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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  [#permalink]

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New post 09 Mar 2016, 13:36
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A
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  95% (hard)

Question Stats:

23% (02:19) correct 77% (02:34) wrong based on 249 sessions

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Re: When a positive integer 'x' is divided by a divisor 'd', the remainder  [#permalink]

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New post 04 Nov 2016, 05:37
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Bunuel wrote:
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.


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
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When a positive integer 'x' is divided by a divisor 'd', the remainder  [#permalink]

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New post 09 Mar 2016, 23:10
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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
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Re: When a positive integer 'x' is divided by a divisor 'd', the remainder  [#permalink]

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New post 02 Nov 2016, 23:29
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Re: When a positive integer 'x' is divided by a divisor 'd', the remainder  [#permalink]

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New post 15 Feb 2019, 05:01
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
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Re: When a positive integer 'x' is divided by a divisor 'd', the remainder  [#permalink]

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New post 24 Apr 2019, 16:21
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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Re: When a positive integer 'x' is divided by a divisor 'd', the remainder  [#permalink]

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New post 28 Aug 2019, 00:43
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.
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Re: When a positive integer 'x' is divided by a divisor 'd', the remainder   [#permalink] 28 Aug 2019, 00:43
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