UPSC Insta–DART (Daily Aptitude and Reasoning Test) 21 Jan 2026
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).
#### Quiz-summary
0 of 5 questions completed
Questions:
#### Information
Best of Luck! 🙂
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading...
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
0 of 5 questions answered correctly
Your time:
Time has elapsed
You have reached 0 of 0 points, (0)
#### Categories
• Not categorized 0%
• Question 1 of 5 1. Question Consider the following including the Question and the Statements: There are 5 persons: P, Q, R, S, and T. Question: How is R related to S? Statements: P is the father of R. Q is the brother of P and S is the daughter of Q. T is the mother of Q. Which one of the following is correct in respect of the above Question and Statements? (a) Statement-1, and Statement-2 are sufficient to answer the Question. (b) Statement-1, and Statement-3 are sufficient to answer the Question. (c) All three statements together are sufficient to answer the Question. (d) All three statements are not sufficient to answer the Question. Correct Answer: (a) Explanation: From (1): P is the father of R ⇒ R is the child of P. From (2): Q is the brother of P ⇒ Q is R’s paternal uncle. S is the daughter of Q ⇒ S is the daughter of R’s uncle. So, using (1) and (2) together: R is the child of P. S is the child of R’s uncle (Q). ⇒ R and S are first cousins. The relation “cousin” does not depend on the gender of R or S, so it is fully determined. Statement (3) only tells us T is the mother of Q, i.e., grandmother of S and aunt/grandmother relation chain, but this is not needed to determine how R is related to S. (1) and (3) together: link P, Q, T but no information about S. (2) and (3) together: link Q, S, T, but nothing about R. Hence, Statement-1 and Statement-2 are sufficient, so option (a) is correct. Incorrect Answer: (a) Explanation: From (1): P is the father of R ⇒ R is the child of P. From (2): Q is the brother of P ⇒ Q is R’s paternal uncle. S is the daughter of Q ⇒ S is the daughter of R’s uncle. So, using (1) and (2) together: R is the child of P. S is the child of R’s uncle (Q). ⇒ R and S are first cousins. The relation “cousin” does not depend on the gender of R or S, so it is fully determined. Statement (3) only tells us T is the mother of Q, i.e., grandmother of S and aunt/grandmother relation chain, but this is not needed to determine how R is related to S. (1) and (3) together: link P, Q, T but no information about S. (2) and (3) together: link Q, S, T, but nothing about R. Hence, Statement-1 and Statement-2 are sufficient, so option (a) is correct.
#### 1. Question
Consider the following including the Question and the Statements:
There are 5 persons: P, Q, R, S, and T.
Question: How is R related to S?
Statements:
• P is the father of R.
• Q is the brother of P and S is the daughter of Q.
• T is the mother of Q.
Which one of the following is correct in respect of the above Question and Statements?
• (a) Statement-1, and Statement-2 are sufficient to answer the Question.
• (b) Statement-1, and Statement-3 are sufficient to answer the Question.
• (c) All three statements together are sufficient to answer the Question.
• (d) All three statements are not sufficient to answer the Question.
Answer: (a)
Explanation:
• From (1): P is the father of R ⇒ R is the child of P.
• P is the father of R ⇒ R is the child of P.
• From (2): Q is the brother of P ⇒ Q is R’s paternal uncle. S is the daughter of Q ⇒ S is the daughter of R’s uncle.
• Q is the brother of P ⇒ Q is R’s paternal uncle.
• S is the daughter of Q ⇒ S is the daughter of R’s uncle.
So, using (1) and (2) together:
• R is the child of P.
• S is the child of R’s uncle (Q). ⇒ R and S are first cousins. The relation “cousin” does not depend on the gender of R or S, so it is fully determined.
• Statement (3) only tells us T is the mother of Q, i.e., grandmother of S and aunt/grandmother relation chain, but this is not needed to determine how R is related to S.
• (1) and (3) together: link P, Q, T but no information about S.
• (2) and (3) together: link Q, S, T, but nothing about R.
Hence, Statement-1 and Statement-2 are sufficient, so option (a) is correct.
Answer: (a)
Explanation:
• From (1): P is the father of R ⇒ R is the child of P.
• P is the father of R ⇒ R is the child of P.
• From (2): Q is the brother of P ⇒ Q is R’s paternal uncle. S is the daughter of Q ⇒ S is the daughter of R’s uncle.
• Q is the brother of P ⇒ Q is R’s paternal uncle.
• S is the daughter of Q ⇒ S is the daughter of R’s uncle.
So, using (1) and (2) together:
• R is the child of P.
• S is the child of R’s uncle (Q). ⇒ R and S are first cousins. The relation “cousin” does not depend on the gender of R or S, so it is fully determined.
• Statement (3) only tells us T is the mother of Q, i.e., grandmother of S and aunt/grandmother relation chain, but this is not needed to determine how R is related to S.
• (1) and (3) together: link P, Q, T but no information about S.
• (2) and (3) together: link Q, S, T, but nothing about R.
Hence, Statement-1 and Statement-2 are sufficient, so option (a) is correct.
• Question 2 of 5 2. Question A train leaves a station every 20 minutes at a uniform speed of 54 km/h. A jeep starting from the same station and moving in the same direction meets a train every 30 minutes. Find the speed of the jeep. (a) 80 km/h (b) 63 km/h (c) 90 km/h (d) 72 km/h Correct Incorrect
#### 2. Question
A train leaves a station every 20 minutes at a uniform speed of 54 km/h. A jeep starting from the same station and moving in the same direction meets a train every 30 minutes. Find the speed of the jeep.
• (a) 80 km/h
• (b) 63 km/h
• (c) 90 km/h
• (d) 72 km/h
• Question 3 of 5 3. Question Find the maximum value of ‘n’ such that 120 × 90 × 25 × 6 is perfectly divisible by 30ⁿ. (a) 1 (b) 2 (c) 3 (d) 4 Correct Answer: (d) Solution: We need 120 × 90 × 25 × 6 to be divisible by 30ⁿ. 30 = 2 × 3 × 5 ⇒ 30ⁿ = 2ⁿ × 3ⁿ × 5ⁿ. Prime factorisation of each term: 120 = 2³ × 3 × 5 90 = 2 × 3² × 5 25 = 5² 6 = 2 × 3 Now count powers: 2’s: 120 (3) + 90 (1) + 6 (1) = 3 + 1 + 1 = 5 3’s: 120 (1) + 90 (2) + 6 (1) = 1 + 2 + 1 = 4 5’s: 120 (1) + 90 (1) + 25 (2) = 1 + 1 + 2 = 4 So the product = 2⁵ × 3⁴ × 5⁴ × (other primes if any). Write in terms of 30: = (2⁴ × 3⁴ × 5⁴) × 2¹ = 30⁴ × 2 The maximum power of 30 that divides this expression is therefore 30⁴. So the maximum value of ‘n’ is 4. Hence, option (d) is correct. Incorrect Answer: (d) Solution: We need 120 × 90 × 25 × 6 to be divisible by 30ⁿ. 30 = 2 × 3 × 5 ⇒ 30ⁿ = 2ⁿ × 3ⁿ × 5ⁿ. Prime factorisation of each term: 120 = 2³ × 3 × 5 90 = 2 × 3² × 5 25 = 5² 6 = 2 × 3 Now count powers: 2’s: 120 (3) + 90 (1) + 6 (1) = 3 + 1 + 1 = 5 3’s: 120 (1) + 90 (2) + 6 (1) = 1 + 2 + 1 = 4 5’s: 120 (1) + 90 (1) + 25 (2) = 1 + 1 + 2 = 4 So the product = 2⁵ × 3⁴ × 5⁴ × (other primes if any). Write in terms of 30: = (2⁴ × 3⁴ × 5⁴) × 2¹ = 30⁴ × 2 The maximum power of 30 that divides this expression is therefore 30⁴. So the maximum value of ‘n’ is 4. Hence, option (d) is correct.
#### 3. Question
Find the maximum value of ‘n’ such that 120 × 90 × 25 × 6 is perfectly divisible by 30ⁿ.
Answer: (d)
Solution: We need 120 × 90 × 25 × 6 to be divisible by 30ⁿ. 30 = 2 × 3 × 5 ⇒ 30ⁿ = 2ⁿ × 3ⁿ × 5ⁿ.
Prime factorisation of each term:
120 = 2³ × 3 × 5 90 = 2 × 3² × 5 25 = 5² 6 = 2 × 3
Now count powers:
2’s: 120 (3) + 90 (1) + 6 (1) = 3 + 1 + 1 = 5
3’s: 120 (1) + 90 (2) + 6 (1) = 1 + 2 + 1 = 4
5’s: 120 (1) + 90 (1) + 25 (2) = 1 + 1 + 2 = 4
So the product = 2⁵ × 3⁴ × 5⁴ × (other primes if any).
Write in terms of 30:
= (2⁴ × 3⁴ × 5⁴) × 2¹ = 30⁴ × 2
The maximum power of 30 that divides this expression is therefore 30⁴.
So the maximum value of ‘n’ is 4.
Hence, option (d) is correct.
Answer: (d)
Solution: We need 120 × 90 × 25 × 6 to be divisible by 30ⁿ. 30 = 2 × 3 × 5 ⇒ 30ⁿ = 2ⁿ × 3ⁿ × 5ⁿ.
Prime factorisation of each term:
120 = 2³ × 3 × 5 90 = 2 × 3² × 5 25 = 5² 6 = 2 × 3
Now count powers:
2’s: 120 (3) + 90 (1) + 6 (1) = 3 + 1 + 1 = 5
3’s: 120 (1) + 90 (2) + 6 (1) = 1 + 2 + 1 = 4
5’s: 120 (1) + 90 (1) + 25 (2) = 1 + 1 + 2 = 4
So the product = 2⁵ × 3⁴ × 5⁴ × (other primes if any).
Write in terms of 30:
= (2⁴ × 3⁴ × 5⁴) × 2¹ = 30⁴ × 2
The maximum power of 30 that divides this expression is therefore 30⁴.
So the maximum value of ‘n’ is 4.
Hence, option (d) is correct.
• Question 4 of 5 4. Question An amount of ₹72 was spent on notebooks and pens. A notebook costs ₹8 and a pen costs ₹4. Which one of the following statements is correct? (a) More pens were bought than notebooks. (b) More notebooks were bought than pens. (c) The number of notebooks and pens must be equal. (d) We cannot determine whether they bought more notebooks or more pens. Correct Answer: (d) Solution: Equation: 8n + 4p = 72 Divide by 4: 2n + p = 18 Try values: Case 1: n = 5 → p = 8 → More pens Case 2: n = 6 → p = 6 → Equal Case 3: n = 7 → p = 4 → More notebooks Since all three outcomes are possible, we cannot determine which one is more. Hence, option (d) is correct. Incorrect Answer: (d) Solution: Equation: 8n + 4p = 72 Divide by 4: 2n + p = 18 Try values: Case 1: n = 5 → p = 8 → More pens Case 2: n = 6 → p = 6 → Equal Case 3: n = 7 → p = 4 → More notebooks Since all three outcomes are possible, we cannot determine which one is more. Hence, option (d) is correct.
#### 4. Question
An amount of ₹72 was spent on notebooks and pens. A notebook costs ₹8 and a pen costs ₹4. Which one of the following statements is correct?
• (a) More pens were bought than notebooks.
• (b) More notebooks were bought than pens.
• (c) The number of notebooks and pens must be equal.
• (d) We cannot determine whether they bought more notebooks or more pens.
Answer: (d)
Solution:
Equation: 8n + 4p = 72 Divide by 4: 2n + p = 18
Try values:
Case 1: n = 5 → p = 8 → More pens
Case 2: n = 6 → p = 6 → Equal
Case 3: n = 7 → p = 4 → More notebooks
Since all three outcomes are possible, we cannot determine which one is more.
Hence, option (d) is correct.
Answer: (d)
Solution:
Equation: 8n + 4p = 72 Divide by 4: 2n + p = 18
Try values:
Case 1: n = 5 → p = 8 → More pens
Case 2: n = 6 → p = 6 → Equal
Case 3: n = 7 → p = 4 → More notebooks
Since all three outcomes are possible, we cannot determine which one is more.
Hence, option (d) is correct.
• Question 5 of 5 5. Question A Question is given followed by two Statements I and II. Consider the Question and the Statements. A and B together can complete a job. Question: In how many days can A alone complete the job? Statement I: A and B together can complete the job in 6 days, and B alone can complete it in 9 days. Statement II: A is 50% more efficient than B. Which one of the following is correct in respect of the above Question and the Statements? (a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone (b) The Question can be answered by using either Statement alone (c) The Question can be answered by the Statements using both together, but cannot be answered using either Statement alone (d) The Question cannot be answered even by using both the Statements together Correct Answer: (a) Explanation: From Statement I: Let total work = 1 unit. A + B together = 1/6 per day, B = 1/9 per day So A = 1/6 − 1/9 = (3 − 2)/18 = 1/18 per day ⇒ A alone takes 18 days. So Statement I alone is sufficient. From Statement II: Let B’s work rate = r. Then A’s rate = 1.5r. Total rate A + B = 2.5r, but we do not know how long they take together or alone, so we cannot find A’s exact days. So Statement II alone is not sufficient. Hence, the Question can be answered by using one of the Statements alone (Statement I), but not by using Statement II alone. So option (a) is correct. Incorrect Answer: (a) Explanation: From Statement I: Let total work = 1 unit. A + B together = 1/6 per day, B = 1/9 per day So A = 1/6 − 1/9 = (3 − 2)/18 = 1/18 per day ⇒ A alone takes 18 days. So Statement I alone is sufficient. From Statement II: Let B’s work rate = r. Then A’s rate = 1.5r. Total rate A + B = 2.5r, but we do not know how long they take together or alone, so we cannot find A’s exact days. So Statement II alone is not sufficient. Hence, the Question can be answered by using one of the Statements alone (Statement I), but not by using Statement II alone. So option (a) is correct.
#### 5. Question
A Question is given followed by two Statements I and II. Consider the Question and the Statements.
A and B together can complete a job.
Question: In how many days can A alone complete the job?
Statement I: A and B together can complete the job in 6 days, and B alone can complete it in 9 days. Statement II: A is 50% more efficient than B.
Which one of the following is correct in respect of the above Question and the Statements?
• (a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
• (b) The Question can be answered by using either Statement alone
• (c) The Question can be answered by the Statements using both together, but cannot be answered using either Statement alone
• (d) The Question cannot be answered even by using both the Statements together
Answer: (a)
Explanation: From Statement I: Let total work = 1 unit. A + B together = 1/6 per day, B = 1/9 per day So A = 1/6 − 1/9 = (3 − 2)/18 = 1/18 per day ⇒ A alone takes 18 days. So Statement I alone is sufficient.
From Statement II: Let B’s work rate = r. Then A’s rate = 1.5r. Total rate A + B = 2.5r, but we do not know how long they take together or alone, so we cannot find A’s exact days. So Statement II alone is not sufficient.
Hence, the Question can be answered by using one of the Statements alone (Statement I), but not by using Statement II alone. So option (a) is correct.
Answer: (a)
Explanation: From Statement I: Let total work = 1 unit. A + B together = 1/6 per day, B = 1/9 per day So A = 1/6 − 1/9 = (3 − 2)/18 = 1/18 per day ⇒ A alone takes 18 days. So Statement I alone is sufficient.
From Statement II: Let B’s work rate = r. Then A’s rate = 1.5r. Total rate A + B = 2.5r, but we do not know how long they take together or alone, so we cannot find A’s exact days. So Statement II alone is not sufficient.
Hence, the Question can be answered by using one of the Statements alone (Statement I), but not by using Statement II alone. So option (a) is correct.
• Official Facebook Page HERE
• Follow our Twitter Account HERE