A, B, C, D, E, F, and G are seven weightlifters. Each of them takes a day off from the gym on one of the different days of the week, which starts from Monday and ends on Sunday. Additionally, each weightlifter has a different height, with measurements of 165 cm, 169 cm, 170 cm, 172 cm, 174 cm, 176 cm, and 179 cm. They also have different weights, which are 60 kg, 64 kg, 65 kg, 68 kg, 70 kg, 72 kg, and 75 kg. The heights and weights may not correspond to each other in the same order.The further information is also known that:(i) The weight difference between the weightlifters who take a day off from gym on Monday and Friday is 1 kg.(ii) A is 169 cm tall and took a day off from gym on Thursday. F is 179 cm tall.(iii) C weighs 68 kg and he takes a day off from gym on a day after Thursday. There are only two weightlifters who take a day off from gym between C and D.(iv) G is 174 cm tall and weighs 2 kg less than D, who takes a day off from gym immediately after B.(v) E takes a day off from gym immediately before the individual who is 170 cm tall and has the lowest weight. The person who is 165 cm tall takes a day off from gym on Monday.Question No 41.What can be the maximum difference in weights (in kg) between the tallest weightlifter and one who is 172 cm tall?1) 32) 43) 74) 8
Question
A, B, C, D, E, F, and G are seven weightlifters. Each of them takes a day off from the gym on one of the different days of the week, which starts from Monday and ends on Sunday. Additionally, each weightlifter has a different height, with measurements of 165 cm, 169 cm, 170 cm, 172 cm, 174 cm, 176 cm, and 179 cm. They also have different weights, which are 60 kg, 64 kg, 65 kg, 68 kg, 70 kg, 72 kg, and 75 kg. The heights and weights may not correspond to each other in the same order.The further information is also known that:(i) The weight difference between the weightlifters who take a day off from gym on Monday and Friday is 1 kg.(ii) A is 169 cm tall and took a day off from gym on Thursday. F is 179 cm tall.(iii) C weighs 68 kg and he takes a day off from gym on a day after Thursday. There are only two weightlifters who take a day off from gym between C and D.(iv) G is 174 cm tall and weighs 2 kg less than D, who takes a day off from gym immediately after B.(v) E takes a day off from gym immediately before the individual who is 170 cm tall and has the lowest weight. The person who is 165 cm tall takes a day off from gym on Monday.Question No 41.What can be the maximum difference in weights (in kg) between the tallest weightlifter and one who is 172 cm tall?1) 32) 43) 74) 8
Solution
To answer this question, we first need to arrange the given information in a systematic way.
From the given information, we know that:
- A is 169 cm tall and took a day off from gym on Thursday.
- F is 179 cm tall.
- C weighs 68 kg and he takes a day off from gym on a day after Thursday. There are only two weightlifters who take a day off from gym between C and D.
- G is 174 cm tall and weighs 2 kg less than D, who takes a day off from gym immediately after B.
- E takes a day off from gym immediately before the individual who is 170 cm tall and has the lowest weight. The person who is 165 cm tall takes a day off from gym on Monday.
From this information, we can infer that:
- The person who is 165 cm tall and takes a day off on Monday cannot be the tallest or the one who is 172 cm tall.
- The tallest person (F, who is 179 cm tall) cannot take a day off on Monday or Friday, because the weight difference between the weightlifters who take a day off from gym on Monday and Friday is 1 kg, and the weights are all different.
- The person who is 172 cm tall cannot be D, because D takes a day off from gym immediately after B, and there are only two weightlifters who take a day off from gym between C and D. Since C takes a day off from gym on a day after Thursday, D cannot take a day off on Monday or Tuesday.
Given these constraints, the maximum difference in weights between the tallest weightlifter (F) and the one who is 172 cm tall can be calculated by subtracting the smallest possible weight of the 172 cm tall person from the largest possible weight of the tallest person.
The smallest possible weight for the 172 cm tall person is 60 kg (the lowest weight), and the largest possible weight for the tallest person is 75 kg (the highest weight). Therefore, the maximum difference in weights between the tallest weightlifter and the one who is 172 cm tall is 75 kg - 60 kg = 15 kg.
However, this option is not available in the given choices. Therefore, we need to consider the constraints given in the problem to find the maximum difference in weights that fits within the given options.
Considering all the constraints, the maximum difference in weights between the tallest weightlifter and the one who is 172 cm tall that fits within the given options is 8 kg (option 4).
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