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When a particular positive number is divided by 3, the remainder is 1. If the same number is divided by 5, the remainder is 4. If the difference between the quotients of the division is 3, then find the number.
- a)34
- b)19
- c)49
- d)64
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
When a particular positive number is divided by 3, the remainder is 1....
Let the quotients when this number is divided by 3 and 5 be x and y respectively.
(Note that x will be greater than y as 3 is smaller than 5).
Number = 3x + 1 = 5y + 4
Given that, x – y = 3
On solving both equation we get, x = 6, y=3
Thus the number is 5 × 3 + 4= 19.
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Community Answer
When a particular positive number is divided by 3, the remainder is 1....
To solve this problem, we will use the concept of modular arithmetic.
Let's assume the positive number we are looking for is represented by 'x'.
When 'x' is divided by 3, the remainder is 1. This can be written as:
x ≡ 1 (mod 3)
Similarly, when 'x' is divided by 5, the remainder is 4. This can be written as:
x ≡ 4 (mod 5)
Now, we are given that the difference between the quotients of the division is 3.
We can represent this as:
(x/3) - (x/5) = 3
To simplify this equation, we can find a common denominator:
(5x - 3x) / (3*5) = 3
2x / 15 = 3
Cross-multiplying gives us:
2x = 45
Dividing both sides by 2 gives us the value of 'x':
x = 22.5
However, we are given that 'x' is a positive number. So, 'x' cannot be 22.5.
Therefore, our assumption that 'x' is a decimal number is incorrect.
To find the correct value of 'x', we can substitute the given options into the equations and check which one satisfies both conditions.
Let's start with option B: x = 19
When we divide 19 by 3, the remainder is indeed 1.
Similarly, when we divide 19 by 5, the remainder is 4.
Therefore, option B (19) is the correct answer.
Let's assume the positive number we are looking for is represented by 'x'.
When 'x' is divided by 3, the remainder is 1. This can be written as:
x ≡ 1 (mod 3)
Similarly, when 'x' is divided by 5, the remainder is 4. This can be written as:
x ≡ 4 (mod 5)
Now, we are given that the difference between the quotients of the division is 3.
We can represent this as:
(x/3) - (x/5) = 3
To simplify this equation, we can find a common denominator:
(5x - 3x) / (3*5) = 3
2x / 15 = 3
Cross-multiplying gives us:
2x = 45
Dividing both sides by 2 gives us the value of 'x':
x = 22.5
However, we are given that 'x' is a positive number. So, 'x' cannot be 22.5.
Therefore, our assumption that 'x' is a decimal number is incorrect.
To find the correct value of 'x', we can substitute the given options into the equations and check which one satisfies both conditions.
Let's start with option B: x = 19
When we divide 19 by 3, the remainder is indeed 1.
Similarly, when we divide 19 by 5, the remainder is 4.
Therefore, option B (19) is the correct answer.
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