Consider the number N=21P53Q4
Number of ordered pairs (P, Q) so that the number ‘N' is divisible by 44, is
(A) 2 (B) 3 (C) 4 (D) 5
Answers
Step-by-step explanation:
For a number to be divisible by 44, it has to be divisible by 4 and 11.
So for a number to be divisible by 4, it has to end with 04, 24, 44, 64, 84, etc.(q= 0,2,4,6,8)
To be divisible by 11, sum of odd digits- sum of even digits should be a whole multiple of 11( like 0,11,22,etc.)
If q=0,
Odd digits sum= 2+P+3+4= 9+P
Even digits sum= 1+5+0=6
To be divisible by 11:
Difference= 9+P-6 should be divisible by 11.
Which is possible for P= 8 (difference=11)
If q= 2,
Odd digits sum= 9+P
Even digits sum= 1+5+2= 8
Difference= 9+P-8 should be divisible by 11.
Which is not possible as P cannot be 10, a 2 digit number.
If q=4,
Odd digits sum= 9+P
Even digits sum= 1+5+4= 10
Difference= 9+P-10
Which is possible for P= 1 (difference=0)
If q=6,
Odd digits sum= 9+P
Even digits sum= 1+5+6= 12
Difference= 9+P-12 should be divisible by 11.
Which is possible for P= 3 (difference=0)
If q=8,
Odd digits sum= 9+P
Even digits sum= 1+5+8= 14
Difference= 9+P-14 should be divisible by 11.
Which is possible for P= 5 (difference=0)
Hence the pairs for (P,Q) are as follows:
(8,0);(1,4);(3,6);(5,8)
Thanks!!
Answer:
(B) 3 is the write answered