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Math Expert V
Joined: 02 Sep 2009
Posts: 58434
When a positive integer 'x' is divided by a divisor 'd', the remainder  [#permalink]

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Difficulty:   95% (hard)

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

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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.

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Math Expert V
Joined: 02 Aug 2009
Posts: 7987
Re: When a positive integer 'x' is divided by a divisor 'd', the remainder  [#permalink]

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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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Schools: ISB '19
When a positive integer 'x' is divided by a divisor 'd', the remainder  [#permalink]

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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.
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Current Student D
Joined: 12 Aug 2015
Posts: 2567
Schools: Boston U '20 (M)
GRE 1: Q169 V154 Re: When a positive integer 'x' is divided by a divisor 'd', the remainder  [#permalink]

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Hi chetan2u can you help me with this one.

CC- Abhishek007
Regards
Stone Cold
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Intern  B
Joined: 21 Aug 2018
Posts: 1
Re: When a positive integer 'x' is divided by a divisor 'd', the remainder  [#permalink]

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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
Manager  B
Joined: 20 Apr 2019
Posts: 74
Re: When a positive integer 'x' is divided by a divisor 'd', the remainder  [#permalink]

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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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Intern  B
Joined: 25 Aug 2019
Posts: 4
GMAT 1: 730 Q50 V38 Re: When a positive integer 'x' is divided by a divisor 'd', the remainder  [#permalink]

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