Geometry and Mensuration

51. A number is mistakenly divided by 4 instead of multiplying by 4. What is the percentage change in the result due to this mistake? [2024-II]

(a) 25%
(b) 50%
(c) 72.75%
(d) 93.75%

Correct Answer: (d) 93.75%

Solution:Let number = N

Correct number = 4N

Wrong number = N/4

Required % change = (4N- (N/4)/4N) × 100

(15 × 25)/4 = 93.75%

52. In an examination, 80% of students passed in English, 70% of students passed in Hindi and 15% failed in both the subjects. What is the percentage of students who failed in only one subjects? [2024-II]

(a) 15%
(b) 20%
(c) 25%
(d) 35%

Correct Answer: (b) 20%

Solution:In English → 80% Pass; Fail \%= 100 - 80 = 20% Fail

Hindi 70% Pass; Fail \%= 100 - 700 = 30% Fail

In both subject total Fail = 15%

∴ Number of Fail in only one subject

= (30 - 15) + (20 - 15)

= 15 + 5 = 20%

53. A can X contains 399 litres of petrol and a can Y contains 532 litres of diesel. They are to be bottled in bottles of equal size so that whole of petrol and diesel would be separately bottled. The bottle capacity in terms of litres in an integer. How many different bottle sizes are possible? [2024-II]

(a) 3
(b) 4
(c) 5
(d) 6

Correct Answer: (b) 4

Solution:Here prime factorisation of 399 and 532 gives,

399 =1 * 3 * 7 * 19

532 =1 * 2 * 2 * 7 * 19;

Taking the common factors, we get 1,7, 19 and 7 * 19 = 133;

Therefore bottles of sizes 1 litre, 7 litres and 19 litres and 133 can be used to fill the petrol and diesel. Therefore four different bottle sizes are possible; And hence the answer is option (b)

54. What is the least possible number of cuts required to cut a cube into 64 identical pieces? [2024-II]

(a) 8
(b) 9
(c) 12
(d) 16

Correct Answer: (b) 9

Solution:

Number of cube in each row of each side

= ³√(64) = 4

Now to cut out 4 small cube of equal size we need to cut this at 3 equally distant points on all three adjoining sides.

∴ Number of cut required = 3 + 3 + 3 = 9

Geometry and Mensuration

51. A number is mistakenly divided by 4 instead of multiplying by 4. What is the percentage change in the result due to this mistake? [2024-II]

52. In an examination, 80% of students passed in English, 70% of students passed in Hindi and 15% failed in both the subjects. What is the percentage of students who failed in only one subjects? [2024-II]

54. What is the least possible number of cuts required to cut a cube into 64 identical pieces? [2024-II]

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