Math, asked by ayushsrivas55, 8 months ago

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

Answered by llɱissMaɠiciaŋll
6

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!!

Answered by rajak845304
0

Answer:

(B) 3 is the write answered

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