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by shashank.ism » Tue Feb 09, 2010 12:52 pm
Find the total number of integral solutions of the equation (407)x – (ddd)y = 2589, where ‘ddd’ is a three-digit number.

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by komal » Wed Feb 17, 2010 3:59 am
shashank.ism wrote:Find the total number of integral solutions of the equation (407)x – (ddd)y = 2589, where ‘ddd’ is a three-digit number.

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Note that an equation ax + by = c or ax – by = c cannot have
an integral solution if the highest common factor of ‘a’ and ‘b’
does not divide ‘c’.
Here, 407 = 37 × 11 and ‘ddd’ = d × 37 × 3.
Now, in this case 37 being the highest common factor does
not divide 2589.
Hence, the number of integral solutions of the given equation
is 0.
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by ajith » Wed Feb 17, 2010 4:22 am
shashank.ism wrote:Find the total number of integral solutions of the equation (407)x – (ddd)y = 2589, where ‘ddd’ is a three-digit number.

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3
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Another thread for same question by Shashank again:

https://www.beatthegmat.com/integral-sol ... 52078.html

Please refrain from posting the same question a number of times.
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by harsh.champ » Thu Feb 18, 2010 2:36 am
komal wrote:
shashank.ism wrote:Find the total number of integral solutions of the equation (407)x – (ddd)y = 2589, where ‘ddd’ is a three-digit number.

0
3
2
1
4
Note that an equation ax + by = c or ax – by = c cannot have
an integral solution if the highest common factor of ‘a’ and ‘b’
does not divide ‘c’.
Here, 407 = 37 × 11 and ‘ddd’ = d × 37 × 3.
Now, in this case 37 being the highest common factor does
not divide 2589.
Hence, the number of integral solutions of the given equation
is 0.
Wow,you sure know a lot of rules:-
Note that an equation ax + by = c or ax – by = c cannot have
an integral solution if the highest common factor of ‘a’ and ‘b’
does not divide ‘c’.
But the main problem is it is very difficult to memorize so many of the rules.Isn't there some technique by which I can solve the question without remembering any of the rules?

Note:-Even one mistake in memorizing can lead to getting an easy question wrong.
It takes time and effort to explain, so if my comment helped you please press Thanks button :)



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by harsh.champ » Thu Feb 18, 2010 2:40 am
ajith wrote:
shashank.ism wrote:Find the total number of integral solutions of the equation (407)x – (ddd)y = 2589, where ‘ddd’ is a three-digit number.

0
3
2
1
4
Another thread for same question by Shashank again:

https://www.beatthegmat.com/integral-sol ... 52078.html

Please refrain from posting the same question a number of times.
Hey ajith ,
I saw the post [https://www.beatthegmat.com/integral-sol ... 52078.html]you had mentioned above and saw ur soln. approach.
so x should be a mutiple of 3 -> 3 and 6 are not possible since(407)x will be less than 2589
x=9
(ddd) y = 1074
I didn't get this part as to how x should always be a multiple of 3 and hence 3 & 6 are not possible.
It's getting a bit confusing over here.
Can you explain the soln. in a detailed manner?Thanks in advance.
It takes time and effort to explain, so if my comment helped you please press Thanks button :)



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