UPSC Insta–DART (Daily Aptitude and Reasoning Test) 25 Sep 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 S1 and S2 are given below with regard to two numbers followed by a Question: S1: Their product is 35. S2: Both numbers are prime and their sum is 12. Question: What are the two numbers? Which one of the following is correct in respect of the above Statements and the Question? (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: B Solution: Given that, S1: product = 35 → possible pairs: (1,35), (5,7). Not unique; also 1 is not prime. S2: both prime, sum = 12. Now, Prime pairs summing to 12: only (5,7). (2,10 not prime; 3,9 not prime; 11,1 not prime). So S2 alone gives the unique pair 5 and 7. Hence option (b) is correct. Incorrect Answer: B Solution: Given that, S1: product = 35 → possible pairs: (1,35), (5,7). Not unique; also 1 is not prime. S2: both prime, sum = 12. Now, Prime pairs summing to 12: only (5,7). (2,10 not prime; 3,9 not prime; 11,1 not prime). So S2 alone gives the unique pair 5 and 7. Hence option (b) is correct.
#### 1. Question
Two Statements S1 and S2 are given below with regard to two numbers followed by a Question:
S1: Their product is 35. S2: Both numbers are prime and their sum is 12.
Question: What are the two numbers?
Which one of the following is correct in respect of the above Statements and the Question?
• (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.
Given that,
S1: product = 35 → possible pairs: (1,35), (5,7). Not unique; also 1 is not prime. S2: both prime, sum = 12.
Prime pairs summing to 12: only (5,7). (2,10 not prime; 3,9 not prime; 11,1 not prime). So S2 alone gives the unique pair 5 and 7.
Hence option (b) is correct.
Given that,
S1: product = 35 → possible pairs: (1,35), (5,7). Not unique; also 1 is not prime. S2: both prime, sum = 12.
Prime pairs summing to 12: only (5,7). (2,10 not prime; 3,9 not prime; 11,1 not prime). So S2 alone gives the unique pair 5 and 7.
Hence option (b) is correct.
• Question 2 of 5 2. Question If the product x y = 16, then which of the following must be true? Both x and y must be positive for any value of x and y. If x is positive, y must be negative for any value of x and y. If x is negative, y must be positive for any value of x and y. Select the correct answer using the code given below. (a) 1 only (b) 2 only (c) Both 1 and 2 (d) Neither 1 nor 2 nor 3 Correct Answer: D Solution: Given that, x y = 16 Now, 1st option: take x = −4 and y = −4. Product is 16 but both are negative. Hence not necessarily true. 2nd option: take x = 2 and y = 8. Product is 16 with x positive and y positive, not negative. Hence not necessarily true. 3rd option: take x = −2 and y = −8. Product is 16 with x negative and y negative, not positive. Hence not necessarily true. So no statement must be true. Hence option (d) is correct. Incorrect Answer: D Solution: Given that, x y = 16 Now, 1st option: take x = −4 and y = −4. Product is 16 but both are negative. Hence not necessarily true. 2nd option: take x = 2 and y = 8. Product is 16 with x positive and y positive, not negative. Hence not necessarily true. 3rd option: take x = −2 and y = −8. Product is 16 with x negative and y negative, not positive. Hence not necessarily true. So no statement must be true. Hence option (d) is correct.
#### 2. Question
If the product x y = 16, then which of the following must be true?
• Both x and y must be positive for any value of x and y.
• If x is positive, y must be negative for any value of x and y.
• If x is negative, y must be positive for any value of x and y.
Select the correct answer using the code given below.
• (a) 1 only
• (b) 2 only
• (c) Both 1 and 2
• (d) Neither 1 nor 2 nor 3
Given that,
1st option: take x = −4 and y = −4. Product is 16 but both are negative. Hence not necessarily true.
2nd option: take x = 2 and y = 8. Product is 16 with x positive and y positive, not negative. Hence not necessarily true.
3rd option: take x = −2 and y = −8. Product is 16 with x negative and y negative, not positive. Hence not necessarily true.
So no statement must be true.
Hence option (d) is correct.
Given that,
1st option: take x = −4 and y = −4. Product is 16 but both are negative. Hence not necessarily true.
2nd option: take x = 2 and y = 8. Product is 16 with x positive and y positive, not negative. Hence not necessarily true.
3rd option: take x = −2 and y = −8. Product is 16 with x negative and y negative, not positive. Hence not necessarily true.
So no statement must be true.
Hence option (d) is correct.
• Question 3 of 5 3. Question How many natural numbers are there which give a remainder of 15 when 271 is divided by these natural numbers? (a) 4 (b) 5 (c) 6 (d) 7 Correct Answer: B Solution: Given that, Natural numbers which give a remainder of 15 when 271 is divided by them. Now, Remainder = difference between the dividend and the largest multiple of the divisor not exceeding the dividend. So, if remainder is 15, then 271 − 15 = 256. The divisors of 256 = 1, 2, 4, 8, 16, 32, 64, 128, 256. Since remainder is 15, the divisor must be greater than 15. Possible numbers = 16, 32, 64, 128, 256. Therefore total 5 natural numbers are there. Hence option (b) is correct. Incorrect Answer: B Solution: Given that, Natural numbers which give a remainder of 15 when 271 is divided by them. Now, Remainder = difference between the dividend and the largest multiple of the divisor not exceeding the dividend. So, if remainder is 15, then 271 − 15 = 256. The divisors of 256 = 1, 2, 4, 8, 16, 32, 64, 128, 256. Since remainder is 15, the divisor must be greater than 15. Possible numbers = 16, 32, 64, 128, 256. Therefore total 5 natural numbers are there. Hence option (b) is correct.
#### 3. Question
How many natural numbers are there which give a remainder of 15 when 271 is divided by these natural numbers?
Given that,
Natural numbers which give a remainder of 15 when 271 is divided by them.
Remainder = difference between the dividend and the largest multiple of the divisor not exceeding the dividend.
So, if remainder is 15, then 271 − 15 = 256.
The divisors of 256 = 1, 2, 4, 8, 16, 32, 64, 128, 256.
Since remainder is 15, the divisor must be greater than 15.
Possible numbers = 16, 32, 64, 128, 256.
Therefore total 5 natural numbers are there.
Hence option (b) is correct.
Given that,
Natural numbers which give a remainder of 15 when 271 is divided by them.
Remainder = difference between the dividend and the largest multiple of the divisor not exceeding the dividend.
So, if remainder is 15, then 271 − 15 = 256.
The divisors of 256 = 1, 2, 4, 8, 16, 32, 64, 128, 256.
Since remainder is 15, the divisor must be greater than 15.
Possible numbers = 16, 32, 64, 128, 256.
Therefore total 5 natural numbers are there.
Hence option (b) is correct.
• Question 4 of 5 4. Question A joint family consists of seven members A, B, C, D, E, F and G with three females. F and G are siblings. E is wife of F. B and D are children of F and E, and A is daughter of C. C is child of G and is cousin of B. Who is E? Wife of F Grandmother of A Aunt of C Select the correct answer using the code given below: (a) 1 and 2 only (b) 2 and 3 only (c) 1 and 3 only (d) 1, 2 and 3 Correct Answer: C Solution: Given that, Seven members with three females. F and G are siblings. E is wife of F. B and D are children of F and E. C is child of G and is cousin of B. A is daughter of C. Now, E is wife of F, so statement 1 is correct. A is daughter of C (child of G), not a descendant of E. Hence E is not grandmother of A, so statement 2 is not correct. C is child of G, who is sibling of F. E, being spouse of F, is an aunt to C. Hence statement 3 is correct. Therefore, 1 and 3 only are correct. Hence option (c) is correct. Incorrect Answer: C Solution: Given that, Seven members with three females. F and G are siblings. E is wife of F. B and D are children of F and E. C is child of G and is cousin of B. A is daughter of C. Now, E is wife of F, so statement 1 is correct. A is daughter of C (child of G), not a descendant of E. Hence E is not grandmother of A, so statement 2 is not correct. C is child of G, who is sibling of F. E, being spouse of F, is an aunt to C. Hence statement 3 is correct. Therefore, 1 and 3 only are correct. Hence option (c) is correct.
#### 4. Question
A joint family consists of seven members A, B, C, D, E, F and G with three females. F and G are siblings. E is wife of F. B and D are children of F and E, and A is daughter of C. C is child of G and is cousin of B. Who is E?
• Grandmother of A
Select the correct answer using the code given below:
• (a) 1 and 2 only
• (b) 2 and 3 only
• (c) 1 and 3 only
• (d) 1, 2 and 3
Given that,
Seven members with three females. F and G are siblings. E is wife of F. B and D are children of F and E. C is child of G and is cousin of B. A is daughter of C.
E is wife of F, so statement 1 is correct. A is daughter of C (child of G), not a descendant of E. Hence E is not grandmother of A, so statement 2 is not correct. C is child of G, who is sibling of F. E, being spouse of F, is an aunt to C. Hence statement 3 is correct.
Therefore, 1 and 3 only are correct.
Hence option (c) is correct.
Given that,
Seven members with three females. F and G are siblings. E is wife of F. B and D are children of F and E. C is child of G and is cousin of B. A is daughter of C.
E is wife of F, so statement 1 is correct. A is daughter of C (child of G), not a descendant of E. Hence E is not grandmother of A, so statement 2 is not correct. C is child of G, who is sibling of F. E, being spouse of F, is an aunt to C. Hence statement 3 is correct.
Therefore, 1 and 3 only are correct.
Hence option (c) is correct.
• Question 5 of 5 5. Question P, Q, R, S, T and U are six members of a family. R is the spouse of Q. U is the mother of T and S is the daughter of U. P’s daughter is T and R’s son is P. There are two couples in the family. Which one of the following is correct? (a) Q is the grandfather of T (b) Q is the grandmother of T (c) R is the mother of P (d) T is the granddaughter of Q Correct Answer: D Solution: Given that, R is the spouse of Q. U is the mother of T and S is the daughter of U, so U and S are females. P’s daughter is T, so P is a parent of T. R’s son is P, so P is male and R is a parent of P. There are two couples. Now, Since U is the mother of T and T is the daughter of P, P and U form one couple (parents of T). R is spouse of Q, so R and Q form the other couple. P is son of R (given), hence P is the grandson of Q and R’s spouse Q is the grandparent. T is P’s daughter, so T is the great-grandchild of Q? No, Q → parent of P → grandparent of T. T is a girl (given daughter), so T is the granddaughter of Q. Hence option (d) is correct. Incorrect Answer: D Solution: Given that, R is the spouse of Q. U is the mother of T and S is the daughter of U, so U and S are females. P’s daughter is T, so P is a parent of T. R’s son is P, so P is male and R is a parent of P. There are two couples. Now, Since U is the mother of T and T is the daughter of P, P and U form one couple (parents of T). R is spouse of Q, so R and Q form the other couple. P is son of R (given), hence P is the grandson of Q and R’s spouse Q is the grandparent. T is P’s daughter, so T is the great-grandchild of Q? No, Q → parent of P → grandparent of T. T is a girl (given daughter), so T is the granddaughter of Q. Hence option (d) is correct.
#### 5. Question
P, Q, R, S, T and U are six members of a family. R is the spouse of Q. U is the mother of T and S is the daughter of U. P’s daughter is T and R’s son is P. There are two couples in the family. Which one of the following is correct?
• (a) Q is the grandfather of T
• (b) Q is the grandmother of T
• (c) R is the mother of P
• (d) T is the granddaughter of Q
Given that,
R is the spouse of Q. U is the mother of T and S is the daughter of U, so U and S are females. P’s daughter is T, so P is a parent of T. R’s son is P, so P is male and R is a parent of P. There are two couples.
Since U is the mother of T and T is the daughter of P, P and U form one couple (parents of T). R is spouse of Q, so R and Q form the other couple. P is son of R (given), hence P is the grandson of Q and R’s spouse Q is the grandparent. T is P’s daughter, so T is the great-grandchild of Q? No, Q → parent of P → grandparent of T. T is a girl (given daughter), so T is the granddaughter of Q.
Hence option (d) is correct.
Given that,
R is the spouse of Q. U is the mother of T and S is the daughter of U, so U and S are females. P’s daughter is T, so P is a parent of T. R’s son is P, so P is male and R is a parent of P. There are two couples.
Since U is the mother of T and T is the daughter of P, P and U form one couple (parents of T). R is spouse of Q, so R and Q form the other couple. P is son of R (given), hence P is the grandson of Q and R’s spouse Q is the grandparent. T is P’s daughter, so T is the great-grandchild of Q? No, Q → parent of P → grandparent of T. T is a girl (given daughter), so T is the granddaughter of Q.
Hence option (d) is correct.
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