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Previous Year Topic Wise Questions With Solutions: Arithmetical Reasoning | CSAT Preparation - UPSC PDF Download

Q1. Three teams P, Q, R participated in a tournament in which the teams play with one another exactly once. A win fetches a team 2 points and a draw 1 point. A team gets no point for a loss. Each team scored exactly one goal in the tournament. The team P got 3 points, Q got 2 points and R got 1 point. Which of the following statements is/are correct? 
I. The result of the match between P and Q is a draw with the score 0 -0. 
II. The number of goals scored by R against Q is 1. 
Which of the statements given above is/are correct?    (2025)
(a) I only 
(b) II only 
(c) Both I and II 
(d) Neither I nor II

Previous Year Topic Wise Questions With Solutions: Arithmetical Reasoning | CSAT Preparation - UPSCView Answer  Previous Year Topic Wise Questions With Solutions: Arithmetical Reasoning | CSAT Preparation - UPSC

Ans: (c)
Teams play each other exactly once, so there are 3 matches in total.

  • P vs Q
  • P vs R
  • Q vs R

Team P (3 points): P must have won 1 match and drawn 1 match.
Team Q (2 points): Q must have drawn both the matches.
Team R (1 point): R must have lost 1 match and drawn 1 match.
As P has won one match and R has lost one match, it’s obvious that P must have defeated R.
As a team must score at least one goal to win, P must have scored its lone goal in this match.
So, scoreline of P-R match would have been 1-0.
Now, P cannot have scored any other goal in the tournament. Which means that scoreline of PQ match would have been 0-0.
So, the scoreline of Q-R match would have been 1-1.
So, both statements are correct.
Hence, option (c) is the correct answer.

Q2. Let p, q, r and s be distinct positive integers. Let p, q be odd and r, s be even. Consider the following statements: 
1. (p-r)2 (qs) is even. 
2. (q-s)q2 s is even. 
3. (q + r)2 (p + s) is odd. 
Which of the statements given above are correct?     (2024)
(a) 1 and 2 only 
(b) 2 and 3 only 
(c) 1 and 3 only 
(d) 1, 2 and 3

Previous Year Topic Wise Questions With Solutions: Arithmetical Reasoning | CSAT Preparation - UPSCView Answer  Previous Year Topic Wise Questions With Solutions: Arithmetical Reasoning | CSAT Preparation - UPSC

Ans: (d)
p and q are odd numbers.
Similarly, r and s are even numbers.
Statement 1: (p - r)2 (qs) is even, as s is an even number. This statement is correct.
Statement 2: (q - s)q2 s is even, as s is an even number. This statement is correct.
Statement 3: (q + r)2 (p + s) is odd, as both (q + r) and (p + s) are odd. This statement is correct.

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FAQs on Previous Year Topic Wise Questions With Solutions: Arithmetical Reasoning - CSAT Preparation - UPSC

1. What is Arithmetical Reasoning and how is it relevant for UPSC exams?
Ans.Arithmetical Reasoning involves the ability to solve problems using basic arithmetic and logical reasoning skills. It is relevant for UPSC exams as it tests candidates on their quantitative aptitude, which is essential for various competitive exams and civil services selection. This section typically includes questions on number series, percentages, ratios, and relationships among numbers, which are crucial for decision-making and analytical thinking in administrative roles.
2. What types of questions can be expected in the Arithmetical Reasoning section of UPSC exams?
Ans. In the Arithmetical Reasoning section, candidates can expect questions that cover a range of topics, including but not limited to, basic operations (addition, subtraction, multiplication, division), problems on ages, time and work, profit and loss, percentage calculations, and ratio and proportion. These questions often require candidates to apply logical reasoning to arrive at the correct answer.
3. How can candidates effectively prepare for the Arithmetical Reasoning section in UPSC exams?
Ans. Candidates can effectively prepare for the Arithmetical Reasoning section by practicing regularly with previous years' question papers and sample papers. They should focus on understanding concepts and formulas, work on time management to solve problems quickly, and take mock tests to gauge their performance. Additionally, reviewing mistakes and focusing on weak areas can help improve accuracy and speed.
4. Are there any specific strategies to tackle complex Arithmetical Reasoning problems in the UPSC exams?
Ans. Yes, some effective strategies include breaking down complex problems into smaller, manageable parts, using diagrams or charts for visual representation, and identifying keywords that indicate specific operations or relationships. Candidates should also practice estimation techniques to quickly eliminate unlikely options in multiple-choice questions and ensure that they read questions carefully to avoid common mistakes.
5. What resources are recommended for studying Arithmetical Reasoning for UPSC exams?
Ans. Recommended resources for studying Arithmetical Reasoning include standard mathematics textbooks that cover quantitative aptitude, online platforms offering practice tests and video lectures, and coaching materials specifically designed for UPSC preparation. Additionally, solving previous years' question papers and participating in study groups can enhance understanding and retention of concepts.
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