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

Question

When a positive integer 'x' is divided by a divisor 'd', the remainder is 24. What is d?

(1) When 2x is divided by d, the remainder is 23.
(2) When 3x is divided by d, the remainder is 22.

chetan2u · Accepted Answer

Hi  stonecold ,

The extra info from the statement is that d will be greater than 24...

Let's see the statements 
1) when 2x is divided by d, remainder is 23...
Remainder when 2x is divided by d, remainder will also be 2*24 as when x is div by d, remainder is 24...
But this is equal to 23, so d is 48-23 or 25...
Suff

2) similarly 3x div by d will give 3*24=72...
But it is 22, so d or multiple of d will be 72-22=50..
All factors of 50 but greater than 24 will also be answer..
So answer are 50 and 25
Insuff

Ans A

Hope it helps

vardhanindaram · Answer

The equations for the above question are
dQ1+ 24= X ...1
dQ2+ 23=2X ...2
dQ3+ 22=3X ...3
Substituting 1 in 2
d(Q2-2Q1)=25 ....4
Substituting 1 in 3
d(Q3- 3Q1)=50 ...5
Now as we know that the remainder is 24 when d divides some number x,this means d definitely has to be greater than 24.
Therefore d>24
From Eq4, d multiplied by some number gives 25,which means d<=25.But we know d>24.
Therefore d=25.
Now from Eq5, d<=50 and d>24 cannot give us the answer.
Therefore we can say answer can be found from first clue.
Answer A

stonecold · Answer

Hi  chetan2u  can you help me with this one.

CC-  Abhishek007 
Regards
Stone Cold

oleonw · Answer

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

JDF · Answer

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

Posted from my mobile device

anshsharma2k · Answer

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.

Manku · Answer

TarunKumar1234 · Answer

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.

bumpbot · Answer

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

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

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