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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....
To solve this problem, we can use the concept of modular arithmetic.

Let's assume the positive number we are looking for is represented by "x".

Given that when x is divided by 3, the remainder is 1, we can write this as:
x ≡ 1 (mod 3)

Similarly, when x is divided by 5, the remainder is 4, we can write this as:
x ≡ 4 (mod 5)

We are also given that the difference between the quotients of the division is 3. This means that if we divide x by 3 and divide x by 5, and then subtract the two quotients, the result is 3. Mathematically, we can represent this as:
(x/3) - (x/5) = 3

To simplify this equation, we can find a common denominator for the two fractions:
(5x - 3x) / (3 * 5) = 3
2x / 15 = 3

Now, we can solve for x by multiplying both sides of the equation by 15:
2x = 3 * 15
2x = 45
x = 45 / 2
x = 22.5

However, the question specifically asks for a positive number. Since x is not an integer, we need to find the next positive integer that satisfies the given conditions.

The next positive integer that satisfies the conditions is 23. Let's verify this:

23 ≡ 1 (mod 3)
23 ≡ 4 (mod 5)

Now, let's check if the difference between the quotients of the division is 3:
(23/3) - (23/5) = 7.67 - 4.6 = 3.07

So, the number that satisfies all the given conditions is 23. Thus, the correct answer is option B.
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Community 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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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)34b)19c)49d)64Correct answer is option 'B'. Can you explain this answer?
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