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
Rahul bought 20 shoes and 12 slippers. He marked-up the shoes by 15% on the cost price of each, and the slippers by Rs 20 on the cost price of each. He sold 75% of the shoes and 8 slippers and made a profit of Rs 385. If the cost of a slipper is 60% the cost of a shoe and he got no return on unsold items, what was his overall profit or loss?
Correct
Solution (a)
Let the CP of 1 shoe = S
Thus, the CP of 1 slipper = 0.6S
Given that, SP of 1 shoe = 1.15 S and SP of 1 slipper = 0.6S+20
75% of shoes = 15
Also, 15*1.15*S + 8*(0.6S+20) – 15S – 8*0.6*S = 385 [SP – CP = Profit]
Thus, solving we get S = 100
Hence, total CP of 20 shoes and 12 slippers = 20*100 + 12*60 = 2,720
SP of 15 shoes and 8 slippers = 15*1.15*100 + 8*80 = 2,365
Thus, the overall loss = 2,365 – 2,720 = 355 Rs.
Hence, option a is correct
Incorrect
Solution (a)
Let the CP of 1 shoe = S
Thus, the CP of 1 slipper = 0.6S
Given that, SP of 1 shoe = 1.15 S and SP of 1 slipper = 0.6S+20
75% of shoes = 15
Also, 15*1.15*S + 8*(0.6S+20) – 15S – 8*0.6*S = 385 [SP – CP = Profit]
Thus, solving we get S = 100
Hence, total CP of 20 shoes and 12 slippers = 20*100 + 12*60 = 2,720
SP of 15 shoes and 8 slippers = 15*1.15*100 + 8*80 = 2,365
Thus, the overall loss = 2,365 – 2,720 = 355 Rs.
Hence, option a is correct
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Question 2 of 5
2. Question
If N = (18n2+ 9n + 8)/n; where N belongs to integer. How many integral solutions of N are possible?
Correct
Solution (b)
The given expression can be broken as: 18n2/n + 9n/n + 8/n.
This gives us: 18n + 9 + 8/n. Now we can see that whatever the value of ‘n’, 18n + 9 will always give an integral value. Therefore, it now depends upon 8/n only ⇒ n can have any integral value, which is a factor of 8. The integers, which will satisfy this condition, are ±1, ±2, ±8, ±4. Thus, in total, n can take 8 values.
Incorrect
Solution (b)
The given expression can be broken as: 18n2/n + 9n/n + 8/n.
This gives us: 18n + 9 + 8/n. Now we can see that whatever the value of ‘n’, 18n + 9 will always give an integral value. Therefore, it now depends upon 8/n only ⇒ n can have any integral value, which is a factor of 8. The integers, which will satisfy this condition, are ±1, ±2, ±8, ±4. Thus, in total, n can take 8 values.
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Question 3 of 5
3. Question
Find the unit digit of the following expression: (213)34 × (576)456 × (55)86.
Correct
Solution (d)
Whenever an even unit digit and a 5 at the unit digit are present, they will always give a 0 at the unit digit, no matter if any other number is present or not.
Hence, with this approach, this question proves to be a sitter. The unit digit of the expression will be 0.
Incorrect
Solution (d)
Whenever an even unit digit and a 5 at the unit digit are present, they will always give a 0 at the unit digit, no matter if any other number is present or not.
Hence, with this approach, this question proves to be a sitter. The unit digit of the expression will be 0.
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Question 4 of 5
4. Question
In a party there are 25 persons present. If each of them shakes hand with all the other persons only once, in total how many handshakes will take place?
Correct
Solution (a)
Out of 25 persons, the first person will shake hand with 24 persons. The second person will shake hand with 23 persons (because he has already shaken hand with first person). The third person will shake hand with 22 persons and so on. The second last person shakes hand with only one person. And last will shake hand with none (because he has already shaken hand with all persons).
In order to find the total number of handshakes you have to add all the natural numbers from 1 to 24 i.e. ∑ 24.
We know that the sum of first n natural numbers is given by, ∑n = n(n+1)/2
∑24 = 24 x 25/2 = 300 handshakes.
Incorrect
Solution (a)
Out of 25 persons, the first person will shake hand with 24 persons. The second person will shake hand with 23 persons (because he has already shaken hand with first person). The third person will shake hand with 22 persons and so on. The second last person shakes hand with only one person. And last will shake hand with none (because he has already shaken hand with all persons).
In order to find the total number of handshakes you have to add all the natural numbers from 1 to 24 i.e. ∑ 24.
We know that the sum of first n natural numbers is given by, ∑n = n(n+1)/2
∑24 = 24 x 25/2 = 300 handshakes.
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Question 5 of 5
5. Question
The length, breadth and height of a room are in the ratio 3:2:1. If the breadth and height are halved and the length is doubled, then the total area of the four walls of the room will
Correct
Solution (c)
In the present case, let Length = l = 3x, Breadth = b = 2x, Height = h = x
Then, Area of four walls = 2 (l + b) h = 2(3x + 2x) x = 10x2.
Now as Length gets doubled = 6x, Breadth halved = x, Height halved = x/2.
New area of four walls = 2 (6x + x)* x/2 = 7x2.
Hence, (10x2 – 7x2)/ 10x2 = 30
Thus there is a decrease of 30%.
Incorrect
Solution (c)
In the present case, let Length = l = 3x, Breadth = b = 2x, Height = h = x
Then, Area of four walls = 2 (l + b) h = 2(3x + 2x) x = 10x2.
Now as Length gets doubled = 6x, Breadth halved = x, Height halved = x/2.
New area of four walls = 2 (6x + x)* x/2 = 7x2.
Hence, (10x2 – 7x2)/ 10x2 = 30
Thus there is a decrease of 30%.
