When a certain number is divided by 222, it leaves a remainder of 35, another number when divided by 407 leaves a remainder 47. What is the remainder when the sum of these two numbers is divided by 37?
Answer:
Answer:
Sum of two numbers are: 222p + 35 + 407q + 47
= 222p + 407q + 74 + 8
Now,
222 = 2 x 37 x 3 = 6 x 37
407 = 11 x 37
Therefore, 222p + 35 + 407q + 47 = 37(6p + 11q + 2) + 8
So, when 222p + 35 + 407q + 47 is divided by 37, we get a
Remainder of 8.
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