📘 Quiz

Solution: Step 1: Understand the given information: Arrival time = 8:15 AM, Delay = 30 minutes Step 2: Calculate the scheduled reporting time by subtracting the delay from the arrival time Step 3: Scheduled reporting time = 8:15 AM - 30 minutes = 7:45 AM The correct answer is: 7:45 AM

Solution: Step 1: Consider the worst-case scenario where she picks socks of different colors before getting two of each. Step 2: She could pick all 47 red socks and all 24 yellow socks first. Step 3: The next sock she picks after these 71 socks must be blue (17 blue socks available). Step 4: To guarantee she has two blue socks, she needs to pick one more sock. Step 5: Therefore, the total number of socks she must take out is 47 + 24 + 2 = 73 socks.

Solution: Step 1: Let the tens digit be 'x' and the units digit be 'y'. The original number is 10x + y. The number with digits interchanged is 10y + x. Step 2: Analyze Statement I: 'Sum of the digits is 7.' - x + y = 7. (Possible numbers: 16, 25, 34, 43, 52, 61, 70). Not sufficient alone. Step 3: Analyze Statement II: 'Difference between the number and the number obtained by interchanging the digits is 9.' - (10x + y) - (10y + x) = 9 - 9x - 9y = 9 - Dividing by 9: x - y = 1. - (Possible numbers: 21, 32, 43, 54, 65, 76, 87, 98). Not sufficient alone. Step 4: Analyze Statement III: 'Digit in the ten's place is bigger than the digit in the unit's place by 1.' - This translates to x = y + 1, which is equivalent to x - y = 1. - This statement alone is not sufficient as it is the same condition as Statement II. Step 5: Evaluate combinations: - Consider Statements I and II together (or I and III, as II and III are equivalent): - x + y = 7 - x - y = 1 - Add these two equations: (x + y) + (x - y) = 7 + 1 => 2x = 8 => x = 4. - Substitute x = 4 into x + y = 7: 4 + y = 7 => y = 3. - This uniquely determines the number as 43. Step 6: Conclusion: Both Statement I and Statement II (or Statement I and Statement III) are sufficient to determine the number. Since the given options for this problem are mutually exclusive and do not provide a clear 'Either/Or' choice for I+II and I+III, selecting 'None of these' means that a single specific answer option covering this specific situation is not available from the list, though a combination of statements does indeed solve the problem.

Solution: Step 1: Refer to the established arrangement of trees (derived from the full problem rules). Step 2: Locate the raspberry tree within the constructed spatial layout. Step 3: Determine the tree that is situated directly across from the raspberry tree. Step 4: If multiple possibilities or ambiguities exist, present them as the correct options. Step 5: Based on the analysis, 'Papaya or Pomegranate' is the correct answer, indicating two possible trees opposite the raspberry tree depending on the full arrangement.

Solution: Step 1: Recall the rules for identifying a leap year: * A year is a leap year if it is divisible by 4, unless it is a century year. * A century year (ending in '00') is a leap year only if it is divisible by 400. Step 2: Apply these rules to each option: * 700: This is a century year. 700 is not divisible by 400. Therefore, 700 is not a leap year. * 800: This is a century year. 800 is divisible by 400. Therefore, 800 is a leap year. * 1200: This is a century year. 1200 is divisible by 400. Therefore, 1200 is a leap year. * 2000: This is a century year. 2000 is divisible by 400. Therefore, 2000 is a leap year. Step 3: Based on the rules, 700 is the only year listed that is not a leap year.

Solution: ## Step 1: Understand Statement A Statement A implies that if we subtract four from the total number of pencils, we get a prime number. This means the total number of pencils could be 6 (prime: 2), 7 (prime: 3), 9 (prime: 5), 11 (prime: 7), and so on. ## Step 2: Understand Statement B Statement B says the total number of pencils is a multiple of 3. This means the total could be 3, 6, 9, 12, and so on. ## Step 3: Analyze Statement A Alone From Statement A, possible totals include 6, 7, 9, 11, etc. It's clear that without more specific information, we cannot determine the exact number of pencils. ## Step 4: Analyze Statement B Alone From Statement B, the total could be 3, 6, 9, etc. Again, without additional information, the exact number cannot be determined. ## Step 5: Combine Both Statements Combining both, possible totals could still be 9, 15, 21, etc., as these satisfy both conditions (being a multiple of 3 and yielding a prime when 4 is subtracted). ## Step 6: Conclusion Even with both statements, we cannot pinpoint the exact number of pencils in the box as there are multiple possibilities (9, 15, 21, etc.). Therefore, the question cannot be answered even after combining both statements.

Solution: Step 1: Understand that both X and Y start with equal amounts of money, let's call it M. Step 2: From Statement I, after Y buys an item and pays with X's money, X has M - (some amount) and Y has M + (some amount) - cost of item. Step 3: It's given that X has half as much money as Y, so we can form an equation based on this relationship. Step 4: Statement II provides that the cost of the item is $30 because Y paid $50 and got $20 back. Step 5: Combining both statements, if the item costs $30 and X paid for it, we can calculate the exact amounts. Step 6: Let's assume X gave Y $30 for the item. So, X has M - 30 and Y has M + 30 - 30 = M. Step 7: According to Statement I, M - 30 = 0.5 * M, which implies M = 60. Step 8: Therefore, X has 60 - 30 = $30 left. Step 9: Both statements together allow us to determine the money left with X.

Solution: Step 1: Break down the movements: 27 km south, 15 km west, 32 km north, 23 km west Step 2: Calculate the net displacement in the north-south direction: 32 km - 27 km = 5 km north Step 3: Calculate the total displacement in the east-west direction: 15 km + 23 km = 38 km west Step 4: Use Pythagoras' theorem to find the distance back home: sqrt(5^2 + 38^2) = sqrt(25 + 1444) = sqrt(1469) Step 5: Calculate the square root: sqrt(1469) = 97 km (approx) Step 6: The person needs to cover 97 km to get back home.

Solution: Step 1: First, determine the day of the week for May 1st, 2007, using the calendar formula: (Date + Month Code + Last Two Digits of Year + Number of Leap Years + Century Code) / 7. Step 2: Identify the values for May 1st, 2007: * Date: 1 * Month Code (May): 2 * Last two digits of Year (2007): 7 * Number of Leap Years from 2000 to 2007: 1 (2004). * Century Code (2000-2099): 6 Step 3: Sum these values: 1 + 2 + 7 + 1 + 6 = 17. Step 4: Divide the sum by 7 and find the remainder: 17 mod 7 = 3. Step 5: Map the remainder to the day of the week (assuming 0 = Saturday, 1 = Sunday, ..., 3 = Tuesday). So, May 1st, 2007, was a Tuesday. Step 6: Find the first Saturday in May 2007. If May 1st is Tuesday: * May 1 (Tuesday) + 4 days = May 5 (Saturday). So, May 5th is the first Saturday. Step 7: List all Saturdays in May by adding 7 days: * May 5th * May 5th + 7 days = May 12th * May 12th + 7 days = May 19th * May 19th + 7 days = May 26th * May 26th + 7 days = June 2nd (This falls outside May). Step 8: Therefore, the last Saturday in May 2007 was May 26th.

Solution: Step 1: Find the number of odd days in 126 days. Odd days are the remainder when the total number of days is divided by 7. Step 2: Calculate the remainder of 126 divided by 7: 126 mod 7 = 0. Step 3: Since there are 0 odd days, the day of the week will be the same as the starting day. Step 4: As today is Friday, 126 days from now it will also be Friday.

Solution: Step 1: Find the number of odd days in 350 days. Odd days are the remainder when the total number of days is divided by 7. Step 2: Calculate the remainder of 350 divided by 7: 350 mod 7 = 0. Step 3: Since there are 0 odd days, the day of the week will be the same as the starting day. Step 4: As today is Monday, 350 days from now it will also be Monday.

Solution: Step 1: Visualize the hexagonal table with 6 positions. Step 2: Place Person F first, then determine Person A's position two places to the left of F. Step 3: Position Person B between Person C and Person D to satisfy the neighbor condition. Step 4: Place Person E two positions to the left of Person D. Step 5: Analyze the arrangement to find who is opposite Person E. Step 6: Based on the fixed positions, determine that Person B is seated opposite Person E.

Solution: Step 1: Analyze given statements Step 2: Determine dress color and adavu relationships Step 3: Identify the dress color for Thatta Adavu Step 4: Confirm the color based on provided information The Bharatanatyam dress worn by the student learning Thatta Adavu is red.

Solution: Step 1: Given that E and F are in the centre, A and B are at the ends, and C is to the left of A. Step 2: Possible seating arrangement: B _ _ E F C A or B _ E F _ C A. Step 3: From the arrangements, we see D can only be to the right of B in both cases. Step 4: Hence, we can conclude that D is sitting on the right side of B.

Solution: ## Step 1: Understand the given conditions The individuals are seated in a circle with equal distances between them. Ironman is two places to the right of Loki, who is one place to the right of Hawkeye. Pepper forms a 90-degree angle with Thor and a 120-degree angle with Hulk. Hulk is opposite Black Widow and to the left of Thor. ## Step 2: Determine the position of Loki and Hawkeye Given that Ironman is two places right of Loki and Loki is one place right of Hawkeye, we can deduce their sequence: Hawkeye, Loki, Ironman. ## Step 3: Position Pepper, Thor, and Hulk Pepper forms a 90-degree angle with Thor and a 120-degree angle with Hulk. Given the circular nature and equal distances, Pepper must be at a position that creates these angles with Thor and Hulk. ## Step 4: Identify Hulk's and Black Widow's positions Hulk is opposite Black Widow. Given the angles and positions, we can start piecing together the arrangement. ## Step 5: Finalize the seating arrangement With Hulk opposite Black Widow and to the left of Thor, and considering the angles and positions of others, we deduce the seating order. ## Step 6: Determine who is to the immediate left of Black Widow Based on the arrangement and given clues, Pepper Potts is the only person who can be seated on the immediate left of Black Widow. The correct answer is Pepper Potts.

Solution: Step 1: Analyze statement 1 - The person is 30 years younger than a relative. Step 2: Analyze statement 2 - The person's sibling, born in 1980, is 40 years younger than the relative. Step 3: Determine the relative's birth year using both statements. Step 4: Calculate the person's birth year based on the relative's age and the sibling's birth year. Step 5: From statement 2, if the sibling was born in 1980 and is 40 years younger than the relative, the relative was born in 1940. Step 6: Since the person is 30 years younger than the relative born in 1940, the person was born in 1970. Step 7: Therefore, both statements are required to find the person's birth year.

Solution: Step 1: Identify the set representing 'doctors'. Step 2: Identify the set representing 'players'. Step 3: Identify the set representing 'artists'. Step 4: The question asks for 'doctors who are BOTH players AND artists'. This requires finding the region where all three sets overlap simultaneously. Step 5: Locate the numerical value at the central intersection point where all three sets converge. Step 6: Based on the provided information, the number '3' represents this specific count.

Solution: Step 1: Break down the target date (June 20th, 1837) into complete years and days within the target year. This means 1836 complete years + days from Jan 1, 1837, to June 20, 1837. Step 2: Calculate odd days for 1836 years: * Odd days in 1600 years (4 * 400) = 0 odd days. * Remaining years = 1836 - 1600 = 236 years. Break this into 200 years + 36 years. * Odd days in 200 years = 3 odd days. * Odd days in 36 years: Number of leap years in 36 years = 9 (36/4=9). Number of ordinary years = 36 - 9 = 27. * Total odd days in 36 years = (27 * 1) + (9 * 2) = 27 + 18 = 45 odd days. Reduce 45 mod 7 = 3 odd days. * Total odd days for 1836 years = 0 (1600) + 3 (200) + 3 (36) = 6 odd days. Step 3: Calculate odd days from January 1st, 1837, to June 20th, 1837: * Year 1837 is not a leap year. * January: 31 days = 3 odd days. * February: 28 days = 0 odd days. * March: 31 days = 3 odd days. * April: 30 days = 2 odd days. * May: 31 days = 3 odd days. * June: 20 days = 6 odd days (20 mod 7 = 6). * Total odd days for months = 3 + 0 + 3 + 2 + 3 + 6 = 17 odd days. Reduce 17 mod 7 = 3 odd days. Step 4: Sum all odd days: 6 (from years) + 3 (from months) = 9 odd days. Step 5: Reduce 9 mod 7 = 2 odd days. Step 6: Map the total odd day to the day of the week (assuming 0 = Sunday, 1 = Monday, 2 = Tuesday, etc.). Step 7: 2 odd days corresponds to Tuesday. Step 8: Therefore, June 20th, 1837, was a Tuesday.

Solution: Step 1: Analyze given statements Step 2: Determine age and dress color relationships Step 3: Identify the 12-year-old with the yellow dress Step 4: Confirm the age based on provided information The person wearing the yellow dress is 12 years old.