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
Amitabh has a certain number of toffees, such that if he distributes them amongst ten children he has nine left, if he distributes amongst nine children he would have eight left, if he distributes amongst eight children he would have seven left … and so on until if he distributes amongst five children he should have four left. What is the second lowest number of toffees he could have with him.
Correct
Solution:- D
The least number would be (LCM of 10,9,8,7,6 and 5-1)= 2519. The second least number = 2520* 2-1=5039.
Incorrect
Solution:- D
The least number would be (LCM of 10,9,8,7,6 and 5-1)= 2519. The second least number = 2520* 2-1=5039.
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Question 2 of 5
2. Question
If’a’ is a natural number and HCF of a, a + 5 is 5. If the LCM of the two numbers is a three-digit number, then what is the difference between the maximum and minimum possible values of the smaller number?
Correct
Solution: D
Let a=5k then a+5=5(k+1). Both k, k+1 are co-prime.
LCM of a, a+5=5*k*(k+1)
For k=4, 5k(k+1)=100
So minimum possible value of small number is 20. Maximum value of k for which the LCM is a three digit number is 13.
Maximum possible value of the smallest number =65
So the required difference = 65-20=45
Incorrect
Solution: D
Let a=5k then a+5=5(k+1). Both k, k+1 are co-prime.
LCM of a, a+5=5*k*(k+1)
For k=4, 5k(k+1)=100
So minimum possible value of small number is 20. Maximum value of k for which the LCM is a three digit number is 13.
Maximum possible value of the smallest number =65
So the required difference = 65-20=45
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Question 3 of 5
3. Question
The least number which when divided by 6, 9, 12, 15, 18 leaves the same remainder 2 in each case, is:
Correct
Answer: (d) 182
Explanation:
Given numbers are 6,9, 12, 15, 18
LCM of given numbers=180
So, 180+2=182 is the number that leaves 2 as a remainder.
Hence option d is correct.
Incorrect
Answer: (d) 182
Explanation:
Given numbers are 6,9, 12, 15, 18
LCM of given numbers=180
So, 180+2=182 is the number that leaves 2 as a remainder.
Hence option d is correct.
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Question 4 of 5
4. Question
What is the LCM of 2/3 , 7/9 and 14/15 ?
Correct
Answer: (b)14/3
Explanation:
LCM(2/3, 7/9, 14/15)=LCM(2,7,14)/HCF(3,9,15)=14/3
Incorrect
Answer: (b)14/3
Explanation:
LCM(2/3, 7/9, 14/15)=LCM(2,7,14)/HCF(3,9,15)=14/3
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Question 5 of 5
5. Question
The sum of two numbers is 232 and their HCF is 29. What is the number of such pairs of numbers satisfying above condition?
Correct
Answer: (b) two
Explanation:
Explain it
Let the two numbers be 29x and 29y
29x + 29y =232
x+y=8
Co-primes of (x, y) =(1,7)(3,5)
Since, once such pair is ( 29 * 1 and 29 * 7 )=29 and 203
Hence, the other pair is ( 29 * 3 and 29 * 5 )=87 and 145.
Hence, option b is correct.
- Gandhi established Tolstoy Farm in 1910 while supervising the satyagraha by South African Indians. The farm aimed to be a self-supporting agricultural commune that provided for basic needs and emphasized personal growth and spiritual understanding through hard labour.
- Tolstoy Farm as Gandhi’s Laboratory: Tolstoy Farm served as a laboratory for Gandhi to experiment with various principles and ideals, including diet, nature cure, harmonious living with nature, brahmacharya, and more.
- This reflected a shared philosophy with Count Leo Tolstoy and Henry David Thoreau
Revival Efforts: Tolstoy Farm fell into disrepair during the Apartheid era. Post-1994, part of the farm has been developed into a ‘Peace Garden,’ and there are plans to involve the local community and teach Gandhian ideals.
Incorrect
Answer: (b) two
Explanation:
Explain it
Let the two numbers be 29x and 29y
29x + 29y =232
x+y=8
Co-primes of (x, y) =(1,7)(3,5)
Since, once such pair is ( 29 * 1 and 29 * 7 )=29 and 203
Hence, the other pair is ( 29 * 3 and 29 * 5 )=87 and 145.
Hence, option b is correct.
