IASbaba’s Daily CSAT Practice Test
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Daily CSAT Practice Test
Everyday 5 Questions from Aptitude, Logical Reasoning, and Reading Comprehension will be covered from Monday to Saturday.
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Question 1 of 5
1. Question
A solid sphere is melted and recast into a right circular cone with a base radius equal to the radius of the sphere. What is the ratio of the height and radius of the cone so formed?
Correct
Solution (d)
Let the radius of solid sphere be r.
The volume of sphere, VS = 4/3 πr³
It is melted and recast into a right circular cone of radius r and height h.
The volume of cone, VC = 1/3 πr²h
The same volume of material is used for recasting. Therefore,
VS = VC
4/3 πr³ = 1/3 πr²h
h = 4r
h/r = 4
Incorrect
Solution (d)
Let the radius of solid sphere be r.
The volume of sphere, VS = 4/3 πr³
It is melted and recast into a right circular cone of radius r and height h.
The volume of cone, VC = 1/3 πr²h
The same volume of material is used for recasting. Therefore,
VS = VC
4/3 πr³ = 1/3 πr²h
h = 4r
h/r = 4
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Question 2 of 5
2. Question
The average age of 3 children in a family is 20% of the average age of the father and the eldest child. The total age of the mother and the youngest child is 39 years. If the father’s age is 26 years, what is the age of the second child?
Correct
Solution (d)
Let ‘A’ be the age of eldest son. ‘B’ be the age of second son, ‘C’ be the age of youngest son, ‘F’ be the age of the father and ‘M’ be the age of mother.
Therefore, 20/100(F+A/2) = A+B+C/3
⇒ 3F = 7A + 10B + 10C and M+C = 39
We know that, F = 26 years, thus, 7A + 10B +10C = 78 and M+C = 39
There are 4 variables and two equations, thus the value of B cannot be determined.
Incorrect
Solution (d)
Let ‘A’ be the age of eldest son. ‘B’ be the age of second son, ‘C’ be the age of youngest son, ‘F’ be the age of the father and ‘M’ be the age of mother.
Therefore, 20/100(F+A/2) = A+B+C/3
⇒ 3F = 7A + 10B + 10C and M+C = 39
We know that, F = 26 years, thus, 7A + 10B +10C = 78 and M+C = 39
There are 4 variables and two equations, thus the value of B cannot be determined.
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Question 3 of 5
3. Question
A man is stranded on a deserted island. All he has to drink is a 20 litre bottle of Mango juice. To conserve his drink, he decides that on the first day he would drink one litre juice and refill the bottle back up with water. On the 2nd day he would drink 2 litres mixture and refill the bottle with water. On the 3rd day he would drink 3 litres mixture and so on. By the time all the Mango juice is gone, how much water has he drunk?
Correct
Solution (a)
It is given that the man has 20 litre bottle of Mango juice. Also, he will drink 1 litre on the first day and refill the bottle with water, will drink 2 litres on the second day and refill the bottle, will drink 3 litres on the third day and refill the bottle, and so on till the 20th day. Thus at the end of 20 days, he must have drunk (1 + 2 + 3 + 4 + ….. +18 + 19 + 20) = 210 litres of the liquid
Out of those 210 litres, 20 litres is the Mango juice which he had initially. Hence, he must have drunk 190 litres of water.
Incorrect
Solution (a)
It is given that the man has 20 litre bottle of Mango juice. Also, he will drink 1 litre on the first day and refill the bottle with water, will drink 2 litres on the second day and refill the bottle, will drink 3 litres on the third day and refill the bottle, and so on till the 20th day. Thus at the end of 20 days, he must have drunk (1 + 2 + 3 + 4 + ….. +18 + 19 + 20) = 210 litres of the liquid
Out of those 210 litres, 20 litres is the Mango juice which he had initially. Hence, he must have drunk 190 litres of water.
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Question 4 of 5
4. Question
If every second Saturday and all Sundays are holidays in a 31 days month beginning on Sunday, then how many working days are there in that month?
Correct
Solution (d)
It is given that the month begins with Sunday. So, 1st, 8th, 15th, 22nd, 29th days will be Sundays whereas 14th and 28th days are second Saturdays. Thus, there are 7 holidays in all.
Hence, the number of working days = 31 – 7 =24
Incorrect
Solution (d)
It is given that the month begins with Sunday. So, 1st, 8th, 15th, 22nd, 29th days will be Sundays whereas 14th and 28th days are second Saturdays. Thus, there are 7 holidays in all.
Hence, the number of working days = 31 – 7 =24
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Question 5 of 5
5. Question
Consider the set S = {2, 3, 4…., 2n+1}, where n is a positive integer greater than 2019. If X is the average of the odd integers in set S and Y is the average of the even integers in set S. What is the value of X – Y?
Correct
Solution (b)
The odd numbers in the set are 3, 5, 7…2n+1
Sum of the odd numbers = 3+5+7+…+ (2n+1) = n2+2n
Average of odd numbers = n2+2n/n = n+2
Sum of even numbers = 2 + 4 + 6 +…+ 2n = 2(1+2+3+…+n) = 2*n*(n+1)/2 = n(n+1)
Average of even numbers = n(n+1)/n = n+1
So, difference between the averages of even and odd numbers = 1
Incorrect
Solution (b)
The odd numbers in the set are 3, 5, 7…2n+1
Sum of the odd numbers = 3+5+7+…+ (2n+1) = n2+2n
Average of odd numbers = n2+2n/n = n+2
Sum of even numbers = 2 + 4 + 6 +…+ 2n = 2(1+2+3+…+n) = 2*n*(n+1)/2 = n(n+1)
Average of even numbers = n(n+1)/n = n+1
So, difference between the averages of even and odd numbers = 1
