Aptitude - Numbers - Discussion
Discussion Forum : Numbers - General Questions (Q.No. 46)
46.
In dividing a number by 585, a student employed the method of short division. He divided the number successively by 5, 9 and 13 (factors 585) and got the remainders 4, 8, 12 respectively. If he had divided the number by 585, the remainder would have been
Answer: Option
Explanation:
5 | x z = 13 x 1 + 12 = 25
--------------
9 | y - 4 y = 9 x z + 8 = 9 x 25 + 8 = 233
--------------
13| z - 8 x = 5 x y + 4 = 5 x 233 + 4 = 1169
--------------
| 1 -12
585) 1169 (1
585
---
584
---
Therefore, on dividing the number by 585, remainder = 584.
Discussion:
39 comments Page 4 of 4.
Suneetha said:
1 decade ago
@Dharamveer.
Divided the number successively by 5, 9 and 13 (factors 585) and got the remainders 4, 8, 12 respectively.
Dividers are 5, 9, 13.
Remainders are 4, 8, 12.
k = divider-remainder = 5-4 = 9-8 = 13-12 = 1.
Divided the number successively by 5, 9 and 13 (factors 585) and got the remainders 4, 8, 12 respectively.
Dividers are 5, 9, 13.
Remainders are 4, 8, 12.
k = divider-remainder = 5-4 = 9-8 = 13-12 = 1.
Dharamveer said:
1 decade ago
@Sudhir.
How can we say that the value of k=1.
How can we say that the value of k=1.
Sudhir said:
1 decade ago
On dividing a number by a,b,c if we get a-k, b-k nd c-k as remainder respectively then that number will be N*LCM of[a,b,c]-k.
therefore:
=N*[lcm of 5,9,13]-1
=N*[585]-1
=N*584
=584 here N=1
therefore:
=N*[lcm of 5,9,13]-1
=N*[585]-1
=N*584
=584 here N=1
Chandru said:
1 decade ago
Thanks Ms. Arthy.
FEuR!aN [- _ -] said:
1 decade ago
Thanks manideep.
(1)
Neelu said:
1 decade ago
Thanku arti. For helping to understand this problem in easy way.
(1)
Nikhil said:
1 decade ago
thnx arti
(1)
Manideep said:
1 decade ago
@ Arti
Let the number be x.
Now given x=5a+4, a=9b+8, b=13c+12...
By reverse substitution you get
a = 9(13c + 12) + 8 = (13*9)c + 116
x = 5[(13 * 9)c + 116] + 4 = 585c + 584
So this when divided by 585 you get 584 as reminder.
Thank you :)
Let the number be x.
Now given x=5a+4, a=9b+8, b=13c+12...
By reverse substitution you get
a = 9(13c + 12) + 8 = (13*9)c + 116
x = 5[(13 * 9)c + 116] + 4 = 585c + 584
So this when divided by 585 you get 584 as reminder.
Thank you :)
(3)
Arti said:
1 decade ago
Hi, can any one please explain it I'm not able to understand how's these equation are working. Sorry but Im not able to understand. : (.
(1)
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