When a + b is divided by 12, the Remainder is 8. When a - b is divided by 12 the Remainder is 6. If a > b, then find the Remainder when ab is divided by 6?
Answer:
a + b = 12p + 8
a - b = 12q + 6
therefore a = [12(p + q + 1) + 2]/2 = 6(p + q + 1) + 1
b = 6 (p + q) + 1
now, ab = [6(p + q +1) + 1] x [6(p + q) + 1]
on multiplication, all terms except 1 x 1 will be a multiple of 6
so, ab/6 will have a Remainder of 1.
Answer:
a + b = 12p + 8
a - b = 12q + 6
therefore a = [12(p + q + 1) + 2]/2 = 6(p + q + 1) + 1
b = 6 (p + q) + 1
now, ab = [6(p + q +1) + 1] x [6(p + q) + 1]
on multiplication, all terms except 1 x 1 will be a multiple of 6
so, ab/6 will have a Remainder of 1.
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