# 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 ?
339
349
369
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 1 of 5.

Souriddha Sen said:   4 days ago
@All.

According to me, "The least value of p for which. " ---the question didn't ask for the least value that satisfies the conditions. The question implies a unique number: "What is THE number?", not "What might be one such number/what is the smallest such number?".

Since the conditions given does not have a unique solution, "Data inadequate" should be the correct answer.

Kasala ravichandra said:   1 year ago
if x = 13a - 11.
13a = x-11.
a = x-11/13
The ans a)339 sub in x place.

a = 339-11/13 = 25.2=> Not divisible by 13.
...take ans b)349 sub x place
a=349-11/13=26
So, 349 is completely divisible by 13 then the option B is the correct answer.
(5)

Nilesh said:   1 year ago
(1)

Jashpawar said:   2 years ago
p=26?

How explain.

Kritesh Kumar said:   2 years ago
9 and 26 are the no's From which if we use it in an equation it will be divisible by 17.

So In this case, we can also use 9 as it is the least one, so 128 could be the answer, but there is no option for 128 that's why they have taken 26 as the least one and obtained the answer as 349.

Correct me if I am wrong.
(1)

CHETHAN said:   3 years ago
How P = 26?

Pleas explain.
(1)

Surya said:   3 years ago
How can we get p value? Please explain.

Sudhanshu said:   3 years ago
Here is a simpler way for all of you.

Let no. be N, then;

N = 13a+11. > N-11 =13a (eq. 1).
N = 17b+9. > N-9 =17b (eq. 2).

Thus eq 1 and 2 suggest that N-11 should be divisible by 13 and N-9 should be divisible by 17.
N=349 satisfies both conditions!
(7)

Satya said:   3 years ago
13p + 11 = 17q + 9.

q = (2 + 13p)/17.

To find the least value of p for which q = (2 + 13p)/17 is a whole number; The divisor must completely divide the dividend.

( i.e. denominator must completely divide the numerator.)

So the possible dividends are 170, 340, 510, ....

With Dividend 170,
(2 + 13p) = 170------------> p = 12.9..... , i.e. a fraction.

With dividend 340,
(2 + 13p) = 340 ------------> p = 26 i.e. a whole number.
(1)

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.