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A number when divided by a divisor leaves a remainder of $24$. When twice the original number is divided by the same divisor, the remainder is $11$. What is the value of the divisor?

1. $12$
2. $13$
3. $35$
4. $37$
5. $59$
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Lets say x is the number and divisor is k

We can write x= qk+24

2x=2(qk+24)=2qk+48=2qk+37+11

Since the remainder is 11 both 2qk and 37 must be divided by k. Note that since remainder was 24 earlier k>24. From options only 37 divided 37.
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