UPSC Insta–DART (Daily Aptitude and Reasoning Test) 3 Sep 2025

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 A pack of 52 cards contains four different colors cards each color contains cards numbered from 1 to 13. Cards are drawn randomly from the pack. Consider the following statements: Smallest number of attempts, which will always get full set of atleast one color 49. Smallest number of attempts, which will always get atleast one card of each color is 40. Which of the statements given above is/are correct? (a) 1 only (b) 2 only (c) Both 1 and 2 (d) Neither 1 nor 2 Correct Answer: (c) Solution Statement 1 is correct: For full set of one color we have to take the worst case. Worst case is one card of each color remaining in the pack till the last ie till we withdraw 48 cards. Next card withdraw is bound to fulfill atleast one set of color. So number of attempts is 49. Statement 2 is correct: For getting at least one card of each color, i.e. getting all color cards, the worst case is one color is totally left out until others are drawn, i.e. 13 x 3 i.e. 39 cards are drawn. The next card i.e. 40 th card when we draw, it is bound to give atleast one cards of all color. Hence, option (c) is correct Incorrect Answer: (c) Solution Statement 1 is correct: For full set of one color we have to take the worst case. Worst case is one card of each color remaining in the pack till the last ie till we withdraw 48 cards. Next card withdraw is bound to fulfill atleast one set of color. So number of attempts is 49. Statement 2 is correct: For getting at least one card of each color, i.e. getting all color cards, the worst case is one color is totally left out until others are drawn, i.e. 13 x 3 i.e. 39 cards are drawn. The next card i.e. 40 th card when we draw, it is bound to give atleast one cards of all color. Hence, option (c) is correct

#### 1. Question

A pack of 52 cards contains four different colors cards each color contains cards numbered from 1 to 13. Cards are drawn randomly from the pack. Consider the following statements:

• Smallest number of attempts, which will always get full set of atleast one color 49.

• Smallest number of attempts, which will always get atleast one card of each color is 40.

Which of the statements given above is/are correct?

• (a) 1 only

• (b) 2 only

• (c) Both 1 and 2

• (d) Neither 1 nor 2

Answer: (c)

Solution

Statement 1 is correct: For full set of one color we have to take the worst case. Worst case is one card of each color remaining in the pack till the last ie till we withdraw 48 cards. Next card withdraw is bound to fulfill atleast one set of color. So number of attempts is 49.

Statement 2 is correct: For getting at least one card of each color, i.e. getting all color cards, the worst case is one color is totally left out until others are drawn, i.e. 13 x 3 i.e. 39 cards are drawn. The next card i.e. 40 th card when we draw, it is bound to give atleast one cards of all color. Hence, option (c) is correct

Answer: (c)

Solution

• Question 2 of 5 2. Question In a quiz competition, three friends A, B and C scored a total of 60 points. The ratio of points scored by A to points scored by B is equal to the ratio of points scored by B to points scored by C. Value–I = Points scored by A Value–II = Points scored by B Value–III = Points scored by C Which one of the following is correct? (a) Value–I < Value–II < Value–III (b) Value–III < Value–II < Value–I (c) Value–II < Value–I < Value–III (d) Cannot be determined due to insufficient data Correct Answer: (d) Explanation: Given: A + B + C = 60 and A/B = B/C ⇒ B² = A × C. If B = 20, then A = 15 or 25, C = 25 or 15. Case 1: A < B < C ⇒ 15 < 20 < 25. Case 2: C < B < A ⇒ 15 < 20 < 25 but in reverse roles ⇒ C < B < A. Thus, either Value–I < Value–II < Value–III or Value–III < Value–II < Value–I is possible. Hence, the answer cannot be determined uniquely ⇒ option (d) is correct. Incorrect Answer: (d) Explanation: Given: A + B + C = 60 and A/B = B/C ⇒ B² = A × C. If B = 20, then A = 15 or 25, C = 25 or 15. Case 1: A < B < C ⇒ 15 < 20 < 25. Case 2: C < B < A ⇒ 15 < 20 < 25 but in reverse roles ⇒ C < B < A. Thus, either Value–I < Value–II < Value–III or Value–III < Value–II < Value–I is possible. Hence, the answer cannot be determined uniquely ⇒ option (d) is correct.

#### 2. Question

In a quiz competition, three friends A, B and C scored a total of 60 points. The ratio of points scored by A to points scored by B is equal to the ratio of points scored by B to points scored by C.

Value–I = Points scored by A Value–II = Points scored by B Value–III = Points scored by C

Which one of the following is correct?

• (a) Value–I < Value–II < Value–III

• (b) Value–III < Value–II < Value–I

• (c) Value–II < Value–I < Value–III

• (d) Cannot be determined due to insufficient data

Answer: (d)

Explanation: Given: A + B + C = 60 and A/B = B/C ⇒ B² = A × C.

If B = 20, then A = 15 or 25, C = 25 or 15. Case 1: A < B < C ⇒ 15 < 20 < 25. Case 2: C < B < A ⇒ 15 < 20 < 25 but in reverse roles ⇒ C < B < A.

Thus, either Value–I < Value–II < Value–III or Value–III < Value–II < Value–I is possible.

Hence, the answer cannot be determined uniquely ⇒ option (d) is correct.

Answer: (d)

Explanation: Given: A + B + C = 60 and A/B = B/C ⇒ B² = A × C.

If B = 20, then A = 15 or 25, C = 25 or 15. Case 1: A < B < C ⇒ 15 < 20 < 25. Case 2: C < B < A ⇒ 15 < 20 < 25 but in reverse roles ⇒ C < B < A.

Thus, either Value–I < Value–II < Value–III or Value–III < Value–II < Value–I is possible.

Hence, the answer cannot be determined uniquely ⇒ option (d) is correct.

• Question 3 of 5 3. Question Set A contains all the odd numbers between 101 and 151, both inclusive. Set B contains all the odd numbers between 221 and 271, both inclusive. What is the difference between the sum of the elements of set A and that of set B? (a) 2520 (b) 2880 (c) 3000 (d) 3120 Correct Answer: (d) Set A: {101, 103, 105, …, 151} → Set of 26 consecutive positive odd numbers Set B: {221, 223, 225, …, 271} → Set of 26 consecutive positive odd numbers Difference between the 1st terms = 221 − 101 = 120, between 2nd terms also 120, and so on. Each term in set B is 120 more than the corresponding term in set A. So, total difference = 26 × 120 = 3120. Hence option (d) is correct. Incorrect Answer: (d) Set A: {101, 103, 105, …, 151} → Set of 26 consecutive positive odd numbers Set B: {221, 223, 225, …, 271} → Set of 26 consecutive positive odd numbers Difference between the 1st terms = 221 − 101 = 120, between 2nd terms also 120, and so on. Each term in set B is 120 more than the corresponding term in set A. So, total difference = 26 × 120 = 3120. Hence option (d) is correct.

#### 3. Question

Set A contains all the odd numbers between 101 and 151, both inclusive. Set B contains all the odd numbers between 221 and 271, both inclusive. What is the difference between the sum of the elements of set A and that of set B?

Answer: (d) Set A: {101, 103, 105, …, 151} → Set of 26 consecutive positive odd numbers Set B: {221, 223, 225, …, 271} → Set of 26 consecutive positive odd numbers Difference between the 1st terms = 221 − 101 = 120, between 2nd terms also 120, and so on. Each term in set B is 120 more than the corresponding term in set A. So, total difference = 26 × 120 = 3120. Hence option (d) is correct.

• Question 4 of 5 4. Question A Question is given followed by two Statements I and II. Consider the Question and the Statements. There are three distinct prime numbers whose sum is 31. Question: What are those three numbers? Statement‑I: None of the numbers is 2. Statement‑II: One of the numbers is 13. 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 using both the Statements together, but cannot be answered using either Statement alone. d) The Question cannot be answered even by using both the Statements together. Correct Ans) a Exp) Option a is the correct answer. From the Question: sum of the three distinct primes = 31. From Statement‑I (none is 2): all three are odd primes. Many triples work, e.g., (3, 11, 17), (5, 7, 19), (7, 11, 13). Hence, I alone is not sufficient. From Statement‑II (one number is 13): then the other two must sum to 18. Distinct primes adding to 18 are only (7, 11). Hence the unique triple is (13, 7, 11). II alone is sufficient. Therefore, the question can be answered by using one of the statements alone (Statement‑II), but not the other. Incorrect Ans) a Exp) Option a is the correct answer. From the Question: sum of the three distinct primes = 31. From Statement‑I (none is 2): all three are odd primes. Many triples work, e.g., (3, 11, 17), (5, 7, 19), (7, 11, 13). Hence, I alone is not sufficient. From Statement‑II (one number is 13): then the other two must sum to 18. Distinct primes adding to 18 are only (7, 11). Hence the unique triple is (13, 7, 11). II alone is sufficient. Therefore, the question can be answered by using one of the statements alone (Statement‑II), but not the other.

#### 4. Question

A Question is given followed by two Statements I and II. Consider the Question and the Statements.

There are three distinct prime numbers whose sum is 31.

Question: What are those three numbers?

Statement‑I: None of the numbers is 2. Statement‑II: One of the numbers is 13.

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 using both the Statements together, but cannot be answered using either Statement alone.

• d) The Question cannot be answered even by using both the Statements together.

Ans) a

Exp) Option a is the correct answer.

From the Question: sum of the three distinct primes = 31.

From Statement‑I (none is 2): all three are odd primes. Many triples work, e.g., (3, 11, 17), (5, 7, 19), (7, 11, 13). Hence, I alone is not sufficient.

From Statement‑II (one number is 13): then the other two must sum to 18. Distinct primes adding to 18 are only (7, 11). Hence the unique triple is (13, 7, 11). II alone is sufficient.

Therefore, the question can be answered by using one of the statements alone (Statement‑II), but not the other.

Ans) a

Exp) Option a is the correct answer.

From the Question: sum of the three distinct primes = 31.

From Statement‑I (none is 2): all three are odd primes. Many triples work, e.g., (3, 11, 17), (5, 7, 19), (7, 11, 13). Hence, I alone is not sufficient.

From Statement‑II (one number is 13): then the other two must sum to 18. Distinct primes adding to 18 are only (7, 11). Hence the unique triple is (13, 7, 11). II alone is sufficient.

Therefore, the question can be answered by using one of the statements alone (Statement‑II), but not the other.

• Question 5 of 5 5. Question Consider the following statements: Statement I: There are exactly 74 numbers between 100 and 1000 which are divisible by 12. Statement II: There are exactly 112 three-digit numbers that are divisible by 9. Which among the above-mentioned statement/s is/are correct? (a) I only (b) II only (c) Both I and II (d) Neither I nor II Correct Answer: D Statement I: Numbers between 100 and 1000 divisible by 12 We find the first and last three-digit numbers divisible by 12: Smallest = 108 Largest =996 Now, count them: so Statement I is incorrect. Statement : three-digit number 100 to 999 divisible by 9 Smallest 3-digit number = 100 → First divisible by 9 =108 Largest 3-digit number =999 Count: So, Statement 2 is also incorrect. Incorrect Answer: D Statement I: Numbers between 100 and 1000 divisible by 12 We find the first and last three-digit numbers divisible by 12: Smallest = 108 Largest =996 Now, count them: so Statement I is incorrect. Statement : three-digit number 100 to 999 divisible by 9 Smallest 3-digit number = 100 → First divisible by 9 =108 Largest 3-digit number =999 Count: So, Statement 2 is also incorrect.

#### 5. Question

Consider the following statements: Statement I: There are exactly 74 numbers between 100 and 1000 which are divisible by 12. Statement II: There are exactly 112 three-digit numbers that are divisible by 9. Which among the above-mentioned statement/s is/are correct?

• (a) I only

• (b) II only

• (c) Both I and II

• (d) Neither I nor II

Statement I: Numbers between 100 and 1000 divisible by 12

We find the first and last three-digit numbers divisible by 12:

• Smallest = 108

• Largest =996

Now, count them: so Statement I is incorrect.

Statement : three-digit number 100 to 999 divisible by 9

• Smallest 3-digit number = 100 → First divisible by 9 =108

• Largest 3-digit number =999

Count: So, Statement 2 is also incorrect.