Problem Solving

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?

A. 12
B. 15
C. 20
D. 28
E. 35

Please explain. Thanks. OA - E

One of the numbers could be 18 -
18 divided by 5 leaves 3 as remainder;
18 divided by 7 leaves 4 as remainder;

Not sure which the other number is...How do we find such numbers?

Integer x is divided by 5, the remainder is 3;

Here the first integer will be 3 just go on adding 5 to it and write down 10-12 such numbers:

3 8 13 18 23 28 33 38 43 48 53 58

when y is divided by 7, the remainder is 4;

Here the first integer will be 4 just go on adding 7 to it and write down 10-12 such numbers:

4 11 18 25 32 39 46 53..... we got 2 common numbers....18 and 53

since x > y; x = 53 and y = 18
x - y = 53 - 18 = 35

Ans E.

Perfect...thanks!

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?

so when x-y is divided by 5 the remainder is 0 (3-3 =0)

also when x-y is divided by 7 remainder is 0 (4-4 =0)

so 5&7 are factors of x-y

i.e 5*7= 35 is a factor of x-y

E