Mathematics

The total area of the 64 small squares is 400 cm², so each small square has an area of 400/64 = 6.25 cm². The side length of each small square is √6.25 = 2.5 cm. The chessboard has 8 squares per side, so its side length without the border is 8 × 2.5 = 20 cm. Adding the 3 cm border on each side adds 6 cm total, so the full side length is 20 + 6 = 26 cm. However, the question asks for the length of each side of the chessboard itself, which is 20 cm (without the border). Therefore, the correct answer is 20 cm (option B). Since the original correct answer was D (26 cm), which includes the border, but the question asks for the chessboard side length, the correct answer is B.

The calculation is performed as follows: First, add 2758 and 20581 to get 23339. Then subtract 17889 from 23339, resulting in 5450. Option B is 5450, which is the correct answer.

The problem states: 20% of 40 + ?% of 80 = 120. First, calculate 20% of 40, which is (20/100)*40 = 8. Let the unknown percentage be x%. Then the equation becomes 8 + (x/100)*80 = 120. Simplifying, (x/100)*80 = 120 - 8 = 112. This gives 0.8x = 112, so x = 112 / 0.8 = 140. Therefore, the value of '?' is 140%, which corresponds to option A. The original answer given as D (180) is incorrect. The options represent the percentage values directly, so the correct answer is A (140).

Jameel starts at floor 11 going up at 57 floors/min, and Nasir starts at floor 51 going down at 63 floors/min. Let t be the time in minutes when they meet. Jameel's floor: 11 + 57t; Nasir's floor: 51 - 63t. Setting equal: 11 + 57t = 51 - 63t → 120t = 40 → t = 1/3 min. Substitute back: floor = 11 + 57*(1/3) = 11 + 19 = 30. However, this calculation shows 30, which matches option C, but let's verify carefully: 11 + 57*(1/3) = 11 + 19 = 30; 51 - 63*(1/3) = 51 - 21 = 30. So the correct floor is 30, matching option C. Therefore, the original correct_answer 'C' is correct. The explanation was missing and is now provided. The topic is 'Relative Motion' and difficulty is medium due to rate and algebra involved.

Let the number of children be x. Each child gets x/8 notebooks, so total notebooks = x * (x/8) = x^2/8. If the number of children is halved (x/2), each gets 16 notebooks, so total notebooks = (x/2) * 16 = 8x. Equate total notebooks: x^2/8 = 8x, which simplifies to x^2 = 64x, so x = 64 (ignoring zero). Total notebooks = 64^2/8 = 512.

First, evaluate inside the brackets step-by-step using order of operations: 8 – 4 / 2 * 3 – 1 + 1 + (4 + 2) – 2 * 2 equals 8 – 2 * 3 – 1 + 1 + 6 – 4, which simplifies to 8 – 6 – 1 + 1 + 6 – 4 = 4. Half of 4 is 2. Adding 7 gives 7 + 2 = 9.

Performing the calculation step-by-step: 22004 - 29303 = -7299; then -7299 + 101299 = 94000; finally 94000 - 59532 = 34468. Among the given options, 34468 is closest to 34500, which corresponds to option C. Therefore, the correct answer is C, not A.

To determine descending order, compare the fractions: 8/15 ≈ 0.533, 9/13 ≈ 0.692, 6/11 ≈ 0.545. The order 8/15, 9/13, 6/11 is not descending since 9/13 > 6/11 > 8/15. Checking option A: 8/15 (0.533), 9/13 (0.692), 6/11 (0.545) is not descending. Option C is 9/13 (0.692), 6/11 (0.545), 8/15 (0.533), which is descending. Therefore, option C is correct. The initial explanation was missing, so it has been added. The topic is fractions and ordering, and difficulty is medium due to fraction comparison.

First, subtract 1236 from 7394, which equals 6158. Then subtract 4652 from 6158, resulting in 1506. Therefore, the correct answer is 1506, option A.

The equation is 21345 * 45 = 4270 * x. Calculating the left side: 21345 * 45 = 960,525. To find x, divide 960,525 by 4270, which gives approximately 224.95. Among the options, 225 (option C) is the closest and correct answer.