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The weights of five boxes are 10, 20, 50, 70, and 90 kilograms. Which of the following cannot be the total weight (in kilograms) of any combination of these boxes?
- a)180
- b)220
- c)240
- d)200
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The weights of five boxes are 10, 20, 50, 70, and 90 kilograms. Which ...
→ Taking three boxes weights are 20, 70 and 90 kilograms and the total weight of combination is 180 Kilograms.
→ Taking four boxes weights are 10, 50, 70 and 90 kilograms and the total weight of combination is 220 Kilograms.
→ Taking all boxes weights are 10, 20, 50, 70 and 90 kilograms and the total weight of combination is 240 Kilograms.
→ There is no combination of boxes from which total weight can be 200 kilograms.
→ Taking four boxes weights are 10, 50, 70 and 90 kilograms and the total weight of combination is 220 Kilograms.
→ Taking all boxes weights are 10, 20, 50, 70 and 90 kilograms and the total weight of combination is 240 Kilograms.
→ There is no combination of boxes from which total weight can be 200 kilograms.
Most Upvoted Answer
The weights of five boxes are 10, 20, 50, 70, and 90 kilograms. Which ...
Given information:
The weights of the five boxes are 10, 20, 50, 70, and 90 kilograms.
To find:
The total weight that cannot be obtained by any combination of these boxes.
Solution:
To find the total weight that cannot be obtained by any combination of these boxes, we need to find the sum of all possible combinations of the given weights.
Step 1: Find all possible combinations of the given weights.
We have 5 boxes with weights 10, 20, 50, 70, and 90 kilograms. We can use the concept of binary numbers to represent all possible combinations. Each box weight can be either included (1) or excluded (0) in a combination.
Using binary numbers, we can represent all the possible combinations as follows:
00000 (0 kg)
00001 (10 kg)
00010 (20 kg)
00011 (30 kg)
00100 (50 kg)
00101 (60 kg)
00110 (70 kg)
00111 (80 kg)
01000 (90 kg)
01001 (100 kg)
01010 (110 kg)
01011 (120 kg)
01100 (140 kg)
01101 (150 kg)
01110 (160 kg)
01111 (170 kg)
10000 (200 kg)
10001 (210 kg)
10010 (220 kg)
10011 (230 kg)
10100 (250 kg)
10101 (260 kg)
10110 (270 kg)
10111 (280 kg)
11000 (290 kg)
11001 (300 kg)
11010 (310 kg)
11011 (320 kg)
11100 (340 kg)
11101 (350 kg)
11110 (360 kg)
11111 (370 kg)
Step 2: Identify the weights that cannot be obtained.
By examining the list of possible combinations, we can see that the weights that cannot be obtained are 180 kg, 200 kg, 220 kg, 240 kg, and so on.
Answer:
The total weight that cannot be obtained by any combination of these boxes is 200 kg. Therefore, the correct answer is option D.
The weights of the five boxes are 10, 20, 50, 70, and 90 kilograms.
To find:
The total weight that cannot be obtained by any combination of these boxes.
Solution:
To find the total weight that cannot be obtained by any combination of these boxes, we need to find the sum of all possible combinations of the given weights.
Step 1: Find all possible combinations of the given weights.
We have 5 boxes with weights 10, 20, 50, 70, and 90 kilograms. We can use the concept of binary numbers to represent all possible combinations. Each box weight can be either included (1) or excluded (0) in a combination.
Using binary numbers, we can represent all the possible combinations as follows:
00000 (0 kg)
00001 (10 kg)
00010 (20 kg)
00011 (30 kg)
00100 (50 kg)
00101 (60 kg)
00110 (70 kg)
00111 (80 kg)
01000 (90 kg)
01001 (100 kg)
01010 (110 kg)
01011 (120 kg)
01100 (140 kg)
01101 (150 kg)
01110 (160 kg)
01111 (170 kg)
10000 (200 kg)
10001 (210 kg)
10010 (220 kg)
10011 (230 kg)
10100 (250 kg)
10101 (260 kg)
10110 (270 kg)
10111 (280 kg)
11000 (290 kg)
11001 (300 kg)
11010 (310 kg)
11011 (320 kg)
11100 (340 kg)
11101 (350 kg)
11110 (360 kg)
11111 (370 kg)
Step 2: Identify the weights that cannot be obtained.
By examining the list of possible combinations, we can see that the weights that cannot be obtained are 180 kg, 200 kg, 220 kg, 240 kg, and so on.
Answer:
The total weight that cannot be obtained by any combination of these boxes is 200 kg. Therefore, the correct answer is option D.
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The weights of five boxes are 10, 20, 50, 70, and 90 kilograms. Which of the following cannot be the total weight (in kilograms) of any combination of these boxes?a)180b)220c)240d)200Correct answer is option 'D'. Can you explain this answer?
Question Description
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