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A number when divided by a divisor leaves a remainder of 24. [#permalink]
 07 Apr 2007, 23:45
Question Stats:
75% (03:02) correct
25% (02:57) wrong based on 4 sessions
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) 13
B) 59
C) 35
D) 37
E) 12
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?
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Director
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I am sorry, but described steps have mistakes in it.
My quick way of solving this would be:
1) a= d+24
2) 2a=kd+11
3) multiply step 1 by 2 and subtruct 1 from 2
4) 0=d(k-2)-37
5) because 37 is prime number, eq would make sense if k=3, hence answer would be 37 (D)
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Director
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botirvoy wrote: I am sorry, but described steps have mistakes in it.
My quick way of solving this would be:
1) a= d+24
2) 2a=kd+11
3) multiply step 1 by 2 and subtruct 1 from 2
4) 0=d(k-2)-37
5) because 37 is prime number, eq would make sense if k=3, hence answer would be 37 (D)
Hi, Thanks. I know. Hence the answer. Will you let me know what mistakes you found.
Also, how does a = d+24 when the prob says "a number when divided by a divisor leaves a remainder of 24"? Is this some sort of shortcut?
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Re: Remainder fun!! [#permalink]
08 Apr 2007, 11:54
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) 13
B) 59
C) 35
D) 37
E) 12
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?
See since remainder is 24 therefore the divisor D is > 24. Now by given info we have
N = (D x k) + 24
When 2N is divided by D the remainder will be 24 x 2 = 48 but since it is 11 this means that D = 48 - 11 = 37
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Manager
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make x/y=z+24
and 2x/y=z+11
so it equals 37
D
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Director
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andrehaui wrote: make x/y=z+24
D
strictly speaking, x/y =z+24 is not correct (it implies x=zy+z24, which is not what we want to do), as garr was trying to do as well.
Garr, when I wrote a=d+24, it is of the form a=dk+r, where I really considered when k=1
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Senior Manager
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Re: Remainder fun!! [#permalink]
09 Apr 2007, 18:35
techjanson wrote: 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) 13
B) 59
C) 35
D) 37
E) 12
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? See since remainder is 24 therefore the divisor D is > 24. Now by given info we have N = (D x k) + 24 When 2N is divided by D the remainder will be 24 x 2 = 48 but since it is 11 this means that D = 48 - 11 = 37 Wow...
I solved it similarly to how botirvoy solved it but your explanation is quite intuitive.
Thanks! 
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Re: Remainder fun!! [#permalink]
09 Apr 2007, 19:31
ricokevin wrote: techjanson wrote: 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) 13
B) 59
C) 35
D) 37
E) 12
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? See since remainder is 24 therefore the divisor D is > 24. Now by given info we have N = (D x k) + 24 When 2N is divided by D the remainder will be 24 x 2 = 48 but since it is 11 this means that D = 48 - 11 = 37 Wow... I solved it similarly to how botirvoy solved it but your explanation is quite intuitive. Thanks! :-D glad you liked it ricokevin :)
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Intern
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how abt we solve it this way :-
Since the x%y = 24 and 2x%y = 11 we can eliminate AE
since the divisor has to be greater than 24.
also it means 48%y = 11. Hence the answer is 37.
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Director
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Let the number is N, the divisor = D,
I will make the two equations-
N = xD+24
2N = yD+11
where x and y are integers
Solving them: D(y-2x) = 37
as D is also integer and 37 is a prime number, the D should be 37 to satisfy the above equation.
Hence answer is 'D'
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Re: A number when divided by a divisor leaves a remainder of 24. [#permalink]
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]
03 Feb 2013, 16:44
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