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 2 of 4.
Deepak M said:
8 years ago
Thanks @Monica.
(1)
FEuR!aN [- _ -] said:
1 decade ago
Thanks manideep.
(1)
Anvesh said:
9 years ago
@Manjeet Singh.
It's given that first, he divided by 5.
Means 5q + 4 = d.
Now it's no more d,
He divided q by 9 and so on.
Means 9x + 8 = q.
Now read the question, you will get it.
Thank you.
It's given that first, he divided by 5.
Means 5q + 4 = d.
Now it's no more d,
He divided q by 9 and so on.
Means 9x + 8 = q.
Now read the question, you will get it.
Thank you.
(1)
Om pandey said:
9 years ago
First thing to keep in mind is, the number is divided SUCCESSIVELY by 5, 9, 13.
Thus N = 5a + 4 or 5a - 1.
a = 9b + 8 or 9b - 1.
b = 13c + 12 or 13 - 1.
So the remainder in each case is 1. LCM of 5, 9, 13 is 585 so the remainder will be same (its a theorem) if divide by the LCM.
Therefore N = 585d - 1 rem= 584.
Thus N = 5a + 4 or 5a - 1.
a = 9b + 8 or 9b - 1.
b = 13c + 12 or 13 - 1.
So the remainder in each case is 1. LCM of 5, 9, 13 is 585 so the remainder will be same (its a theorem) if divide by the LCM.
Therefore N = 585d - 1 rem= 584.
(1)
Ramesh said:
9 years ago
Hello, all.
What is the reverse substitution?
What is the reverse substitution?
(1)
Anujan said:
9 years ago
Thank you very much @Manideep.
(1)
Nikhil said:
1 decade ago
thnx arti
(1)
Kalkesh said:
1 decade ago
Please any one explain me in easy way.
(1)
Pabitra said:
6 years ago
Anyone, please explain this for me.
(1)
Mohit said:
5 years ago
Thanks @Arati.
(1)
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