Considering the alarming importance of CSAT in UPSC CSE Prelims exam and with enormous requests we received recently, InsightsIAS has started Daily CSAT Test to ensure students practice CSAT Questions on a daily basis. Regular Practice would help one overcome the fear of CSAT too.We are naming this initiative as Insta– DART – Daily Aptitude and Reasoning Test. We hope you will be able to use DART to hit bull’s eye in CSAT paper and comfortably score 100+ even in the most difficult question paper that UPSC can give you in CSP-2021. Your peace of mind after every step of this exam is very important for us.
Looking forward to your enthusiastic participation (both in sending us questions and solving them on daily basis on this portal).
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Question 1 of 5
1. Question
In a tournament of 3 teams X, Y, Z, each plays once with the other. Win = 2 points, draw = 1 point. Each team scored exactly 2 goals in total. Points are: X = 2, Y = 2, Z = 2.
Which is correct?I. All matches were drawn.
II. Every match had exactly 2 goals in total.Correct
Answer: (c)
Solution:
If all teams end with 2 points, they must all draw their two matches. Hence all matches drawn.
Since each team scored exactly 2 goals, over two matches each averaged 1 goal per game. So every match must have ended 1–1.
Both statements are correct.
Answer = (c).Incorrect
Answer: (c)
Solution:
If all teams end with 2 points, they must all draw their two matches. Hence all matches drawn.
Since each team scored exactly 2 goals, over two matches each averaged 1 goal per game. So every match must have ended 1–1.
Both statements are correct.
Answer = (c). -
Question 2 of 5
2. Question
A laptop was stolen. Three suspects X, Y, and Z were questioned. Exactly one is guilty. Statements:
X: I did not cheat. Y cheated.
Y: Z did not cheat. I did not cheat.
Z: I did not cheat. X is lying.Who cheated?
Correct
Answer: (a)
Solution
Case 1: X is guilty. Then X’s two statements are false, so X did cheat and Y did not.
– Y is innocent, so “Z did not cheat” is true and “I did not cheat” is true.
– Z is innocent, so “I did not cheat” is true and “X is lying” is true.
All consistent. Works.Case 2: Y is guilty. Then Y’s two statements are false, so Z did cheat and Y did cheat; two guilty, impossible.
Case 3: Z is guilty. Then Z’s two statements are false, so Z did cheat and X is not lying. If X is truthful, then “Y cheated” must be true, giving two guilty, impossible.
Hence X cheated. Answer (a).
Incorrect
Answer: (a)
Solution
Case 1: X is guilty. Then X’s two statements are false, so X did cheat and Y did not.
– Y is innocent, so “Z did not cheat” is true and “I did not cheat” is true.
– Z is innocent, so “I did not cheat” is true and “X is lying” is true.
All consistent. Works.Case 2: Y is guilty. Then Y’s two statements are false, so Z did cheat and Y did cheat; two guilty, impossible.
Case 3: Z is guilty. Then Z’s two statements are false, so Z did cheat and X is not lying. If X is truthful, then “Y cheated” must be true, giving two guilty, impossible.
Hence X cheated. Answer (a).
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Question 3 of 5
3. Question
Let p + q = 12, where p and q are integers.
Value I = Maximum value of p × q when p, q are positive integers.
Value II = Maximum value of p × q when p ≥ –3, q ≥ –7.Which one of the following is correct?
Correct
Answer: (c)
Solution:
For positives: Value I = 6 × 6 = 36.For Value II: If both negative, maximum = (–3) × (–7) = 21.
If both positive, maximum = 6 × 6 = 36.
So Value II = 36.
But if p = 12, q = 0 (allowed), product = 0, less. So maximum remains 36.Hence, Value I = 36 and Value II = 36. Correction: they are equal.
So the right answer is (c) Value I = Value II.Incorrect
Answer: (c)
Solution:
For positives: Value I = 6 × 6 = 36.For Value II: If both negative, maximum = (–3) × (–7) = 21.
If both positive, maximum = 6 × 6 = 36.
So Value II = 36.
But if p = 12, q = 0 (allowed), product = 0, less. So maximum remains 36.Hence, Value I = 36 and Value II = 36. Correction: they are equal.
So the right answer is (c) Value I = Value II. -
Question 4 of 5
4. Question
In a hockey match, team X playing against team Y was behind by 2 goals with 5 minutes remaining. Does team X win the match?
Statement I: Team Y did not score any goal in the last 5 minutes.
Statement II: Team X scored exactly 2 goals in the last 5 minutes.Correct
Answer: (c)
Solution:
With 5 minutes left: Y − X = 2.Using Statement I alone: If Y scores 0, the result depends on how many X scores. Not sufficient.
Using Statement II alone: If X scores 2, the result depends on whether Y also scores. Not sufficient.
Using both together: X scores 2 and Y scores 0 in the last 5 minutes. Starting from a 2-goal deficit, X exactly catches up. Final outcome is a draw, so X does not win. Together they are sufficient to answer “No”.
Hence, option (c).
Incorrect
Answer: (c)
Solution:
With 5 minutes left: Y − X = 2.Using Statement I alone: If Y scores 0, the result depends on how many X scores. Not sufficient.
Using Statement II alone: If X scores 2, the result depends on whether Y also scores. Not sufficient.
Using both together: X scores 2 and Y scores 0 in the last 5 minutes. Starting from a 2-goal deficit, X exactly catches up. Final outcome is a draw, so X does not win. Together they are sufficient to answer “No”.
Hence, option (c).
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Question 5 of 5
5. Question
Three prime numbers p, q, and r, each less than 30, satisfy p − q = q − r. How many distinct possible values can (p + q + r) take?
Correct
Answer: (c)
Solution:
Again p, q, r are in arithmetic progression.
Primes under 30: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.Prime A.P. triples and sums:
3, 5, 7 → 15
3, 7, 11 → 21
5, 11, 17 → 33
7, 13, 19 → 39
11, 17, 23 → 51
17, 23, 29 → 69
3, 11, 19 → 33
5, 17, 29 → 51Distinct sums: 15, 21, 33, 39, 51, 69. Count is 6. Hence option (c).
Incorrect
Answer: (c)
Solution:
Again p, q, r are in arithmetic progression.
Primes under 30: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.Prime A.P. triples and sums:
3, 5, 7 → 15
3, 7, 11 → 21
5, 11, 17 → 33
7, 13, 19 → 39
11, 17, 23 → 51
17, 23, 29 → 69
3, 11, 19 → 33
5, 17, 29 → 51Distinct sums: 15, 21, 33, 39, 51, 69. Count is 6. Hence option (c).
