UPSC Insta–DART (Daily Aptitude and Reasoning Test) 28 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 If a number P is a two-digit natural number which when multiplied by 3 gives a three-digit number ending in digit Q, then consider the following statements and a question: Statement I: Q is half of P. Statement II: Q is an odd number. Question: What is the value of P? Which one of the following is correct in respect of the above Statements and the Question? (a) Statement I alone is sufficient to answer the Question. (b) Statement II alone is sufficient to answer the Question. (c) Statement I and Statement II together are sufficient to answer the Question. (d) Statement I and Statement II together are insufficient to answer the Question. Correct Answer – D Explanation: Incorrect Answer – D Explanation:
#### 1. Question
If a number P is a two-digit natural number which when multiplied by 3 gives a three-digit number ending in digit Q, then consider the following statements and a question:
Statement I: Q is half of P. Statement II: Q is an odd number.
Question: What is the value of P?
Which one of the following is correct in respect of the above Statements and the Question?
• (a) Statement I alone is sufficient to answer the Question.
• (b) Statement II alone is sufficient to answer the Question.
• (c) Statement I and Statement II together are sufficient to answer the Question.
• (d) Statement I and Statement II together are insufficient to answer the Question.
Answer – D
Explanation:
Answer – D
Explanation:
• Question 2 of 5 2. Question If the sum of two numbers X and Y is 50, then consider the following statements and a question: Statement I: X is 10 more than twice Y. Statement II: Y is an even number. Question: What is the value of X? Which one of the following is correct with respect to above statements (a) Statement I alone is sufficient to answer the question (b) Statement II alone is sufficient to answer the question (c) Statement I and Statement II together are sufficient to answer the question (d) Statement I and Statement II together are insufficient to answer the question Correct Answer – A Solution – Statement I alone: X = 2Y + 10 and X + Y = 50 ⇒ (2Y + 10) + Y = 50 ⇒ 3Y + 10 = 50 ⇒ 3Y = 40 ⇒ Y = 40/3 ⇒ X = 2 × (40/3) + 10 = 80/3 + 10 ⇒ Unique ⇒ Sufficient. Statement II alone: Y even and X + Y = 50 ⇒ many possibilities ⇒ Not sufficient. Conclusion: (a) Statement I alone is sufficient. Incorrect Answer – A Solution – Statement I alone: X = 2Y + 10 and X + Y = 50 ⇒ (2Y + 10) + Y = 50 ⇒ 3Y + 10 = 50 ⇒ 3Y = 40 ⇒ Y = 40/3 ⇒ X = 2 × (40/3) + 10 = 80/3 + 10 ⇒ Unique ⇒ Sufficient. Statement II alone: Y even and X + Y = 50 ⇒ many possibilities ⇒ Not sufficient. Conclusion: (a) Statement I alone is sufficient.
#### 2. Question
If the sum of two numbers X and Y is 50, then consider the following statements and a question:
Statement I: X is 10 more than twice Y. Statement II: Y is an even number. Question: What is the value of X?
Which one of the following is correct with respect to above statements
• (a) Statement I alone is sufficient to answer the question
• (b) Statement II alone is sufficient to answer the question
• (c) Statement I and Statement II together are sufficient to answer the question
• (d) Statement I and Statement II together are insufficient to answer the question
Answer – A
Solution – Statement I alone: X = 2Y + 10 and X + Y = 50 ⇒ (2Y + 10) + Y = 50 ⇒ 3Y + 10 = 50 ⇒ 3Y = 40 ⇒ Y = 40/3 ⇒ X = 2 × (40/3) + 10 = 80/3 + 10 ⇒ Unique ⇒ Sufficient.
Statement II alone: Y even and X + Y = 50 ⇒ many possibilities ⇒ Not sufficient.
Conclusion: (a) Statement I alone is sufficient.
Answer – A
Solution – Statement I alone: X = 2Y + 10 and X + Y = 50 ⇒ (2Y + 10) + Y = 50 ⇒ 3Y + 10 = 50 ⇒ 3Y = 40 ⇒ Y = 40/3 ⇒ X = 2 × (40/3) + 10 = 80/3 + 10 ⇒ Unique ⇒ Sufficient.
Statement II alone: Y even and X + Y = 50 ⇒ many possibilities ⇒ Not sufficient.
Conclusion: (a) Statement I alone is sufficient.
• Question 3 of 5 3. Question From the first 200 natural numbers, how many are not divisible by any of 2, 3, 5, or 7? (a) 42 (b) 47 (c) 44 (d) 45 Correct Answer: (b) Explanation: Using Inclusion–Exclusion for 1–200: By 2,3,5,7: 100+66+40+28=234 Subtract pairs: 33+20+14+13+9+5=94 Add triples: 6+4+2+1=13 Quadruple: 000 Count divisible by at least one = 234−94+13=153 Not divisible by any = 200−153= 47 Incorrect Answer: (b) Explanation: Using Inclusion–Exclusion for 1–200: By 2,3,5,7: 100+66+40+28=234 Subtract pairs: 33+20+14+13+9+5=94 Add triples: 6+4+2+1=13 Quadruple: 000 Count divisible by at least one = 234−94+13=153 Not divisible by any = 200−153= 47
#### 3. Question
From the first 200 natural numbers, how many are not divisible by any of 2, 3, 5, or 7?
Answer: (b)
Explanation: Using Inclusion–Exclusion for 1–200:
• By 2,3,5,7: 100+66+40+28=234
• Subtract pairs: 33+20+14+13+9+5=94
• Add triples: 6+4+2+1=13
• Quadruple: 000
Count divisible by at least one = 234−94+13=153
Not divisible by any = 200−153= 47
Answer: (b)
Explanation: Using Inclusion–Exclusion for 1–200:
• By 2,3,5,7: 100+66+40+28=234
• Subtract pairs: 33+20+14+13+9+5=94
• Add triples: 6+4+2+1=13
• Quadruple: 000
Count divisible by at least one = 234−94+13=153
Not divisible by any = 200−153= 47
• Question 4 of 5 4. Question Consider the sequence AB_CC_A_BCCC_BBC_C that follows a certain pattern. Which one of the following completes the sequence? (a) B, C, B, C, A (b) A, C, B, C, A (c) B, C, B, A, C (d) C, B, B, A, C Correct Answer:(c) Given: AB_CC_A_BCCC_BBC_C Since, there are 18 letters in the series, we can divide them in groups of 6 or 3. Dividing them in groups of 6, we get: [ A B _ C C _ ] ; [ A _ B C C C ] ; [ _ B B C _ C ] The pattern being repeated is ABBCCC. So, we can fill in the blanks as follows: [ A B B C C C ] ; [ A B B C C C ] ; [ A B B C C C ] Therefore, the required letters to complete the sequence are: B, C, B, A, C Incorrect Answer:(c) Given: AB_CC_A_BCCC_BBC_C Since, there are 18 letters in the series, we can divide them in groups of 6 or 3. Dividing them in groups of 6, we get: [ A B _ C C _ ] ; [ A _ B C C C ] ; [ _ B B C _ C ] The pattern being repeated is ABBCCC. So, we can fill in the blanks as follows: [ A B B C C C ] ; [ A B B C C C ] ; [ A B B C C C ] Therefore, the required letters to complete the sequence are: B, C, B, A, C
#### 4. Question
Consider the sequence
AB_CC_A_BCCC_BBC_C that follows a certain pattern. Which one of the following completes the sequence?
• (a) B, C, B, C, A
• (b) A, C, B, C, A
• (c) B, C, B, A, C
• (d) C, B, B, A, C
Answer:(c)
Given: AB_CC_A_BCCC_BBC_C
Since, there are 18 letters in the series, we can divide them in groups of 6 or 3. Dividing them in groups of 6, we get:
[ A B _ C C _ ] ; [ A _ B C C C ] ; [ _ B B C _ C ]
The pattern being repeated is ABBCCC. So, we can fill in the blanks as follows:
[ A B B C C C ] ; [ A B B C C C ] ; [ A B B C C C ]
Therefore, the required letters to complete the sequence are: B, C, B, A, C
Answer:(c)
Given: AB_CC_A_BCCC_BBC_C
Since, there are 18 letters in the series, we can divide them in groups of 6 or 3. Dividing them in groups of 6, we get:
[ A B _ C C _ ] ; [ A _ B C C C ] ; [ _ B B C _ C ]
The pattern being repeated is ABBCCC. So, we can fill in the blanks as follows:
[ A B B C C C ] ; [ A B B C C C ] ; [ A B B C C C ]
Therefore, the required letters to complete the sequence are: B, C, B, A, C
• Question 5 of 5 5. Question If 6∗8=106 8 = 106∗8=10 and 11∗60=6111 60 = 6111∗60=61, then what is 33∗5633 5633∗56 equal to? (a) 61 (b) 64 (c) 65 (d) 67 Correct Answer: (c) The given numbers are Pythagorean triplets, wherein: a2+b2=c2 So, (62+82)=36+64=100=102 And, (112+602)=121+3600=3721=612 Similarly, (332+562)=1089+3136=4225=652 Hence, 33∗56=6533 56 = 6533∗56=65. Incorrect Answer: (c) The given numbers are Pythagorean triplets, wherein: a2+b2=c2 So, (62+82)=36+64=100=102 And, (112+602)=121+3600=3721=612 Similarly, (332+562)=1089+3136=4225=652 Hence, 33∗56=6533 * 56 = 6533∗56=65.
#### 5. Question
If 6∗8=106 8 = 106∗8=10 and 11∗60=6111 60 = 6111∗60=61, then what is 33∗5633 * 5633∗56 equal to?
Answer: (c) The given numbers are Pythagorean triplets, wherein: a2+b2=c2
So, (62+82)=36+64=100=102 And, (112+602)=121+3600=3721=612
Similarly, (332+562)=1089+3136=4225=652
Hence, 33∗56=6533 * 56 = 6533∗56=65.
Answer: (c) The given numbers are Pythagorean triplets, wherein: a2+b2=c2
So, (62+82)=36+64=100=102 And, (112+602)=121+3600=3721=612
Similarly, (332+562)=1089+3136=4225=652
Hence, 33∗56=6533 * 56 = 6533∗56=65.
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