Two different numbers when divided by a divisor left reminder 11 and 21 respectively. When their sum was divided by the same divisor reminder was 4. what is the divisor?Options28891535
Question
Two different numbers when divided by a divisor left reminder 11 and 21 respectively. When their sum was divided by the same divisor reminder was 4. what is the divisor?Options28891535
Solution
Let's denote the two different numbers as A and B, and the divisor as D.
From the problem, we know that:
A = D*x + 11 (equation 1)
B = D*y + 21 (equation 2)
where x and y are the quotient when A and B are divided by D respectively.
Also, we know that:
A + B = D*z + 4 (equation 3)
where z is the quotient when (A+B) is divided by D.
Substituting equation 1 and 2 into equation 3, we get:
Dx + 11 + Dy + 21 = D*z + 4
Simplifying, we get:
D*(x+y) + 32 = D*z + 4
Subtracting D*(x+y) from both sides, we get:
32 = D*(z - x - y) + 4
Subtracting 4 from both sides, we get:
28 = D*(z - x - y)
So, the divisor D must be a factor of 28.
Looking at the options, the only factors of 28 are 1, 2, 4, 7, 14, and 28.
So, the divisor D must be 7 or 14.
However, since the remainders when A and B are divided by D are 11 and 21, which are both greater than 7, the divisor D cannot be 7.
Therefore, the divisor D must be 14.
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