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
In an exhibition, visitors were charged ₹30 on the first day, ₹20 on the second day and ₹10 on the third day. The number of visitors on the three days was in the ratio 2 : 3 : 5. What was the average charge per visitor for the exhibition?
Correct
Answer: (c)
Explanation:
Average charge per visitor = Total collection / Total visitorsLet the number of visitors on the three days be 2x, 3x and 5x.
Total collection
= 30 × 2x + 20 × 3x + 10 × 5x
= 60x + 60x + 50x
= 170xTotal visitors
= 2x + 3x + 5x
= 10xAverage charge per visitor
= 170x / 10x
= ₹17Hence, the correct answer is (c).
Incorrect
Answer: (c)
Explanation:
Average charge per visitor = Total collection / Total visitorsLet the number of visitors on the three days be 2x, 3x and 5x.
Total collection
= 30 × 2x + 20 × 3x + 10 × 5x
= 60x + 60x + 50x
= 170xTotal visitors
= 2x + 3x + 5x
= 10xAverage charge per visitor
= 170x / 10x
= ₹17Hence, the correct answer is (c).
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Question 2 of 5
2. Question
The price of a diamond is proportional to the square of its weight. A diamond weighing 10 grams costs ₹1,00,000. If it breaks into two parts in the ratio 3 : 2, what is the loss in value?
Correct
Answer: (c)
Explanation:
Price is proportional to the square of weight.Let the two parts be 3x and 2x.
So total weight = 5x = 10 grams.Original value ∝ (5x)² = 25x²
After breaking, total value ∝ (3x)² + (2x)²
= 9x² + 4x²
= 13x²So, loss in value ∝ 25x² − 13x² = 12x²
Therefore, loss fraction = 12/25 of original value.
Loss = 12/25 × 1,00,000
= ₹48,000Hence, the correct answer is (c).
Incorrect
Answer: (c)
Explanation:
Price is proportional to the square of weight.Let the two parts be 3x and 2x.
So total weight = 5x = 10 grams.Original value ∝ (5x)² = 25x²
After breaking, total value ∝ (3x)² + (2x)²
= 9x² + 4x²
= 13x²So, loss in value ∝ 25x² − 13x² = 12x²
Therefore, loss fraction = 12/25 of original value.
Loss = 12/25 × 1,00,000
= ₹48,000Hence, the correct answer is (c).
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Question 3 of 5
3. Question
A solid cube is painted Yellow, White and Orange such that opposite faces are of the same colour. The cube is cut into 81 cubes of two different sizes such that 72 cubes are small and 9 cubes are big. None of the faces of the bigger cubes is painted Orange. How many cubes have only one face painted?
Correct
Answer: (c)
Explanation:
Since none of the bigger cubes has Orange on any face, the two Orange faces must be the top and bottom layers made entirely of small cubes.Now 72 small cubes means 36 small cubes on each of the two opposite Orange faces.
So each Orange face is divided into 6 × 6 small cubes.The remaining middle portion consists of 9 big cubes, that is a 3 × 3 arrangement.
From the two 6 × 6 small-cube faces, cubes with only one face painted are the inner cubes:
On one face = (6 − 2)² = 16
On two faces = 16 + 16 = 32Now look at the 3 × 3 middle layer of big cubes.
Among these, the 4 edge-middle big cubes have exactly one face painted.
The 4 corner big cubes have 2 faces painted, and the centre big cube has no face painted.So total cubes with only one face painted
= 32 + 4 = 36Hence, the correct answer is (c).
Incorrect
Answer: (c)
Explanation:
Since none of the bigger cubes has Orange on any face, the two Orange faces must be the top and bottom layers made entirely of small cubes.Now 72 small cubes means 36 small cubes on each of the two opposite Orange faces.
So each Orange face is divided into 6 × 6 small cubes.The remaining middle portion consists of 9 big cubes, that is a 3 × 3 arrangement.
From the two 6 × 6 small-cube faces, cubes with only one face painted are the inner cubes:
On one face = (6 − 2)² = 16
On two faces = 16 + 16 = 32Now look at the 3 × 3 middle layer of big cubes.
Among these, the 4 edge-middle big cubes have exactly one face painted.
The 4 corner big cubes have 2 faces painted, and the centre big cube has no face painted.So total cubes with only one face painted
= 32 + 4 = 36Hence, the correct answer is (c).
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Question 4 of 5
4. Question
Set A contains all the odd numbers between 51 and 99, both inclusive. Set B contains all the odd numbers between 91 and 139, both inclusive. What is the difference between the sum of the elements of set B and that of set A?
Correct
Incorrect
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Question 5 of 5
5. Question
A milkman purchases milk at ₹x per litre and sells it at ₹3x per litre. He mixes 5 litres of water with every 10 litres of pure milk. What is the profit percentage?
Correct
Incorrect
