alex.gellatly wrote:When positive integer x is divided by 5, the remainder is 3; and when x is divided by 7, the remainder is 4. When positive integer y is divided by 5, the remainder is 3; and when y is divided by 7, the remainder is 4. If x>y, which of the following must be a factor of x-y?
12
15
20
28
35
When positive integer x is divided by 5, the remainder is 3.
In other words, x is 3 more than a multiple of 5:
x = 5a + 3 = 3, 8, 13,
18, 23...
When x is divided by 7, the remainder is 4.
In other words, x is 4 more than a multiple of 7:
x = 7b + 4 = 4, 11,
18...
The smallest value common to both lists is 18.
This means that x is 18 more than a multiple of the product of the two divisors (5 and 7):
x = 35c + 18 = 18, 53, 88, 123...
Since all of the same conditions apply to y:
y = 35d + 18 = 18, 53, 88, 123...
Thus:
x-y = (35c + 18) - (35d + 18) = 35(c-d), implying that x-y is a multiple of 35.
The correct answer is
E.
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