The correct meaningful sequence is: Plant -> Cotton -> Yarn -> Cloth -> Saree. Step 8: The corresponding numerical order is 2, 4, 1, 5, 3.
13
Determine the number of girls in Shravan's class who are taller than him, based on the provided ranking statements.
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Solution: Step 1: Analyze Statement I. 'When students of Shravan's class are ranked in descending order of their heights, Shravan's rank is 17th from the top among all the students and 12th among boys.' From 'Shravan's rank is 17th from the top among all students', there are 17 - 1 = 16 students taller than Shravan overall. From 'Shravan's rank is 12th among boys', there are 12 - 1 = 11 boys taller than Shravan. Number of girls taller than Shravan = (Total students taller than Shravan) - (Boys taller than Shravan) = 16 - 11 = 5 girls. Statement I alone is sufficient. Step 2: Analyze Statement II. 'Shravan's rank from the bottom on the basis of height among boys is 18th and among all students, 29th.' This statement provides ranks from the bottom. To find the number of people taller than him, we need his rank from the top or the total number of students/boys. Without this, we cannot determine the number of girls taller than him. Statement II alone is insufficient. Step 3: Conclude. Statement I alone is sufficient to determine the number of girls taller than Shravan.
14
How many distinct sequences can be formed by arranging the letters of the word ALLAHABAD?
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Solution: Step 1: Count the total number of letters in the word ALLAHABAD, which is 9. Step 2: Identify and count any repeated letters: - The letter 'A' appears 4 times. - The letter 'L' appears 2 times. - The letters 'H', 'B', 'D' each appear 1 time. Step 3: Use the permutation formula for repeated letters: n! / (p1! * p2! * ...), where n is the total number of letters and p_i are the counts of repeated letters. Step 4: Calculate the number of ways: 9! / (4! * 2!). Step 5: Compute the factorials: 9! = 362,880; 4! = 24; 2! = 2. Step 6: Perform the division: 362,880 / (24 * 2) = 362,880 / 48 = 7560.
15
Arrange the following stages of a job recruitment process in a logical order: 1. Probation, 2. Interview, 3. Selection, 4. Appointment, 5. Advertisement, 6. Application.
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Solution: Step 1: Outline the typical steps an individual goes through when seeking a job. Step 2: A job begins with an 'Advertisement' (5) by the employer. Step 3: Interested candidates submit an 'Application' (6). Step 4: Qualified applicants are called for an 'Interview' (2). Step 5: After interviews, a 'Selection' (3) decision is made. Step 6: The selected candidate receives an 'Appointment' (4) letter. Step 7: The new employee typically undergoes a 'Probation' (1) period. Step 8: The correct sequence is 5, 6, 2, 3, 4, 1.
16
Identify the current seating position of T.
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Solution: Step 1: Analyze the given seating arrangement information (assumed to be provided in a preceding context for the puzzle). Step 2: Deduce the specific location of individual T relative to other people in the arrangement. Step 3: Pinpoint T's position, identifying it as "To the immediate right of V" based on the complete arrangement.
17
How many distinct arrangements are possible for the letters in the word WEDDING?
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Solution: Step 1: Count the total number of letters in the word WEDDING, which is 7. Step 2: Identify any repeated letters. The letter 'D' appears 2 times. Step 3: Use the permutation formula for repeated letters: n! / (p1! * p2! * ...). Step 4: Calculate the number of ways: 7! / 2!. Step 5: Compute the factorials: 7! = 5040; 2! = 2. Step 6: Perform the division: 5040 / 2 = 2520.
18
Arrange the following words to illustrate a natural process or transformation: 1. Table, 2. Tree, 3. Wood, 4. Seed, 5. Plant.
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Solution: Step 1: Consider the life cycle of a tree and its subsequent use. Step 2: Life begins with a 'Seed' (4). Step 3: The seed grows into a 'Plant' (5). Step 4: The plant matures into a 'Tree' (2). Step 5: 'Wood' (3) is harvested from a tree. Step 6: 'Table' (1) is an item manufactured from wood. Step 7: The correct sequence is 4, 5, 2, 3, 1.
19
How many distinct arrangements of the letters in the word MATHEMATICS are possible if all the vowels must always stay grouped together?
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Solution: Step 1: Identify the letters in MATHEMATICS. There are 11 letters in total. Step 2: Identify the vowels (A, E, I, A) and consonants (M, T, H, M, T, C, S). - Vowels: A, A, E, I (4 vowels, with 'A' repeated 2 times). - Consonants: M, M, T, T, H, C, S (7 consonants, with 'M' repeated 2 times and 'T' repeated 2 times). Step 3: Treat the block of 4 vowels (AAEI) as a single unit. Now we need to arrange this vowel block along with the 7 consonants. This gives us 8 'units' to arrange: M, T, H, M, T, C, S, (AAEI). Step 4: Identify repeated letters among these 8 units. The letter 'M' appears 2 times, and the letter 'T' appears 2 times. Step 5: Number of ways to arrange these 8 units (with 'M' repeated twice and 'T' repeated twice) = 8! / (2! * 2!). Step 6: Calculate 8! / (2! * 2!) = 40,320 / (2 * 2) = 40,320 / 4 = 10,080 ways. Step 7: Now, consider the arrangements within the vowel block (AAEI). There are 4 letters in this block, with 'A' repeated 2 times. Step 8: Number of ways to arrange the vowels within their block = 4! / 2! = (4 * 3 * 2 * 1) / (2 * 1) = 24 / 2 = 12 ways. Step 9: Apply the product rule: multiply the number of ways to arrange the main units by the number of ways to arrange letters within the vowel block. Step 10: Total number of ways = 10,080 * 12 = 120,960.
20
During a community event, Person A is standing in a row of 30 people. If Person A is 12th from the right side, what is Person A's position from the left side?
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Solution: Step 1: Total people in the row = 30 Step 2: Position of Person A from the right = 12 Step 3: People to the left of Person A = 30 - 12 = 18 Step 4: Position of Person A from the left = 18 + 1 = 19
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