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 fruit seller has Apples, Oranges, and Bananas in the following ratio: 4 : 9 : 11. There are more number of Oranges than Apples by a number that is a multiple of both 5 and 8. What is the minimum number of fruits in his shop?
Correct
Answer: (b)
Difference between Oranges and Apples
= 9x − 4x
= 5xThis difference is a multiple of both 5 and 8.
So, 5x must be divisible by 40.Hence, the minimum value of x = 8.
Therefore, total number of fruits
= (4 + 9 + 11)x
= 24 × 8
= 192Incorrect
Answer: (b)
Difference between Oranges and Apples
= 9x − 4x
= 5xThis difference is a multiple of both 5 and 8.
So, 5x must be divisible by 40.Hence, the minimum value of x = 8.
Therefore, total number of fruits
= (4 + 9 + 11)x
= 24 × 8
= 192 -
Question 2 of 5
2. Question
The difference between any two natural numbers is 12. What can be said about the natural numbers which are divisible by 4 and lie between these two numbers?
Correct
Answer: (c)
Explanation
Consider two numbers 1 and 13 (difference = 12).
Numbers divisible by 4 between them: 4, 8, 12 → 3 numbers.Now consider 4 and 16.
Numbers divisible by 4 between them: 8, 12 → 2 numbers.Thus, depending on the starting point, the count varies.
Hence, there can be more than one such number.
Incorrect
Answer: (c)
Explanation
Consider two numbers 1 and 13 (difference = 12).
Numbers divisible by 4 between them: 4, 8, 12 → 3 numbers.Now consider 4 and 16.
Numbers divisible by 4 between them: 8, 12 → 2 numbers.Thus, depending on the starting point, the count varies.
Hence, there can be more than one such number.
-
Question 3 of 5
3. Question
Consider the following statements and a question:
Question: In which direction is A with respect to D?
Statement I: B is to the north of D and A is to the west of B. C is to the east of D.
Statement II: C is to the north of D and A is to the west of C. B is to the south of D.Which one of the following is correct in respect of the above Statements and the Question?
Correct
Answer: (c)
Explanation
From Statement I:
B is north of D, and A is west of B → A lies in the northwest direction from D.
So, direction of A w.r.t D is determined.From Statement II:
C is north of D, and A is west of C → again A lies northwest of D.
So, direction is determined here as well.Thus, each statement alone is sufficient.
Incorrect
Answer: (c)
Explanation
From Statement I:
B is north of D, and A is west of B → A lies in the northwest direction from D.
So, direction of A w.r.t D is determined.From Statement II:
C is north of D, and A is west of C → again A lies northwest of D.
So, direction is determined here as well.Thus, each statement alone is sufficient.
-
Question 4 of 5
4. Question
Traders P and Q buy two goods for Rs. 1000 and Rs. 2000 respectively. Trader P marks his goods up by p%, while trader Q marks his goods up by 3p% and offers a discount of p%. If both make the same non-zero profit, then what is p in percentage terms?
Correct
Answer: (d)
For Trader P, cost price = Rs. 1000.
After marking up by p%, profit = 1000 × p/100 = 10pFor Trader Q, cost price = Rs. 2000.
Marked price = 2000 × (1 + 3p/100)After discount of p%, selling price = 2000 × (1 + 3p/100)(1 − p/100)
Profit percentage for Q:
(1 + 3p/100)(1 − p/100) − 1
= 1 + 2p/100 − 3p²/10000 − 1
= 2p/100 − 3p²/10000
So, profit of Q = 2000 × [2p/100 − 3p²/10000]
= 40p − 0.6p²
Now, both profits are equal:
10p = 40p − 0.6p²
0.6p² = 30p
p = 50
Hence, p = 50%.
So, option (d) is correct.Incorrect
Answer: (d)
For Trader P, cost price = Rs. 1000.
After marking up by p%, profit = 1000 × p/100 = 10pFor Trader Q, cost price = Rs. 2000.
Marked price = 2000 × (1 + 3p/100)After discount of p%, selling price = 2000 × (1 + 3p/100)(1 − p/100)
Profit percentage for Q:
(1 + 3p/100)(1 − p/100) − 1
= 1 + 2p/100 − 3p²/10000 − 1
= 2p/100 − 3p²/10000
So, profit of Q = 2000 × [2p/100 − 3p²/10000]
= 40p − 0.6p²
Now, both profits are equal:
10p = 40p − 0.6p²
0.6p² = 30p
p = 50
Hence, p = 50%.
So, option (d) is correct. -
Question 5 of 5
5. Question
A cab service provider has following rate chart for rides:
(I) For the first 8 km of the ride, fare will be Rs. 7 per km.
(II) After first 8 km, fare will be charged at Rs. 11 per km.
(III) If the passenger requests a halt before reaching the destination and keeps the cab waiting, then waiting charge will be Rs. 8 per minute. Waiting charge will also be applicable if the cab gets stuck in traffic.Kavita Rao went to meet her friend, who lives 20 kms away from Kavita’s home. She booked a cab and was charged Rs. 260 for the journey. If Kavita stopped the cab at a stationery shop on the way, and the cab was stuck in traffic jam for 3 minutes, then find how much time did Kavita Rao take at the stationery shop?
Correct
Answer: (a)
Explanation:
Fare for first 8 km = 8 × 7 = Rs. 56
Fare for remaining 12 km = 12 × 11 = Rs. 132So, total distance fare = 56 + 132 = Rs. 188
Total fare charged = Rs. 260
So, waiting charge = 260 − 188 = Rs. 72Waiting charge per minute = Rs. 8
Therefore, total waiting time = 72/8 = 9 minutesOut of this, 3 minutes were due to traffic jam.
Hence, Kavita spent 6 minutes at the stationery shop.Therefore, option (a) is correct.
Incorrect
Answer: (a)
Explanation:
Fare for first 8 km = 8 × 7 = Rs. 56
Fare for remaining 12 km = 12 × 11 = Rs. 132So, total distance fare = 56 + 132 = Rs. 188
Total fare charged = Rs. 260
So, waiting charge = 260 − 188 = Rs. 72Waiting charge per minute = Rs. 8
Therefore, total waiting time = 72/8 = 9 minutesOut of this, 3 minutes were due to traffic jam.
Hence, Kavita spent 6 minutes at the stationery shop.Therefore, option (a) is correct.
