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Question 1 / 16
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1
Calculate the product of all the numerical digits displayed on a standard telephone dial.
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Solution: Step 1: Identify all the numbers present on a standard telephone dial. These numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Step 2: Understand the property of multiplication: any number multiplied by zero results in zero. Step 3: Since the set of numbers on the dial includes '0', when all these numbers are multiplied together, the presence of '0' will make the entire product zero. Product = 0 * 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 = 0.
2
Determine the minimum number of ducks required to satisfy the following formation descriptions simultaneously: two ducks are in front of a duck, two ducks are behind a duck, and a duck is positioned between two other ducks.
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Solution: Step 1: This is a riddle that relies on the interpretation of 'a duck' as a single, specific duck within the group. Step 2: Consider a linear arrangement of ducks to achieve the minimum number. Step 3: Let's assume there are 3 ducks: Duck 1, Duck 2, Duck 3, arranged in a single file line. Step 4: Check if the conditions are met: * 'Two ducks in front of a duck': Duck 1 and Duck 2 are in front of Duck 3. (This condition is satisfied for Duck 3). * 'Two ducks behind a duck': Duck 2 and Duck 3 are behind Duck 1. (This condition is satisfied for Duck 1). * 'A duck between two ducks': Duck 2 is positioned between Duck 1 and Duck 3. (This condition is satisfied for Duck 2). Step 5: All three conditions can be simultaneously satisfied with only 3 ducks. Step 6: Therefore, the smallest number of ducks is 3.
3
The technique of solving problems by testing different values for an unknown is known as:
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Solution: Step 1: Identify the problem-solving method described. Step 2: Recognize that the method involves systematically trying various values. Step 3: Match the description to the correct term. Step 4: The method is called the "Trial and error method".
4
Three boxes are labeled incorrectly with 'apples', 'oranges', and 'apples and oranges'. By opening one box and taking out one fruit without looking, you can correctly label all boxes. Which box should be opened?
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Solution: Step 1: Understand that since all labels are incorrect, the box labeled 'apples and oranges' cannot have both. Step 2: If you open the box labeled 'apples and oranges' and find an apple, you know it only contains apples. Step 3: The box labeled 'oranges' must then contain both, as it can't contain only oranges. Step 4: The remaining box labeled 'apples' must contain only oranges. Step 5: Therefore, opening the box labeled 'apples and oranges' allows correct labeling of all boxes.
5
How many doctors are currently practicing in this town? Statement I: There is one doctor for every seven hundred residents. Statement II: The town contains 16 wards, and each ward has a number of doctors equivalent to the total number of wards.
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Solution: Step 1: Analyze Statement I. The statement 'There is one doctor per seven hundred residents' means Total Doctors = (Total Residents / 700). However, the total number of residents in the town is unknown. Therefore, Statement I alone is not sufficient. Step 2: Analyze Statement II. The statement 'There are 16 wards with each ward having as many doctors as the number of wards' means: * Number of wards = 16. * Doctors per ward = 16. * Total Doctors = Number of wards * Doctors per ward = 16 * 16 = 256. Therefore, Statement II alone is sufficient.
6
A badminton singles tournament involves 30 club members, with an elimination rule where a loss removes a member. Assuming no ties, what is the minimum number of matches required to identify the champion?
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Solution: Step 1: In an elimination tournament, to determine a single winner from 'n' participants, 'n-1' participants must be eliminated. Step 2: Each match played results in one loser being eliminated from the tournament. Step 3: Since there are 30 members, 29 members must lose one game to be eliminated. Step 4: Therefore, a minimum of 29 matches must be played to decide the winner.
7
Two statements are given to determine the value of a variable. Analyze if the statements are sufficient to answer the question.
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Solution: Step 1: Understand the question and statements. Step 2: Analyze Statement I: x - 2y = 7. This equation alone cannot determine the value of x. Step 3: Analyze Statement II: 4x - 28 = 8y. This can be simplified to x - 7 = 2y, which also cannot determine the value of x alone. Step 4: Solve both statements together: From Statement I, express x in terms of y: x = 7 + 2y. Substitute in Statement II: 4(7 + 2y) - 28 = 8y, which simplifies to 28 + 8y - 28 = 8y, indicating that these equations are dependent and have infinite solutions. Step 5: Conclusion: Both statements together are not sufficient to answer the question asked and additional data is needed.
8
Sushil, a salesperson, was to meet a high-profile client. Due to health issues, updates couldn't be obtained. On which day did Sushil meet the client? Given: (i) Sushil did not visit on Thursday or Tuesday. (ii) Sushil visited 2 days before the day after Monday that Ravi contacted the client.
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Solution: Step 1: Analyze Statement i: Sushil did not visit on Thursday or Tuesday. Step 2: Possible days for Sushil's visit: Monday, Wednesday, Friday, Saturday. Step 3: Analyze Statement ii: Sushil visited 2 days before the day after Monday that Ravi contacted the client. Step 4: If Ravi contacted the client on Tuesday (day after Monday), Sushil visited on Saturday. Step 5: Statement ii alone is sufficient to conclude that Sushil met the client on Saturday.
9
Given certain symbolic meanings, evaluate conclusions based on provided statements.
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Solution: ## Step 1: Understand the given symbolic meanings - $: A > B - @: A >= B - *: A = B - **: A < B - #: A <= B ## Step 2: Analyze the given statements - P @ Q => P >= Q - M # N => M <= N - N ** Q => N < Q ## Step 3: Combine the inequalities From P >= Q and Q > N and N >= M, we get: P >= Q > N >= M ## Step 4: Evaluate Conclusion I - P > M is true based on combined inequalities. ## Step 5: Evaluate Conclusion II - P > N is true, but N # P (N <= P) can be true or false based on equality, so II is not definitely true. ## Step 6: Determine the correct answer Since only Conclusion I is definitely true, the answer is: if only the conclusion I is true.
10
A drawer contains 20 black socks and 20 brown socks. If a man must pull out socks in complete darkness, what is the minimum number of socks he needs to take out to guarantee he has a matching pair?
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Solution: Step 1: To guarantee a matching pair, we consider the worst-case scenario. Step 2: The worst-case is that the first two socks drawn are of different colours. Step 3: So, the first sock drawn could be a black sock. Step 4: The second sock drawn could be a brown sock. Step 5: At this point, the man has one black and one brown sock, without a matching pair. Step 6: Any third sock drawn, regardless of its colour (black or brown), must necessarily match one of the two socks already drawn. Step 7: Therefore, he must take out 3 socks to be absolutely sure of having a matching pair.
11
A set S has two properties: (1) if p is in S, then 1/p is in S, and (2) if p and q are in S, then p + q is in S. Is 5 in S? Given: (1) 1/5 is in S, (2) 1/2 is in S
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Solution: Step 1: Analyze the properties of set S. Step 2: Evaluate Statement 1: If 1/5 is in S, then 5 must be in S by property 1. Step 3: Statement 1 alone is sufficient to conclude that 5 is in S. Step 4: Evaluate Statement 2: If 1/2 is in S, we cannot directly conclude that 5 is in S. Step 5: Statement 2 does not provide enough information to conclude that 5 is in S. Step 6: Therefore, Statement 1 alone concludes that 5 is in S.
12
A bird shooter was asked about the number of birds in his bag. He responded: 'All are sparrows except six, all are pigeons except six, and all are ducks except six.' How many birds were in his bag in total?
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Solution: Step 1: Let 'S' be the number of sparrows, 'P' be the number of pigeons, and 'D' be the number of ducks. Step 2: Let 'Total' be the total number of birds in the bag. So, Total = S + P + D. Step 3: "All sparrows but six" means that the non-sparrow birds (pigeons + ducks) sum to 6. Thus, P + D = 6 (Equation 1). Step 4: "All pigeons but six" means that the non-pigeon birds (sparrows + ducks) sum to 6. Thus, S + D = 6 (Equation 2). Step 5: "All ducks but six" means that the non-duck birds (sparrows + pigeons) sum to 6. Thus, S + P = 6 (Equation 3). Step 6: We have a system of three linear equations: 1. P + D = 6 2. S + D = 6 3. S + P = 6 Step 7: From Equation 1 and Equation 2, since P + D = 6 and S + D = 6, it implies that P must be equal to S. Step 8: Substitute P = S into Equation 3: S + S = 6 => 2S = 6 => S = 3. Step 9: Since S = P, then P = 3. Step 10: Substitute P = 3 into Equation 1: 3 + D = 6 => D = 3. Step 11: So, there are 3 sparrows, 3 pigeons, and 3 ducks. Step 12: The total number of birds in the bag = S + P + D = 3 + 3 + 3 = 9.
13
In two different companies, the ratio of male to female employees is given. Which company has a higher ratio of male to female employees?
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Solution: Step 1: Analyze the given ratios for both companies. Step 2: Company A - Let the number of male employees be M and female employees be 0.5M. Step 3: Company B - Let the number of female employees be F and male employees be 2F. Step 4: Calculate the ratio of male to female employees for Company A: M:0.5M = 2:1. Step 5: Calculate the ratio of male to female employees for Company B: 2F:F = 2:1. Step 6: Compare the ratios: Both companies have the same ratio of 2:1. Step 7: Conclusion: The ratio of male to female employees is the same for both companies.
14
Five siblings are assigned to different houses (Blue, Black, Yellow, White, Green) and sports teams (Chess, Football, Tennis, Rugby, Shotput). Given certain constraints, which house is assigned to the sibling who plays Rugby?
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Solution: Step 1: Process given information 1. A (Chess) not in Black house 2. C in White house 3. Tennis in Green house 4. D, B not in Rugby 5. B in Blue house 6. E in Shotput Step 2: Deduce house for Rugby From constraints: C in Rugby and White house Step 3: Conclusion: White house
15
Determine who is the heaviest among A, B, C, and D given two statements. Statement I: A is lighter than B and C but heavier than D. Statement II: C is not the heaviest.
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Solution: Step 1: Analyze Statement I: A
16
A train is traveling at 100 km/hr. What information is needed to find the time it takes to cross platform B? Statement I: The train's length is 500 meters. Statement II: Platform B's length is 1 km.
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Solution: Step 1: Understand that to determine the time taken by the train to cross platform B, we need the total distance covered (length of train + length of platform) and the speed of the train. Step 2: The speed of the train is given as 100 km/hr. Step 3: Statement I provides the length of the train as 500 meters but not the length of platform B. Step 4: Statement II provides the length of platform B as 1 km but not the length of the train. Step 5: Alone, Statement I or Statement II is insufficient because we need both lengths to calculate the time taken. Step 6: Together, both statements provide the necessary information: total distance = 500 meters (train) + 1000 meters (platform) = 1500 meters = 1.5 km. Step 7: Convert the speed to meters per second for uniformity: 100 km/hr = 100 * (1000 / 3600) m/s = 250/9 m/s. Step 8: Calculate the time taken using the formula time = distance / speed. Step 9: Hence, BOTH statements TOGETHER are sufficient to answer, but NEITHER statement ALONE is sufficient.
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