Aptitude - Numbers - Discussion
Discussion Forum : Numbers - General Questions (Q.No. 61)
61.
When a number is divided by 13, the remainder is 11. When the same number is divided by 17, then remainder is 9. What is the number ?
Answer: Option
Explanation:
x = 13p + 11 and x = 17q + 9
13p + 11 = 17q + 9
17q - 13p = 2
| q = |
2 + 13p |
| 17 |
| The least value of p for which q = | 2 + 13p | is a whole number is p = 26 |
| 17 |
x = (13 x 26 + 11)
= (338 + 11)
= 349
Discussion:
47 comments Page 3 of 5.
Pragati said:
5 years ago
P=9 also works and answer=128.
Suchismita said:
5 years ago
Please explain, how we get p=26?
Madhu said:
5 years ago
Let X be the number which we have to find.
From given data we make two equations.
13k+11=X ---> (1)
17m+9 =X ---> (2)
From eq (1).
i.e.
13k+11 = X.
Adding 2 on both sides to make 11 as 13.
13k+11+2=X+2,
13k+13=X+2,
13(k+1)=X+2,
k+1=(X+2)/13,
From the options, X=349 is the only option is exactly dividable by 13.
Like vice eq(2).
Add 8 on both sides to 17.
At last, we get:
m+1=(X+8)/17.
So, X=349 is exactly dividable by 17.
From given data we make two equations.
13k+11=X ---> (1)
17m+9 =X ---> (2)
From eq (1).
i.e.
13k+11 = X.
Adding 2 on both sides to make 11 as 13.
13k+11+2=X+2,
13k+13=X+2,
13(k+1)=X+2,
k+1=(X+2)/13,
From the options, X=349 is the only option is exactly dividable by 13.
Like vice eq(2).
Add 8 on both sides to 17.
At last, we get:
m+1=(X+8)/17.
So, X=349 is exactly dividable by 17.
Jashpawar said:
3 years ago
p=26?
How explain.
How explain.
Pratikshya said:
1 decade ago
I am not able to understand why p is taken as 26? please help me.
Jainendra said:
1 decade ago
Please explain I couldn't understand how he get maximum value.
Anup gupta said:
1 decade ago
Why we consider only minimum ?
Narendra said:
1 decade ago
Explain the reason or any guessing that we can take. If I take here p=9 it also works.
Naveenkumar said:
1 decade ago
Here we have to use options 339=13p+11, p is not a whole number, like that we have to use options, at 349=13p+11, p is whole number.
Raman said:
1 decade ago
So simple 339/13 remainder is 1
349/13 remainder is 11 & same when we divide by 349/17 remainder is 9
So answer is B
349/13 remainder is 11 & same when we divide by 349/17 remainder is 9
So answer is B
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