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I have a few sweets to be distributed. If I keep 2, 3 or 4 in a pack, I am left with one sweet. If I keep 5 in a pack, I am left with none. What is the minimum number of sweets I have to pack and distribute ?
- a)25
- b)37
- c)54
- d)65
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
I have a few sweets to be distributed. If I keep 2, 3 or 4 in a pack, ...
Clearly, the required number would be such that it leaves a remainder of 1 when divided by 2, 3 or 4 and no remainder when divided by 5.
Most Upvoted Answer
I have a few sweets to be distributed. If I keep 2, 3 or 4 in a pack, ...
Given information:
- Keeping 2, 3, or 4 sweets in a pack leaves 1 sweet.
- Keeping 5 sweets in a pack leaves none.
To find the minimum number of sweets to pack and distribute, we need to find the least common multiple (LCM) of 2, 3, 4, and 5, which is the smallest number that is divisible by all four numbers.
Prime factorizing the given numbers:
- 2 = 2
- 3 = 3
- 4 = 2 x 2
- 5 = 5
The LCM of these numbers is the product of their highest powers:
LCM = 2 x 2 x 3 x 5 = 60
This means that we need to have at least 60 sweets to distribute. If we pack them in groups of 2, 3, or 4, we will have 1 sweet left over each time. But if we pack them in groups of 5, we will have no sweets left over.
However, we need to keep in mind that we have to keep 2 sweets for ourselves, so the total number of sweets we need is 60 + 2 = 62.
Therefore, the minimum number of sweets we have to pack and distribute is 62, which is option A.
- Keeping 2, 3, or 4 sweets in a pack leaves 1 sweet.
- Keeping 5 sweets in a pack leaves none.
To find the minimum number of sweets to pack and distribute, we need to find the least common multiple (LCM) of 2, 3, 4, and 5, which is the smallest number that is divisible by all four numbers.
Prime factorizing the given numbers:
- 2 = 2
- 3 = 3
- 4 = 2 x 2
- 5 = 5
The LCM of these numbers is the product of their highest powers:
LCM = 2 x 2 x 3 x 5 = 60
This means that we need to have at least 60 sweets to distribute. If we pack them in groups of 2, 3, or 4, we will have 1 sweet left over each time. But if we pack them in groups of 5, we will have no sweets left over.
However, we need to keep in mind that we have to keep 2 sweets for ourselves, so the total number of sweets we need is 60 + 2 = 62.
Therefore, the minimum number of sweets we have to pack and distribute is 62, which is option A.
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