Number Properties question bank #5

[guest]

See question below. I can only get as far as setting the 2 equations equal to each other (11y=19z), but the rest isn't making sense to me. Please help!



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?

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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

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.

[RA]

-- For 11y=19z to be true, LHS has to be multiple of 19.
-- For 11y to be a multiple of 19, y has to be a multiple of 19.
-- If y is a multiple of 19 then the remainder of y divied by 19 would always be 0.

Hope that helps.

[RonPurewal]

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