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A number when divided by a divisor leaves a remainder of 24.

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Re: divisibility and remainders [#permalink]

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New post 19 Jul 2011, 13:44
A more algebraic solution:

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.

BenchPrepGURU

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

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New post 03 Feb 2013, 16:44
u wrote a/d = x+24
which means a= dx +24d and not dx+24 = a

which is wrong because it changes the whole meaning of the formula dividend(a)= divisor(d)*quotient(x) +remainder(24)

the second mistake which u did was u took the same quotient (x) even when d dividend (a) changed to (2a).

M answering this question years later..but what to do..just saw it!
even i did the same mistakes at my first attempt..but corrected it myself

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

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New post 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)

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

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New post 16 Oct 2013, 13:23
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Re: divisibility and remainders [#permalink]

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New post 12 Nov 2013, 12:45
BenchPrepGURU wrote:
A more algebraic solution:

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.

BenchPrepGURU



What is r3? Would you please elaborate?

Thanks
Cheers!
J :)

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

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New post 12 Nov 2014, 20:08
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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New post 23 Jan 2016, 10:12
Hello from the GMAT Club BumpBot!

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What is the value of the divisor ??? [#permalink]

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New post 20 Apr 2016, 09:12
A number, p when divided by a divisor, q leaves a remainder, r of 24 and
2q mod p = 11 .
What is the value of the divisor, q?

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

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New post 20 Apr 2016, 09:16
adrs33 wrote:
A number, p when divided by a divisor, q leaves a remainder, r of 24 and
2q mod p = 11 .
What is the value of the divisor, q?


Merging topics. Please refer to the discussion on pages 1 and 2.

Also, please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html
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A number, p when divided by a divisor, q leaves a remainder [#permalink]

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New post 20 Apr 2016, 09:59
A number, p when divided by a divisor, q leaves a remainder, r of 24 and
2q mod p = 11 .
What is the value of the divisor, q?

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Re: A number, p when divided by a divisor, q leaves a remainder [#permalink]

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New post 20 Apr 2016, 10:03
adrs33 wrote:
A number, p when divided by a divisor, q leaves a remainder, r of 24 and
2q mod p = 11 .
What is the value of the divisor, q?

Your Q has already been merged earlier. Pl look for solution in that thread and do not post again
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Re: A number when divided by a divisor leaves a remainder of 24. [#permalink]

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New post 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.

(1) a/d = x+24 ----> dx+24 = a
(2) 2(a)/d = x+11 ----> 2(dx+24)/d = x+11 ----> 2dx+48/d = x+11
(3) dx+11 = 2dx+48 ----> -dx=37, dx=-37

I managed to produce the correct answer. Nonetheless, there is something wrong with this. Can/will anyone help?





My doubt is how are you assuming the quotient to be the same for both the equations? Can we get an expert opinion on this?

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

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New post 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

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A number when divided by a divisor leaves a remainder of 24.   [#permalink] 20 Aug 2017, 06:00

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