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 2 of 3.
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.
Techno said:
8 years ago
What a joke, keep hitting during the exams.
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.
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.
Kapil said:
1 decade ago
True B option is also right if we put x=4 and y=3.
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.
Vviswanath reddy said:
1 decade ago
Please explain this method?
Pratul said:
1 decade ago
If x=4 and y=3 then also condition is satisfied and answer is B.
Abdulla said:
1 decade ago
Lets x=4 y=3 then 3x+7y= 33 which is multiple of 11 as well. In this case the ans should be b.
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.
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