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.
Vishnu said:
7 years ago
Thanks for the answer @Ankit Kumar.
Supriya karri said:
7 years ago
Nice explanation, Well said @Monica.
Ankit kumar yadav said:
7 years ago
Hello everyone.
Find reminder this type problem use formula ( 1st reminder + 2nd reminder * 1st factor + 3rd reminder * 1st factor * 2nd factor ) then divided by given number.
Here, ( 4+8*5+12*5*9) /585 = 584/585 = 584 Ans because we know if ( a/a+1 ) then reminder always = a.
Find reminder this type problem use formula ( 1st reminder + 2nd reminder * 1st factor + 3rd reminder * 1st factor * 2nd factor ) then divided by given number.
Here, ( 4+8*5+12*5*9) /585 = 584/585 = 584 Ans because we know if ( a/a+1 ) then reminder always = a.
(3)
Deepak M said:
8 years ago
Thanks @Monica.
(1)
Monica said:
8 years ago
@All.
Successive division means, if a number X is successively divided by say p and q, then first X is divided by p and then the quotient obtained when X is divided by p is then divided by q.
Here let X be the number, since it is successively divided by 5, 9 and 13. We obtain.
X=5q1+4------- (1) (4 is remainder) and then q1 is divided by 9 then.
Q1=9q2+8------- (2) (given 8 is remainder) then.
Q2=13q3+12------ (3) (given 12 is remainder).
Substituting q2 in eq2, we get q1=117q3+116.
Then substituting q1 in equation 1 we get.
X=585q3+584.
Hence 584 is the remainder.
Hope it helps everyone.
Successive division means, if a number X is successively divided by say p and q, then first X is divided by p and then the quotient obtained when X is divided by p is then divided by q.
Here let X be the number, since it is successively divided by 5, 9 and 13. We obtain.
X=5q1+4------- (1) (4 is remainder) and then q1 is divided by 9 then.
Q1=9q2+8------- (2) (given 8 is remainder) then.
Q2=13q3+12------ (3) (given 12 is remainder).
Substituting q2 in eq2, we get q1=117q3+116.
Then substituting q1 in equation 1 we get.
X=585q3+584.
Hence 584 is the remainder.
Hope it helps everyone.
(3)
Jael Jefina J said:
8 years ago
There is a shortcut to solve this problem.
If a number (say X), when divided by d1, d2, d3 (either successively or independently) leaves remainders r1, r2, r3 and if (d1 - r1) = (d2 - r2) = (d3 - r3) = k.
then,
X = L.C.M (d1, d2, d3) - k.
From the question.
(d1,d2,d3) = (5,9,13),
(r1,r2,r3) = (4,8,12).
k = 1.
X = L.C.M(5,9,13)-1 = 585-1 = 584.
(584%585) = 584 (i.e. the remainder).
If a number (say X), when divided by d1, d2, d3 (either successively or independently) leaves remainders r1, r2, r3 and if (d1 - r1) = (d2 - r2) = (d3 - r3) = k.
then,
X = L.C.M (d1, d2, d3) - k.
From the question.
(d1,d2,d3) = (5,9,13),
(r1,r2,r3) = (4,8,12).
k = 1.
X = L.C.M(5,9,13)-1 = 585-1 = 584.
(584%585) = 584 (i.e. the remainder).
(3)
Vijay mittal said:
9 years ago
@Anvesh
How can you suppose like this way?
There is no explanation about d that it is no more and in next term q is used.
How can you suppose like this way?
There is no explanation about d that it is no more and in next term q is used.
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)
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