# Aptitude - Numbers - Discussion

Discussion Forum : Numbers - General Questions (Q.No. 97)
97.
If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the following will be divisible by 11 ?
4x + 6y
x + y + 4
9x + 4y
4x - 9y
Explanation:

By hit and trial, we put x = 5 and y = 1 so that (3x + 7y) = (3 x 5 + 7 x 1) = 22, which is divisible by 11. (4x + 6y) = ( 4 x 5 + 6 x 1) = 26, which is not divisible by 11;

(x + y + 4 ) = (5 + 1 + 4) = 10, which is not divisible by 11;

(9x + 4y) = (9 x 5 + 4 x 1) = 49, which is not divisible by 11;

(4x - 9y) = (4 x 5 - 9 x 1) = 11, which is divisible by 11.

Discussion:
19 comments Page 1 of 2.

Arpit saxena said:   1 year ago
We know that the numbers divisible/multiple by 11s are 11, 22, 33, 44, 55.

So on.

Except for the number 11 which can not be made by using the expression (3x+7y) so we find the other numbers which are least and divisible by 11. Which number could be 22.

So we find the numbers that make 22 which are x=5, y=1. After putting these values in expression we can find 22.

Similarly;

These values can determine which given expression is divisible by 11.

Krishna Thakur said:   1 year ago
@Aall.

If we put x =11 and y =11 then the equation will be;

3*11+7*11= 110, which is also a multiple of 11. And after applying these values to option (a) 4x + 6y this option is also correct.

4*11+6*11 = 110, which is also divisible by 11.

Please correct me, If I am wrong.

Prakash said:   2 years ago
As x=4 and y=3 is required.
So, x + y + 4 is correct answer.

Prakash said:   2 years ago
As x=4 and y=3 is required. So, x+y+4 is the correct answer.

Angel said:   2 years ago
But if I take x as 3 and why as 7 it does satisfy the condition of being divisible by 11 and the correct option is A right?

Akshay jagtap said:   3 years ago
I think the answer is D. Option B only satisfies the condition of X=4 and Y=3 but option D satisfies all conditions like X=5 and Y = 1.

ASWIN UNNIKRISHNAN said:   3 years ago
3x+7y =11 k.

y = (11k -3x)/7.

Put in options:

D) 4x-9y.

Then 4x - 9 (11k-3x)/7.
4x-(99k-27x)/7.
(28x-99k+27x) /7.
(55x+99k)/7.
then 11* (5x+9k)/7.

Because it is divisible by 11.

Techno said:   5 years ago
What a joke, keep hitting during the exams.

Ravi said:   6 years ago
Maybe we have to choose the least multiple of 11 while examining with the hit and trial method therefore the values for x & why will be 5 & 1 respectively and not 3&4.

Fourie said:   6 years ago
3x +7y = 11 m.
7(x + y) = 11 m + 4x.

7) 999 (14
7
----------------
29
28
--------------
19
14
-----------------
5
=> 999 - 5 = 994 = 11 m + 4x = 7(x + y).
So, x = 221 and y = - 79.

Now check, you will get it.