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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
- e)4
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...
If x divided by 11 has a quotient of y and a remainder of 3, x can be expressed as x = 11y + 3, where y is an integer (by definition, a quotient is an integer). If x divided by 19 also has a remainder of 3, we can also express x as x = 19z + 3, where z is an integer.
We can set the two equations equal to each other:
11y + 3 = 19z + 3
11y = 19z
We can set the two equations equal to each other:
11y + 3 = 19z + 3
11y = 19z
The question asks us what the remainder is when y is divided by 19. From the equation we see that 11y is a multiple of 19 because z is an integer. y itself must be a multiple of 19 since 11, the coefficient of y, is not a multiple of 19.
If y is a multiple of 19, the remainder must be zero.
The correct answer is A.
The correct answer is A.
Most Upvoted Answer
When the positive integer x is divided by 11, the quotient is y and th...
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.
Let's first consider the remainder when x is divided by 11. We are given that the remainder is 3. This means that x can be expressed as:
x = 11y + 3
where y is the quotient when x is divided by 11.
Next, let's consider the remainder when x is divided by 19. We are given that the remainder is also 3. This means that x can be expressed as:
x = 19z + 3
where z is the quotient when x is divided by 19.
Now, let's equate the two expressions for x:
11y + 3 = 19z + 3
Simplifying this equation, we get:
11y = 19z
Dividing both sides of the equation by 11, we get:
y = (19/11)z
Since y is an integer, z must be a multiple of 11. Let's substitute z = 11k into the equation:
y = (19/11)(11k)
y = 19k
We can see that y is a multiple of 19. Therefore, when y is divided by 19, the remainder will be 0.
Hence, the correct answer is option A: 0.
Let's first consider the remainder when x is divided by 11. We are given that the remainder is 3. This means that x can be expressed as:
x = 11y + 3
where y is the quotient when x is divided by 11.
Next, let's consider the remainder when x is divided by 19. We are given that the remainder is also 3. This means that x can be expressed as:
x = 19z + 3
where z is the quotient when x is divided by 19.
Now, let's equate the two expressions for x:
11y + 3 = 19z + 3
Simplifying this equation, we get:
11y = 19z
Dividing both sides of the equation by 11, we get:
y = (19/11)z
Since y is an integer, z must be a multiple of 11. Let's substitute z = 11k into the equation:
y = (19/11)(11k)
y = 19k
We can see that y is a multiple of 19. Therefore, when y is divided by 19, the remainder will be 0.
Hence, the correct answer is option A: 0.
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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)0b)1c)2d)3e)4Correct answer is option 'A'. Can you explain this answer?
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