UPSC Insta–DART (Daily Aptitude and Reasoning Test) 25 Aug 2025
Kartavya Desk Staff
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 Two statements are given below followed by a question: S1: The number is greater than one. S2: The number has 3 factors. Question: What is the number if it is a positive integer < 11? Which one of the following is correct with respect to above? (a) S1 alone is sufficient to answer the Question (b) S2 alone is sufficient to answer the Question (c) S1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question (d) S1 and S2 together are not sufficient to answer the Question Correct Answer: D Solution The number is greater than one. So, possible numbers will be: 2, 3……10 Thus, there is no unique solution. Therefore, S1 alone is not sufficient to answer the question. From S2: The number has 3 Factors. 4 and 9 are such numbers, which have only 3 factors. Thus, there is no unique solution. Therefore, S2 alone is not sufficient to answer the question. From S1 and S2: Even on combining S1 and S2, we are not able to find a unique solution. Therefore, S1 and S2 together are not sufficient to answer the question Incorrect Answer: D Solution The number is greater than one. So, possible numbers will be: 2, 3……10 Thus, there is no unique solution. Therefore, S1 alone is not sufficient to answer the question. From S2: The number has 3 Factors. 4 and 9 are such numbers, which have only 3 factors. Thus, there is no unique solution. Therefore, S2 alone is not sufficient to answer the question. From S1 and S2: Even on combining S1 and S2, we are not able to find a unique solution. Therefore, S1 and S2 together are not sufficient to answer the question
#### 1. Question
Two statements are given below followed by a question:
S1: The number is greater than one.
S2: The number has 3 factors.
Question: What is the number if it is a positive integer < 11?
Which one of the following is correct with respect to above?
• (a) S1 alone is sufficient to answer the Question
• (b) S2 alone is sufficient to answer the Question
• (c) S1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question
• (d) S1 and S2 together are not sufficient to answer the Question
The number is greater than one. So, possible numbers will be: 2, 3……10
Thus, there is no unique solution. Therefore, S1 alone is not sufficient to answer the question.
From S2: The number has 3 Factors. 4 and 9 are such numbers, which have only 3 factors. Thus, there is no unique solution.
Therefore, S2 alone is not sufficient to answer the question.
From S1 and S2: Even on combining S1 and S2, we are not able to find a unique solution.
Therefore, S1 and S2 together are not sufficient to answer the question
The number is greater than one. So, possible numbers will be: 2, 3……10
Thus, there is no unique solution. Therefore, S1 alone is not sufficient to answer the question.
From S2: The number has 3 Factors. 4 and 9 are such numbers, which have only 3 factors. Thus, there is no unique solution.
Therefore, S2 alone is not sufficient to answer the question.
From S1 and S2: Even on combining S1 and S2, we are not able to find a unique solution.
Therefore, S1 and S2 together are not sufficient to answer the question
• Question 2 of 5 2. Question A Salesman charges sales tax of x% up to Rs.4,000 and above it he charges y%. A customer pays a total tax of Rs 400 when he purchases goods worth Rs. 6,000 and he pays the total tax of Rs. 2200 for the goods worth Rs. 24,000. The value of x and y is: (a) 4, 6 (b) 2, 3 (c) 5, 10 (d) 2, 4 Correct Answer: C Let the tax slab be: x% on the first ₹4,000 y% on the amount above ₹4,000 For a purchase of ₹6,000: For a purchase of ₹24,000: Subtract (1) from (2): 9y=90⇒y=10. From (1): 2x+10=20⇒2x=10⇒x=5 Hence, x=5%, y=10% Incorrect Answer: C Let the tax slab be: x% on the first ₹4,000 y% on the amount above ₹4,000 For a purchase of ₹6,000: For a purchase of ₹24,000: Subtract (1) from (2): 9y=90⇒y=10. From (1): 2x+10=20⇒2x=10⇒x=5 Hence, x=5%, y=10%
#### 2. Question
A Salesman charges sales tax of x% up to Rs.4,000 and above it he charges y%. A customer pays a total tax of Rs 400 when he purchases goods worth Rs. 6,000 and he pays the total tax of Rs. 2200 for the goods worth Rs. 24,000. The value of x and y is:
Let the tax slab be:
• x% on the first ₹4,000
• y% on the amount above ₹4,000
For a purchase of ₹6,000:
For a purchase of ₹24,000:
Subtract (1) from (2): 9y=90⇒y=10. From (1): 2x+10=20⇒2x=10⇒x=5
Hence, x=5%, y=10%
Let the tax slab be:
• x% on the first ₹4,000
• y% on the amount above ₹4,000
For a purchase of ₹6,000:
For a purchase of ₹24,000:
Subtract (1) from (2): 9y=90⇒y=10. From (1): 2x+10=20⇒2x=10⇒x=5
Hence, x=5%, y=10%
• Question 3 of 5 3. Question Five people M, N, O, P, and Q are sitting in a row. M is sitting next to N, and O is sitting next to P. Now consider: Statement I: Q is sitting at one end of the bench. Statement II: M is sitting at the second position from the right, and Q is not sitting next to N. Statement III: P is sitting to the immediate left of O. Question: What is the position of Q? How many of the given statements are required to answer the question? (a) Only one (b) Only two (c) All three (d) ) None of the above Correct Answer: (d) Solution: Number seats 1–5 (left→right). From Stmt II, M = 4, and NNN is 3 or 5; also QQQ not next to NNN. From Stmt III, P immediately left of O ⇒ (P,O)(P,O)(P,O) is (1,2)(1,2)(1,2) or (2,3)(2,3)(2,3). From Stmt I, Q is at an end. Two valid arrangements that satisfy I, II, III: P O N M Q ⇒ Q=5Q=5Q=5 (with N=3N=3N=3) Q P O M N ⇒ Q=1Q=1Q=1 (with N=5N=5N=5) Since QQQ can be 1 or 5, the position isn’t unique. Answer: (d) None of the above. Incorrect Answer: (d) Solution: Number seats 1–5 (left→right). From Stmt II, M = 4, and NNN is 3 or 5; also QQQ not next to NNN. From Stmt III, P immediately left of O ⇒ (P,O)(P,O)(P,O) is (1,2)(1,2)(1,2) or (2,3)(2,3)(2,3). From Stmt I, Q is at an end. Two valid arrangements that satisfy I, II, III: P O N M Q ⇒ Q=5Q=5Q=5 (with N=3N=3N=3) Q P O M N ⇒ Q=1Q=1Q=1 (with N=5N=5N=5) Since QQQ can be 1 or 5, the position isn’t unique. Answer: (d) None of the above.
#### 3. Question
Five people M, N, O, P, and Q are sitting in a row. M is sitting next to N, and O is sitting next to P. Now consider:
• Statement I: Q is sitting at one end of the bench.
• Statement II: M is sitting at the second position from the right, and Q is not sitting next to N.
• Statement III: P is sitting to the immediate left of O.
Question: What is the position of Q? How many of the given statements are required to answer the question?
• (a) Only one
• (b) Only two
• (c) All three
• (d) ) None of the above
Answer: (d)
Solution:
Number seats 1–5 (left→right). From Stmt II, M = 4, and NNN is 3 or 5; also QQQ not next to NNN. From Stmt III, P immediately left of O ⇒ (P,O)(P,O)(P,O) is (1,2)(1,2)(1,2) or (2,3)(2,3)(2,3). From Stmt I, Q is at an end.
Two valid arrangements that satisfy I, II, III:
P O N M Q ⇒ Q=5Q=5Q=5 (with N=3N=3N=3)
Q P O M N ⇒ Q=1Q=1Q=1 (with N=5N=5N=5)
Since QQQ can be 1 or 5, the position isn’t unique. Answer: (d) None of the above.
Answer: (d)
Solution:
Number seats 1–5 (left→right). From Stmt II, M = 4, and NNN is 3 or 5; also QQQ not next to NNN. From Stmt III, P immediately left of O ⇒ (P,O)(P,O)(P,O) is (1,2)(1,2)(1,2) or (2,3)(2,3)(2,3). From Stmt I, Q is at an end.
Two valid arrangements that satisfy I, II, III:
P O N M Q ⇒ Q=5Q=5Q=5 (with N=3N=3N=3)
Q P O M N ⇒ Q=1Q=1Q=1 (with N=5N=5N=5)
Since QQQ can be 1 or 5, the position isn’t unique. Answer: (d) None of the above.
• Question 4 of 5 4. Question The average age of 60 students is 20 years. When 15 new students are admitted, the average increases by 0.4 years. What must be the average age of the new students? (a) 22 years (b) 23 years (c) 24 years (d) None of these Correct Answer: (a) Explanation: Let the average age of the newly admitted 15 students be x years. So, total age of the 15 new students = 15x Given: Average age of existing 60 students = 20 ⇒ Total age of 60 students = 60 × 20 = 1200 After 15 new students join, total students = 75 New average = 20 + 0.4 = 20.4 ⇒ Total age of 75 students = 75 × 20.4 = 1530 Now set up the equation: 1200 + 15x = 1530 ⇒ 15x = 1530 − 1200 = 330 ⇒ x = 330 ÷ 15 = 22 Hence, the average age of the 15 new students is 22 years Correct option: (a) Incorrect Answer: (a) Explanation: Let the average age of the newly admitted 15 students be x years. So, total age of the 15 new students = 15x Given: Average age of existing 60 students = 20 ⇒ Total age of 60 students = 60 × 20 = 1200 After 15 new students join, total students = 75 New average = 20 + 0.4 = 20.4 ⇒ Total age of 75 students = 75 × 20.4 = 1530 Now set up the equation: 1200 + 15x = 1530 ⇒ 15x = 1530 − 1200 = 330 ⇒ x = 330 ÷ 15 = 22 Hence, the average age of the 15 new students is 22 years Correct option: (a)
#### 4. Question
The average age of 60 students is 20 years. When 15 new students are admitted, the average increases by 0.4 years. What must be the average age of the new students?
• (a) 22 years
• (b) 23 years
• (c) 24 years
• (d) None of these
Answer: (a)
Explanation: Let the average age of the newly admitted 15 students be x years. So, total age of the 15 new students = 15x
Given: Average age of existing 60 students = 20 ⇒ Total age of 60 students = 60 × 20 = 1200
After 15 new students join, total students = 75 New average = 20 + 0.4 = 20.4 ⇒ Total age of 75 students = 75 × 20.4 = 1530
Now set up the equation: 1200 + 15x = 1530 ⇒ 15x = 1530 − 1200 = 330 ⇒ x = 330 ÷ 15 = 22
Hence, the average age of the 15 new students is 22 years Correct option: (a)
Answer: (a)
Explanation: Let the average age of the newly admitted 15 students be x years. So, total age of the 15 new students = 15x
Given: Average age of existing 60 students = 20 ⇒ Total age of 60 students = 60 × 20 = 1200
After 15 new students join, total students = 75 New average = 20 + 0.4 = 20.4 ⇒ Total age of 75 students = 75 × 20.4 = 1530
Now set up the equation: 1200 + 15x = 1530 ⇒ 15x = 1530 − 1200 = 330 ⇒ x = 330 ÷ 15 = 22
Hence, the average age of the 15 new students is 22 years Correct option: (a)
• Question 5 of 5 5. Question Rahul walks from his home to the market at a speed of 4 km/hr and returns by bicycle at a speed of 12 km/hr. If the total time taken for the entire trip is 4 hours, what is the distance between his home and the market? (a) 8 km (b) 6 km (c) 9 km (d) 12 km Correct Answer: D Solution: Let the distance be x km. Time taken while walking = x/4 Time taken while cycling = x/12 Total time = 4 hours So, Take LCM: Incorrect Answer: D Solution: Let the distance be x km. Time taken while walking = x/4 Time taken while cycling = x/12 Total time = 4 hours So, Take LCM:
#### 5. Question
Rahul walks from his home to the market at a speed of 4 km/hr and returns by bicycle at a speed of 12 km/hr. If the total time taken for the entire trip is 4 hours, what is the distance between his home and the market?
Answer: D
Solution: Let the distance be x km.
Time taken while walking = x/4
Time taken while cycling = x/12
Total time = 4 hours
Answer: D
Solution: Let the distance be x km.
Time taken while walking = x/4
Time taken while cycling = x/12
Total time = 4 hours
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