Aptitude - Numbers - Discussion
Discussion Forum : Numbers - General Questions (Q.No. 37)
37.
A 3-digit number 4a3 is added to another 3-digit number 984 to give a 4-digit number 13b7, which is divisible by 11. Then, (a + b) = ?
Answer: Option
Explanation:
4 a 3 | 9 8 4 } ==> a + 8 = b ==> b - a = 8 13 b 7 |
Also, 13 b7 is divisible by 11 
(7 + 3) - (b + 1) = (9 - b)
(9 - b) = 0
b = 9
(b = 9 and a = 1) (a + b) = 10.
Discussion:
35 comments Page 2 of 4.
Uma said:
1 decade ago
Here they give two numbers 4a3 and 983.
And they said when they are added together, we get 13b7.
It means.
4 a 3.
9 8 4.
------
13 b 7.
--------
When we observe this.
If 3+4=7.
4+9=13 then a = 0 or 1.
We get b = 8 or 9.
And also they said that 13 b 7 is divisible by 11.
If we take b = 9 i.e.,
1397 it is divisible by 11.
So b = 9, a = 1.
Now a+b = 9+1 = 10.
And they said when they are added together, we get 13b7.
It means.
4 a 3.
9 8 4.
------
13 b 7.
--------
When we observe this.
If 3+4=7.
4+9=13 then a = 0 or 1.
We get b = 8 or 9.
And also they said that 13 b 7 is divisible by 11.
If we take b = 9 i.e.,
1397 it is divisible by 11.
So b = 9, a = 1.
Now a+b = 9+1 = 10.
(2)
Senthil kumar said:
1 decade ago
Here a=1 is how declared please explain I can't understand?
(1)
Biplab Kumar Halder said:
1 decade ago
If b = 9 then,
4 a 3
9 8 4
-------
13 b 7
(4+9 = 13)(a+8 = 9)(3+4 = 7).
Let see, a+8 = 9.
> a = 9-8.
> a = 1.
4 a 3
9 8 4
-------
13 b 7
(4+9 = 13)(a+8 = 9)(3+4 = 7).
Let see, a+8 = 9.
> a = 9-8.
> a = 1.
Anil sarode said:
1 decade ago
Just use the concept of divisibility of 11 and get the answer.
As number is 13b7 is divisible by 11 the difference of alternate digit must be zero or 11, so 1+b = 3+7 or (1+b) - (3+7) = 0. So you got b = 9.
A+8 = b, a+8 = 9 so a = 1, hence a+b = 10.
As number is 13b7 is divisible by 11 the difference of alternate digit must be zero or 11, so 1+b = 3+7 or (1+b) - (3+7) = 0. So you got b = 9.
A+8 = b, a+8 = 9 so a = 1, hence a+b = 10.
Mukesh kumar said:
1 decade ago
By divisibility rule of 11, we know that it's the difference between sum of number at odd places and sum of no. at even places must be zero or divisible by 11.
Hence we have,
7+3-(b+1), if we put 9 in place of b we get zero hence the condition is satisfied and the no. Is divisible by 11.
So the no. is 1397.
Now subtract 984 from 1397, we get 1397-984 = 413.
Hence a=1 and b=9.
And a+b = 10.
Hence we have,
7+3-(b+1), if we put 9 in place of b we get zero hence the condition is satisfied and the no. Is divisible by 11.
So the no. is 1397.
Now subtract 984 from 1397, we get 1397-984 = 413.
Hence a=1 and b=9.
And a+b = 10.
Raja said:
1 decade ago
Any one please explain the logic.
(1)
Aishu said:
1 decade ago
Luckily in this prob, no formula/logic is required.
4+3=7.
8+a=b.
9+4=13.
Since 9+4 = 13 which means there was no carry from previous.
A carry will happen only if 8+ a >= 10.
i.e a = or > 2.
So a has to be 1!
When a is 1.8+1 = 9!
a=1.
b=9.
4+3=7.
8+a=b.
9+4=13.
Since 9+4 = 13 which means there was no carry from previous.
A carry will happen only if 8+ a >= 10.
i.e a = or > 2.
So a has to be 1!
When a is 1.8+1 = 9!
a=1.
b=9.
Yash said:
1 decade ago
Nice explanation dudes.
Samyuktha said:
1 decade ago
4 a 3
+9 8 4
----------
1 3 b 7
----------
If any any number added to 8 which is greater than 2 or equals to 2 gives a carry so choose the number in place of a which is less than 2.
8+a = 8+1 = 9 which doesn't give a carry so a=1.
4 1 3
+9 8 4
---------
1 3 9 7 -----> which is divisible by 11.
-----------
a=1, b=9.
a+b=1+9=10.
+9 8 4
----------
1 3 b 7
----------
If any any number added to 8 which is greater than 2 or equals to 2 gives a carry so choose the number in place of a which is less than 2.
8+a = 8+1 = 9 which doesn't give a carry so a=1.
4 1 3
+9 8 4
---------
1 3 9 7 -----> which is divisible by 11.
-----------
a=1, b=9.
a+b=1+9=10.
M.devi said:
1 decade ago
I couldn't understand this problem please say it in another method.
(1)
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