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A competition requires Rahul to identify the odd weight in a group of weights, given that all the remaining weights are equal. He is given a regular pan balance to complete this task.
Q.If Rahul starts with 30 weights and is told that the odd weight is lighter than the rest, how many iterations will he require to definitely find out the incorrect weight?
- a)3
- b)4
- c)5
- d)6
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A competition requires Rahul to identify the odd weight in a group of ...
In this case, it is known that the odd weight is lighter.
Rahul will start by dividing the weights into equal lots of 10 weights each.
Iteration 1: Compare Lot 1 and Lot 2.
If they are equal then the odd weight is in Lot 3.
If they are unequal, the odd weight is in the Lot where the pan (of the pan balance) has gone up.
Hence, at the end of the first iteration, Rahul will know which lot of 10 weights has the odd weight.
Iteration 2: Subdivide the identified lot into groups of 3, 3 and 4 and compare the weights of the two groups of 3 weights each.
If they are equal then the odd weight is in the third lot of 4 weights.
If, however, they are unequal, then the odd weight is in the lot which has the lesser weight of the two.
Hence, at the end of the second iteration, Rahul has a smaller group of 3 or 4 weights that contains the odd weight.
Iterations 3 and 4: Divide the 3 weights into (1, 1, 1) or the 4 weights into (1, 1,2) and compare the two groups having one weight each.
Thus, as explained in the previous question, Rahul requires two iterations here.
So, Rahul requires 4 iterations to definitely the odd weight in this case. Hence, option 2.
Rahul will start by dividing the weights into equal lots of 10 weights each.
Iteration 1: Compare Lot 1 and Lot 2.
If they are equal then the odd weight is in Lot 3.
If they are unequal, the odd weight is in the Lot where the pan (of the pan balance) has gone up.
Hence, at the end of the first iteration, Rahul will know which lot of 10 weights has the odd weight.
Iteration 2: Subdivide the identified lot into groups of 3, 3 and 4 and compare the weights of the two groups of 3 weights each.
If they are equal then the odd weight is in the third lot of 4 weights.
If, however, they are unequal, then the odd weight is in the lot which has the lesser weight of the two.
Hence, at the end of the second iteration, Rahul has a smaller group of 3 or 4 weights that contains the odd weight.
Iterations 3 and 4: Divide the 3 weights into (1, 1, 1) or the 4 weights into (1, 1,2) and compare the two groups having one weight each.
Thus, as explained in the previous question, Rahul requires two iterations here.
So, Rahul requires 4 iterations to definitely the odd weight in this case. Hence, option 2.
Most Upvoted Answer
A competition requires Rahul to identify the odd weight in a group of ...
Problem Analysis:
Rahul is given a group of weights, out of which one weight is lighter than the others. He needs to identify the odd weight using a pan balance. The pan balance helps in comparing the weights on both sides and determining if they are equal or not. Rahul is also informed that the odd weight is lighter than the rest.
Solution:
In order to determine the odd weight using the pan balance, Rahul can follow the below steps:
1. Step 1: Divide the weights into two equal groups of 15 each and compare them on the pan balance.
- If the two groups are balanced, it means the odd weight is not present in these 30 weights. In this case, Rahul can eliminate 15 weights and repeat the process with the remaining 15 weights in the next iteration.
- If the two groups are not balanced, it means the odd weight is present in one of the groups of 15 weights. In this case, Rahul can eliminate 15 weights and repeat the process with the remaining 15 weights in the next iteration.
2. Step 2: In the second iteration, Rahul is left with 15 weights. He can repeat the same process as in the first step by dividing these 15 weights into two equal groups of 7 each and comparing them on the pan balance.
- If the two groups are balanced, it means the odd weight is not present in these 15 weights. In this case, Rahul can eliminate 7 weights and repeat the process with the remaining 8 weights in the next iteration.
- If the two groups are not balanced, it means the odd weight is present in one of the groups of 7 weights. In this case, Rahul can eliminate 7 weights and repeat the process with the remaining 8 weights in the next iteration.
3. Step 3: In the third iteration, Rahul is left with 8 weights. He can repeat the same process as in the first step by dividing these 8 weights into two equal groups of 4 each and comparing them on the pan balance.
- If the two groups are balanced, it means the odd weight is not present in these 8 weights. In this case, Rahul can eliminate 4 weights and repeat the process with the remaining 4 weights in the next iteration.
- If the two groups are not balanced, it means the odd weight is present in one of the groups of 4 weights. In this case, Rahul can eliminate 4 weights and repeat the process with the remaining 4 weights in the next iteration.
4. Step 4: In the fourth iteration, Rahul is left with 4 weights. He can repeat the same process as in the first step by dividing these 4 weights into two equal groups of 2 each and comparing them on the pan balance.
- If the two groups are balanced, it means the odd weight is not present in these 4 weights. In this case, Rahul can eliminate 2 weights and repeat the process with the remaining 2 weights in the next iteration.
- If the two groups are not balanced, it means the odd weight is present in one of the groups of 2 weights. In this case, Rahul can eliminate 2 weights and repeat the process with the remaining 2 weights in the next
Rahul is given a group of weights, out of which one weight is lighter than the others. He needs to identify the odd weight using a pan balance. The pan balance helps in comparing the weights on both sides and determining if they are equal or not. Rahul is also informed that the odd weight is lighter than the rest.
Solution:
In order to determine the odd weight using the pan balance, Rahul can follow the below steps:
1. Step 1: Divide the weights into two equal groups of 15 each and compare them on the pan balance.
- If the two groups are balanced, it means the odd weight is not present in these 30 weights. In this case, Rahul can eliminate 15 weights and repeat the process with the remaining 15 weights in the next iteration.
- If the two groups are not balanced, it means the odd weight is present in one of the groups of 15 weights. In this case, Rahul can eliminate 15 weights and repeat the process with the remaining 15 weights in the next iteration.
2. Step 2: In the second iteration, Rahul is left with 15 weights. He can repeat the same process as in the first step by dividing these 15 weights into two equal groups of 7 each and comparing them on the pan balance.
- If the two groups are balanced, it means the odd weight is not present in these 15 weights. In this case, Rahul can eliminate 7 weights and repeat the process with the remaining 8 weights in the next iteration.
- If the two groups are not balanced, it means the odd weight is present in one of the groups of 7 weights. In this case, Rahul can eliminate 7 weights and repeat the process with the remaining 8 weights in the next iteration.
3. Step 3: In the third iteration, Rahul is left with 8 weights. He can repeat the same process as in the first step by dividing these 8 weights into two equal groups of 4 each and comparing them on the pan balance.
- If the two groups are balanced, it means the odd weight is not present in these 8 weights. In this case, Rahul can eliminate 4 weights and repeat the process with the remaining 4 weights in the next iteration.
- If the two groups are not balanced, it means the odd weight is present in one of the groups of 4 weights. In this case, Rahul can eliminate 4 weights and repeat the process with the remaining 4 weights in the next iteration.
4. Step 4: In the fourth iteration, Rahul is left with 4 weights. He can repeat the same process as in the first step by dividing these 4 weights into two equal groups of 2 each and comparing them on the pan balance.
- If the two groups are balanced, it means the odd weight is not present in these 4 weights. In this case, Rahul can eliminate 2 weights and repeat the process with the remaining 2 weights in the next iteration.
- If the two groups are not balanced, it means the odd weight is present in one of the groups of 2 weights. In this case, Rahul can eliminate 2 weights and repeat the process with the remaining 2 weights in the next
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A competition requires Rahul to identify the odd weight in a group of weights, given that all the remaining weights are equal. He is given a regular pan balance to complete this task.Q.If Rahul starts with 30 weights and is told that the odd weight is lighter than the rest, how many iterations will he require to definitely find out the incorrect weight? a)3b)4c)5d)6Correct answer is option 'B'. Can you explain this answer?
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A competition requires Rahul to identify the odd weight in a group of weights, given that all the remaining weights are equal. He is given a regular pan balance to complete this task.Q.If Rahul starts with 30 weights and is told that the odd weight is lighter than the rest, how many iterations will he require to definitely find out the incorrect weight? a)3b)4c)5d)6Correct answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A competition requires Rahul to identify the odd weight in a group of weights, given that all the remaining weights are equal. He is given a regular pan balance to complete this task.Q.If Rahul starts with 30 weights and is told that the odd weight is lighter than the rest, how many iterations will he require to definitely find out the incorrect weight? a)3b)4c)5d)6Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A competition requires Rahul to identify the odd weight in a group of weights, given that all the remaining weights are equal. He is given a regular pan balance to complete this task.Q.If Rahul starts with 30 weights and is told that the odd weight is lighter than the rest, how many iterations will he require to definitely find out the incorrect weight? a)3b)4c)5d)6Correct answer is option 'B'. Can you explain this answer?.
Solutions for A competition requires Rahul to identify the odd weight in a group of weights, given that all the remaining weights are equal. He is given a regular pan balance to complete this task.Q.If Rahul starts with 30 weights and is told that the odd weight is lighter than the rest, how many iterations will he require to definitely find out the incorrect weight? a)3b)4c)5d)6Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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