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?Options91535288
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?Options91535288
Solution
Let's denote the two different numbers as A and B, and the divisor as D.
From the problem, we know that:
A = Dx + 11 (where x is some integer) B = Dy + 21 (where y is some integer)
Adding these two equations, we get:
A + B = D*(x+y) + 32
But we also know from the problem that when A + B is divided by D, the remainder is 4. So we can write this as:
A + B = D*z + 4 (where z is some integer)
Comparing these two equations, we can see that:
D*(x+y) + 32 = D*z + 4
Solving for D, we get:
D = (32 - 4) / (z - x - y)
Since D must be an integer, the only possible values from the options given that satisfy this equation are 28 and 8.
However, since the remainders when A and B are divided by D are 11 and 21 respectively, D must be greater than 21.
Therefore, the only possible value for D is 28.
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