Title: CAT 2018 QA Slot 2: Indian Game Solutions
Question 1:
In a game, there are 10 players. Each player has a unique number from 1 to 10. Players take turns drawing a card from a deck of 10 cards, each labeled with a unique number from 1 to 10. The objective is to draw a card with the same number as the player's number. If a player draws a card with the same number, they win. If not, the turn passes to the next player.
Solution:
Let's consider the probability of a player winning on their first turn. There are 10 cards in the deck, and the player's card is one of them. So, the probability of drawing the correct card on the first turn is 1/10.
For the second turn, there are 9 cards left in the deck. The probability of drawing the correct card on the second turn is 1/9.
Similarly, the probability of drawing the correct card on the third turn is 1/8, and so on.
The probability of a player winning is the sum of the probabilities of winning on each turn:
P(winning) = 1/10 + 1/9 + 1/8 + 1/7 + 1/6 + 1/5 + 1/4 + 1/3 + 1/2 + 1/1
Simplifying the expression, we get:
P(winning) = 10/10 + 10/9 + 10/8 + 10/7 + 10/6 + 10/5 + 10/4 + 10/3 + 10/2 + 10/1
P(winning) = 10(1 + 1/9 + 1/8 + 1/7 + 1/6 + 1/5 + 1/4 + 1/3 + 1/2 + 1)
P(winning) = 10(1 + 0.111 + 0.125 + 0.142857 + 0.166667 + 0.2 + 0.25 + 0.333333 + 0.5 + 1)
P(winning) = 10(3.045)
P(winning) ≈ 30.45%
So, the probability of a player winning the game is approximately 30.45%.
Question 2:
In a game, there are 5 players. Each player has a unique number from 1 to 5. Players take turns drawing a card from a deck of 5 cards, each labeled with a unique number from 1 to 5. The objective is to draw a card with the same number as the player's number. If a player draws a card with the same number, they win. If not, the turn passes to the next player.
Solution:
Let's consider the probability of a player winning on their first turn. There are 5 cards in the deck, and the player's card is one of them. So, the probability of drawing the correct card on the first turn is 1/5.
For the second turn, there are 4 cards left in the deck. The probability of drawing the correct card on the second turn is 1/4.
Similarly, the probability of drawing the correct card on the third turn is 1/3, and so on.
The probability of a player winning is the sum of the probabilities of winning on each turn:
P(winning) = 1/5 + 1/4 + 1/3 + 1/2 + 1/1
Simplifying the expression, we get:
P(winning) = 1/5 + 1/4 + 1/3 + 1/2 + 1
P(winning) = 0.2 + 0.25 + 0.333333 + 0.5 + 1
P(winning) = 2.083333
So, the probability of a player winning the game is approximately 2.083333 or 208.3333%.
Note: This result seems incorrect as the probability cannot exceed 100%. It is possible that there is an error in the problem statement or the solution provided.
嗯，用户让我写一篇关于《CAT 2018 QA Slot 2》的英文解答，内容是印度游戏相关的。首先，我需要确认CAT是什么。CAT通常指Common Admission Test，是印度用于进入MBA院校的考试。2018年的QA部分，也就是Quantitative Ability部分，第二部分题目。用户可能需要详细的题目解析和解答方法。
接下来，我需要回忆或查找CAT 2018 QA Slot 2的具体题目。可能包括数学题，比如代数、几何、概率、数据解读等。由于是印度考试，题目可能涉及本地化的内容，比如商业情景题或者与印度社会相关的数学问题。
用户可能希望得到每道题的详细解答，包括题目原文、解题步骤、可能的错误陷阱以及考试策略。需要确保内容准确，步骤清晰，适合备考的学生参考。同时，用户提到内容要英文，所以整个解答需要用英文撰写，但用户现在需要的是思考过程用中文，所以先处理中文的思考，再输出英文的解答。
可能遇到的挑战是准确回忆或找到CAT 2018 QA Slot 2的具体题目。如果记不清具体题目，可能需要根据常见的CAT QA题型进行推测，或者建议用户提供更多细节。但用户已经指定了标题和内容，可能需要假设一些典型题目，或者参考公开的CAT 2018真题资料。
另外，用户可能希望解答结构清晰，分题目列出，每个题目有解答和解释。可能需要包括时间管理建议，比如如何快速解决难题，或者常见的错误点。例如，CAT考试时间紧张，所以解题技巧如排除法、代入法、逆向思维等可能有用。
还需要注意题目的难度分布，CAT通常分为多个部分，QA部分可能有25题，每题60秒，所以时间管理很重要。解答中应强调如何高效解题，避免在单一题目上花费过多时间。
最后，确保英文解答专业且易于理解，使用学术性的语言但不过于复杂，适合备考学生。可能需要检查是否有重复题目或常见的误解，并在解答中澄清。
Here’s a structured solution guide for CAT 2018 QA Slot 2, focusing on common quantitative aptitude topics and strategic problem-solving approaches. While exact question details may vary, this template aligns with typical CAT QA patterns and provides actionable insights:
CAT 2018 QA Slot 2: Key Topics & Solutions
1. Algebra & Equations
Question Type: Quadratic Equations or Rate Problems
Example:
“Two trains start from stations 300 km apart. Train A travels at 80 km/h, and Train B at 70 km/h. They meet after X hours. If Train B had started 1 hour earlier, they would meet Y hours later. Find X + Y.”
Solution:
Original Meeting Time (X):
( 80X + 70X = 300 ) → ( X = 2.14 ) hours.
Scenario with Delay:
Distance covered by Train B in 1 hour = 70 km. Remaining distance = 230 km.
Combined speed = 150 km/h → Meeting time = ( \frac{230}{150} = 1.53 ) hours.
Total time difference = ( (X + 1) - (1.53) = 2.14 + 1 - 1.53 = 1.61 ).
X + Y = 2.14 + 1.61 ≈ 3.75 (answer rounded to nearest decimal).
Key Tip: Use relative speed and time saved/lost in overlapping scenarios.
2. Geometry & mensuration
Question Type: Circle or Triangle Properties
Example:
“A circle is inscribed in a square of side 10 cm. What is the area of the square not covered by the circle?”
Solution:
Area of square = ( 10^2 = 100 , \text{cm}^2 ).
Radius of circle = ( 5 , \text{cm} ). Area = ( \pi r^2 = 25\pi ).
Uncovered area = ( 100 - 25\pi ≈ 100 - 78.54 = 21.46 , \text{cm}^2 ).
Common Mistake: Forgetting to subtract the circle’s area from the square.
3. Probability & Combinatorics
Question Type: Conditional Probability
Example:
“In a box, 5 red and 3 blue balls. Two balls are drawn. What is the probability both are red, given at least one is red?”
Solution:
Total ways to draw 2 balls = ( C(8,2) = 28 ).
Both red = ( C(5,2) = 10 ).
At least one red = Total – Both blue = ( 28 - C(3,2) = 28 - 3 = 25 ).
Probability = ( \frac{10}{25} = 0.4 ).
Strategy: Use complementary counting for "at least one" problems.
4. Data Interpretation (DI)
Question Type: Table or Graph Analysis
Example:
“Sales data for 4 products (A, B, C, D) over 4 quarters. Q2 sales of B were 20% of Q1 sales of D. Find the ratio of Q2 B to Q1 D.”
Solution:
Let Q1 D = ( x ). Q2 B = ( 0.2x ).
Ratio = ( \frac{0.2x}{x} = 0.2 = \frac{1}{5} ).
Key Tip: Highlight percentages and ratios in DI questions early.
Exam Strategy for CAT QA
Time Allocation:
Spend ≤ 2 minutes per question. Skip and return to hard questions later.
Error Handling:
Avoid overcomplicating algebraic steps. Simplify fractions early.
Answer Verification:
Use estimation (e.g., ( \pi ≈ 3.14 )) to check reasonableness.
Final Note: For precise solutions, cross-reference with official CAT 2018 question papers and answer keys. Practice similar problems to improve speed in overlapping topics like ratios, percentages, and probability.
Let me know if you need further clarification on specific questions! 📚✨
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