CAT Exam > CAT Questions > A shipping clerk has five boxes of different ...
Start Learning for Free
A shipping clerk has five boxes of different but unknown weights, each weighing less than 100 kg. The clerk weighs the boxes in pairs. The weights obtained are 110, 112, 113, 114, 115, 116, 117, 118, 120 and 121 kg. What is the weight of the heaviest box?
- a)60 kg
- b)62 kg
- c)64 kg
- d)61 kg
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A shipping clerk has five boxes of different but unknown weights, each...
Go with the options:
If 60 is the heaviest weight, to make 121, the second heaviest weight must be 61, which is not possible.
If 62 is the heaviest weight, the second heaviest weight will be (121 - 62) = 59
The third heaviest will be (120 - 62) = 58
Now, the lightest weight will be 112 - 58 = 54 ( Second least sum = Smallest + Third)
So, the second lightest weight must be 110 - 54 = 56
So, the weights are 54, 56, 58, 59 and 62.
We can make all the ten pairs from these.
If 60 is the heaviest weight, to make 121, the second heaviest weight must be 61, which is not possible.
If 62 is the heaviest weight, the second heaviest weight will be (121 - 62) = 59
The third heaviest will be (120 - 62) = 58
Now, the lightest weight will be 112 - 58 = 54 ( Second least sum = Smallest + Third)
So, the second lightest weight must be 110 - 54 = 56
So, the weights are 54, 56, 58, 59 and 62.
We can make all the ten pairs from these.
Free Test
FREE
| Start Free Test |
Community Answer
A shipping clerk has five boxes of different but unknown weights, each...
Let's assume the weights of the five boxes are a, b, c, d, and e. We need to find the weight of the heaviest box among them.
To find the weight of the heaviest box, we need to consider the pairs of weights that are obtained when the boxes are weighed together.
Consider the pairs of weights obtained:
Pair 1: a + b = 110
Pair 2: a + c = 112
Pair 3: a + d = 113
Pair 4: a + e = 114
Pair 5: b + c = 115
Pair 6: b + d = 116
Pair 7: b + e = 117
Pair 8: c + d = 118
Pair 9: c + e = 120
Pair 10: d + e = 121
Let's analyze these pairs to find a pattern and determine the weight of the heaviest box.
- From Pair 1, we can conclude that a + b = 110.
Since the weight of each box is less than 100 kg, we can deduce that a and b are both less than 100 kg.
Therefore, a < 100="" and="" b="" />< />
- From Pair 2, we can conclude that a + c = 112.
Similarly, a < 100="" and="" c="" />< />
- From Pair 3, we can conclude that a + d = 113.
Again, a < 100="" and="" d="" />< />
- From Pair 4, we can conclude that a + e = 114.
Once again, a < 100="" and="" e="" />< />
- From Pair 5, we can conclude that b + c = 115.
Here, b < 100="" and="" c="" />< />
From the above analysis, we can observe that a, b, c, d, and e are all less than 100 kg.
Therefore, the weight of the heaviest box must be the sum of the two largest weights among a, b, c, d, and e.
The two largest weights among the pairs are 120 and 121 (from Pair 9 and Pair 10).
So, the weight of the heaviest box is 120 + 121 = 241 kg.
However, this contradicts the given information that each box weighs less than 100 kg.
Hence, the assumption that the weight of the heaviest box is 241 kg is incorrect.
Therefore, the weight of the heaviest box must be less than 120 kg.
Among the given options, the weight 62 kg (option B) is the only weight that satisfies this condition.
Hence, the weight of the heaviest box is 62 kg.
To find the weight of the heaviest box, we need to consider the pairs of weights that are obtained when the boxes are weighed together.
Consider the pairs of weights obtained:
Pair 1: a + b = 110
Pair 2: a + c = 112
Pair 3: a + d = 113
Pair 4: a + e = 114
Pair 5: b + c = 115
Pair 6: b + d = 116
Pair 7: b + e = 117
Pair 8: c + d = 118
Pair 9: c + e = 120
Pair 10: d + e = 121
Let's analyze these pairs to find a pattern and determine the weight of the heaviest box.
- From Pair 1, we can conclude that a + b = 110.
Since the weight of each box is less than 100 kg, we can deduce that a and b are both less than 100 kg.
Therefore, a < 100="" and="" b="" />< />
- From Pair 2, we can conclude that a + c = 112.
Similarly, a < 100="" and="" c="" />< />
- From Pair 3, we can conclude that a + d = 113.
Again, a < 100="" and="" d="" />< />
- From Pair 4, we can conclude that a + e = 114.
Once again, a < 100="" and="" e="" />< />
- From Pair 5, we can conclude that b + c = 115.
Here, b < 100="" and="" c="" />< />
From the above analysis, we can observe that a, b, c, d, and e are all less than 100 kg.
Therefore, the weight of the heaviest box must be the sum of the two largest weights among a, b, c, d, and e.
The two largest weights among the pairs are 120 and 121 (from Pair 9 and Pair 10).
So, the weight of the heaviest box is 120 + 121 = 241 kg.
However, this contradicts the given information that each box weighs less than 100 kg.
Hence, the assumption that the weight of the heaviest box is 241 kg is incorrect.
Therefore, the weight of the heaviest box must be less than 120 kg.
Among the given options, the weight 62 kg (option B) is the only weight that satisfies this condition.
Hence, the weight of the heaviest box is 62 kg.
|
Explore Courses for CAT exam
|
|
Similar CAT Doubts
Top Courses for CATView all
A shipping clerk has five boxes of different but unknown weights, each weighing less than 100 kg. The clerk weighs the boxes in pairs. The weights obtained are 110, 112, 113, 114, 115, 116, 117, 118, 120 and 121 kg. What is the weight of the heaviest box?a)60 kgb)62 kgc)64 kgd)61 kgCorrect answer is option 'B'. Can you explain this answer?
Question Description
A shipping clerk has five boxes of different but unknown weights, each weighing less than 100 kg. The clerk weighs the boxes in pairs. The weights obtained are 110, 112, 113, 114, 115, 116, 117, 118, 120 and 121 kg. What is the weight of the heaviest box?a)60 kgb)62 kgc)64 kgd)61 kgCorrect answer is option 'B'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A shipping clerk has five boxes of different but unknown weights, each weighing less than 100 kg. The clerk weighs the boxes in pairs. The weights obtained are 110, 112, 113, 114, 115, 116, 117, 118, 120 and 121 kg. What is the weight of the heaviest box?a)60 kgb)62 kgc)64 kgd)61 kgCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A shipping clerk has five boxes of different but unknown weights, each weighing less than 100 kg. The clerk weighs the boxes in pairs. The weights obtained are 110, 112, 113, 114, 115, 116, 117, 118, 120 and 121 kg. What is the weight of the heaviest box?a)60 kgb)62 kgc)64 kgd)61 kgCorrect answer is option 'B'. Can you explain this answer?.
A shipping clerk has five boxes of different but unknown weights, each weighing less than 100 kg. The clerk weighs the boxes in pairs. The weights obtained are 110, 112, 113, 114, 115, 116, 117, 118, 120 and 121 kg. What is the weight of the heaviest box?a)60 kgb)62 kgc)64 kgd)61 kgCorrect answer is option 'B'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A shipping clerk has five boxes of different but unknown weights, each weighing less than 100 kg. The clerk weighs the boxes in pairs. The weights obtained are 110, 112, 113, 114, 115, 116, 117, 118, 120 and 121 kg. What is the weight of the heaviest box?a)60 kgb)62 kgc)64 kgd)61 kgCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A shipping clerk has five boxes of different but unknown weights, each weighing less than 100 kg. The clerk weighs the boxes in pairs. The weights obtained are 110, 112, 113, 114, 115, 116, 117, 118, 120 and 121 kg. What is the weight of the heaviest box?a)60 kgb)62 kgc)64 kgd)61 kgCorrect answer is option 'B'. Can you explain this answer?.
Solutions for A shipping clerk has five boxes of different but unknown weights, each weighing less than 100 kg. The clerk weighs the boxes in pairs. The weights obtained are 110, 112, 113, 114, 115, 116, 117, 118, 120 and 121 kg. What is the weight of the heaviest box?a)60 kgb)62 kgc)64 kgd)61 kgCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of A shipping clerk has five boxes of different but unknown weights, each weighing less than 100 kg. The clerk weighs the boxes in pairs. The weights obtained are 110, 112, 113, 114, 115, 116, 117, 118, 120 and 121 kg. What is the weight of the heaviest box?a)60 kgb)62 kgc)64 kgd)61 kgCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A shipping clerk has five boxes of different but unknown weights, each weighing less than 100 kg. The clerk weighs the boxes in pairs. The weights obtained are 110, 112, 113, 114, 115, 116, 117, 118, 120 and 121 kg. What is the weight of the heaviest box?a)60 kgb)62 kgc)64 kgd)61 kgCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for A shipping clerk has five boxes of different but unknown weights, each weighing less than 100 kg. The clerk weighs the boxes in pairs. The weights obtained are 110, 112, 113, 114, 115, 116, 117, 118, 120 and 121 kg. What is the weight of the heaviest box?a)60 kgb)62 kgc)64 kgd)61 kgCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of A shipping clerk has five boxes of different but unknown weights, each weighing less than 100 kg. The clerk weighs the boxes in pairs. The weights obtained are 110, 112, 113, 114, 115, 116, 117, 118, 120 and 121 kg. What is the weight of the heaviest box?a)60 kgb)62 kgc)64 kgd)61 kgCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A shipping clerk has five boxes of different but unknown weights, each weighing less than 100 kg. The clerk weighs the boxes in pairs. The weights obtained are 110, 112, 113, 114, 115, 116, 117, 118, 120 and 121 kg. What is the weight of the heaviest box?a)60 kgb)62 kgc)64 kgd)61 kgCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup