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When the positive integer x is divided by 11, the quotient is y and the remainder 3. When x is divided by 19, the remainder is also 3. What is the remainder when y is divided by 19?
- a)0
- b)1
- c)2
- d)3
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
When the positive integer x is divided by 11, the quotient is y and th...
Both 11 and 19 are Prime Numbers and hence their LCM = 11*19 = 209 is the closest number which can be looked at here.
Now when dividing this number the remainder is 3, so the number being divided i.e. x = 209+3 = 212.
So when 212 is divided by 11, the quotent y = 19 and remainder r = 3.
So when y = 19 is divided by 19, the remainder is 0.
The same will be true for any multiple of 209.
Most Upvoted Answer
When the positive integer x is divided by 11, the quotient is y and th...
Given Information:
- When x is divided by 11, the quotient is y and the remainder is 3.
- When x is divided by 19, the remainder is also 3.
Understanding the Problem:
To find the remainder when y is divided by 19, we need to understand the relationship between x, y, and the remainders when x is divided by 11 and 19.
Solution:
1. Let's assume the value of x to be 11y + 3, as the remainder when x is divided by 11 is 3 and the quotient is y.
2. Since the remainder when x is divided by 19 is also 3, we can write x as 19z + 3.
3. Equating the two expressions for x:
11y + 3 = 19z + 3
11y = 19z
y = 19z/11
y = 19(2z)/11
y = 38z/11
y = 3z + (5z/11)
Remainder when y is divided by 19:
- The term 3z is divisible by 19, so it doesn't contribute to the remainder.
- When 5z/11 is divided by 19, the remainder will be 0.
Therefore, the remainder when y is divided by 19 is 0. Hence, the correct answer is option 'A'.
- When x is divided by 11, the quotient is y and the remainder is 3.
- When x is divided by 19, the remainder is also 3.
Understanding the Problem:
To find the remainder when y is divided by 19, we need to understand the relationship between x, y, and the remainders when x is divided by 11 and 19.
Solution:
1. Let's assume the value of x to be 11y + 3, as the remainder when x is divided by 11 is 3 and the quotient is y.
2. Since the remainder when x is divided by 19 is also 3, we can write x as 19z + 3.
3. Equating the two expressions for x:
11y + 3 = 19z + 3
11y = 19z
y = 19z/11
y = 19(2z)/11
y = 38z/11
y = 3z + (5z/11)
Remainder when y is divided by 19:
- The term 3z is divisible by 19, so it doesn't contribute to the remainder.
- When 5z/11 is divided by 19, the remainder will be 0.
Therefore, the remainder when y is divided by 19 is 0. Hence, the correct answer is option 'A'.
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