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Starting with what's already been discussed, we have N = D(Q1) + 24 2N = D(Q2) + 11

We multiply the first equation by 2 and get 2N = 2D(Q1) + 48 2N = D(Q2) + 11

Subtracting, we get 0 = D(2Q1 - Q2) + 37 Which implies D(2Q1 - Q2) = -37.

Since 37 is prime, D is either 1 or 37. If D were 1, the remainder would always be zero, so it must be 37. (It helps to keep in mind that Q1 and Q2 are both integers). This is a somewhat complex approach, and using your answers is a more efficient method here.

Re: A number when divided by a divisor leaves a remainder of 24. [#permalink]

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31 Jul 2013, 12:33

Easy one from my side:

2N = DB + 11 - (1) N=DA + 24 - (2)

Multiplying Eq (2) by 2 and thereby subtracting both the equations:

2N = DB + 11 2N = 2DA + 48

0=DB - 2DA - 37

=> D (B-2A) = 37

=> D = (37)/(B-2A)

Since 37 is prime and (B-2A) would always be an integer

Hence (D)

Rgds, TGC !
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Re: A number when divided by a divisor leaves a remainder of 24. [#permalink]

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16 Oct 2013, 13:23

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Starting with what's already been discussed, we have N = D(Q1) + 24 2N = D(Q2) + 11

We multiply the first equation by 2 and get 2N = 2D(Q1) + 48 2N = D(Q2) + 11

Subtracting, we get 0 = D(2Q1 - Q2) + 37 Which implies D(2Q1 - Q2) = -37.

Since 37 is prime, D is either 1 or 37. If D were 1, the remainder would always be zero, so it must be 37. (It helps to keep in mind that Q1 and Q2 are both integers). This is a somewhat complex approach, and using your answers is a more efficient method here.

Re: A number when divided by a divisor leaves a remainder of 24. [#permalink]

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12 Nov 2014, 20:08

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A number when divided by a divisor leaves a remainder of 24. [#permalink]

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23 Jan 2016, 10:12

Hello from the GMAT Club BumpBot!

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Re: A number when divided by a divisor leaves a remainder of 24. [#permalink]

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10 Aug 2017, 04:18

ggarr wrote:

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?

A) 12 B) 13 C) 35 D) 37 E) 59

I'm already familiar with the textbook method. I'm trying to discover what's wrong with the below method.

A number when divided by a divisor leaves a remainder of 24. [#permalink]

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20 Aug 2017, 06:00

Let the no be N, q quotient and divisor be D N=Dq+24 N can be =24(q can be 0, 1, 2....) 2N=48 48=Dq+11 Plugin nos from answer choice always start from the middle one. Let divisor be 35 than 48/35 remainder is 13, which is 2 more than 11 plugin 37 48/37=11 Answer