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 ?
Answer: Option
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:
23 comments Page 1 of 3.
Arpit saxena said:
4 years 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.
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.
(1)
Nirmala said:
1 decade ago
Given conditions are
(1) x,y are positive integers and
(2) 3x+7y is multiple of 11.
So we can choose some integers
Lets take, x=2 & y=3 then 3*2+7*3=6+21=27,
27 is not multiple of 11,
These integers can also satisfy (2) condition.
Because we have to choose x=5,y=1 then 3*5+7*1=15+7=22,
22 is multiple of 11.
Like this only we have to choose.
(1) x,y are positive integers and
(2) 3x+7y is multiple of 11.
So we can choose some integers
Lets take, x=2 & y=3 then 3*2+7*3=6+21=27,
27 is not multiple of 11,
These integers can also satisfy (2) condition.
Because we have to choose x=5,y=1 then 3*5+7*1=15+7=22,
22 is multiple of 11.
Like this only we have to choose.
Krishna Thakur said:
4 years 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.
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.
(1)
Fourie said:
9 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.
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.
ASWIN UNNIKRISHNAN said:
6 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.
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.
Ravi said:
8 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.
Akshay jagtap said:
5 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.
Angel said:
5 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?
Narendra said:
1 decade ago
Exactly answer may be B. It will be also possible 3 and 4 by hit and trial case. As how at a time we analyze it's 5 and 1.
Puneet said:
1 decade ago
x=4 and y=3 gives 3x+7y= 12+21 = 33 divisible by 11.
From these values, x+y+4 = 4+3+4 = 11 again divisible by 11.
From these values, x+y+4 = 4+3+4 = 11 again divisible by 11.
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