Select the correct answerA number when divided by a divisor left reminder 23. When twice of the number was divided by the same divisor, reminder was 11. what is the divisor?Options235122534

Let's solve this step by step:

1. Let's denote the number as 'a' and the divisor as 'd'. According to the problem, when 'a' is divided by 'd', the remainder is 23. We can write this as: a = kd + 23, where 'k' is the quotient.

2. The problem also states that when twice the number (2a) is divided by the same divisor 'd', the remainder is 11. We can write this as: 2a = ld + 11, where 'l' is the new quotient.

3. We can substitute the value of 'a' from the first equation into the second equation: 2(kd + 23) = ld + 11.

4. Simplifying this gives: 2kd + 46 = ld + 11.

5. Rearranging terms gives: ld - 2kd = 46 - 11.

6. Simplifying further gives: d(l - 2k) = 35.

7. Since 'd', 'l', and 'k' are all integers (because they represent a divisor and quotients), the only possible value for 'd' that satisfies this equation given the options is 35.

So, the divisor is 35.

Let's denote the number as 'a' and the divisor as 'd'.

From the problem, we know that:

1. a = kd + 23 (where k is some integer)

2. 2a = ld + 11 (where l is some integer)

Substituting the first equation into the second, we get:

2(kd + 23) = ld + 11 2kd + 46 = ld + 11 2kd - ld = 11 - 46 (d)(2k - l) = -35

Since d must be a positive integer (you can't divide by a negative number or zero), and we know that (2k - l) is also an integer, the only way for the product to be -35 is if d = 35 and (2k - l) = -1.

Therefore, the divisor is 35.