When a positive integer 'x' is divided by a divisor 'd', the remainder

I solved it this way: Since remainder is 24, the divisor has to be >24.
Now any number can be written in the form N = DQ + R where D is divisor, Q is quotient and R is remainder.
Hence, We can write the equation x=dy+24 (where d is the divisor and y is the quotient) and from the 1st statement 2x=dz+23 (z is some other quotient > y).
Solving the 2 equations by eliminating x, we get d(z-2y)=25
Now d is > 24 and (z-2y) has to be an integer so there is only one solution that d =25 and z-2y =1. So it is sufficient.
But when we solve for the 2nd statement in the same way, we get d(z-3y)=50, now this can give 2 values of d i.e. d=25 when (z-3y)=2 and d=50 when (z-3y)=1. So it is insufficient.

When a positive integer 'x' is divided by a divisor 'd', the remainder is 24. What is d?
So, the equation is x = p*d +24, where p= integer and d >24.

Stat1: When 2x is divided by d, the remainder is 23.
Now, 2x = q*d +23, let's draw from given equation, 2x = 2*(p*d +24) = r*d + 48, where r= integer
Solving equations, (q-r)*d = 48-23 = 25, as d >24, so we can say, d = 25. Sufficient

Stat2: When 3x is divided by d, the remainder is 22.
Now, 3x = q*d +22, given equation, 3x = 3*(p*d +24) = m*d + 72, where m= integer
Solving equations, (q-m)*d = 72-22 = 50, as d >24, so we can say, d = 25 or 50. Not Sufficient

So, I think A.

Hi chetan2u can you help me with this one.

CC- Abhishek007
Regards
Stone Cold

Hi Guys,

I´m sorry to bother you, but I don´t quite get the existing 2 explanations for this problem.

Would anyone be able to try explaining it to me in a "Remainder for Dummies" kind-a way? :D

Maybe Bunuel or VeritasKarishma

Thanks so much!

Regards, oleonw

I’m with oleonw. I have no idea from the explanations why 1) is sufficient but 2) is not, it honestly makes no sense.

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