Question

IN-1234ab56a is divisible by 22, then possible number of order pair (a
, bj are equal to
LA 4
(B) 5
(C) 6
(D) 7​

Answer 1

Answer:

7

Explanation:

it is 7 ok please give me 5 pionts

Answer 2

The correct question: If N = 1234ab56a is divisible by 22, then the possible number of order pair (a, b) are equal to:

(A) 4

(B) 5

(C) 6

(D) 7​.

The correct answer is option (B). 5.

Given:

N = 1234ab56a.

It is given that N is divisible by 22.

To Find:

We have to find the possible number of order pair (a, b), if N = 1234ab56a is divisible by 22.

Solution:

Given that, N = 1234ab56a.

For a number to be divisible by 22, it has to be divisible by both 2 and 11.

A number is divisible by 2, if it has a 0, 2, 4, 6, or 8 in the ones place.

The number at ones place in N = a.

∴, Possible values of a = 0, 2, 4, 6, and 8.

A number is divisible by 11, if the sum of the digits in the odd places and the sum of the digits in the even places difference is a multiple of 11 or 0.

i.e., For N to be divisible by 11, the value of $(1 + 3 + a + 5 + a) - (2 + 4 + b + 6)$ must be equal to zero or multiple of 11.

$(1 + 3 + a + 5 + a) - (2 + 4 + b + 6)$

⇒ $(9 + 2a) - (12 + b)$

⇒ $2a - b - 3.$

Since the highest possible value of a is 8, we can consider only the following condition.

$2a - b - 3 = 0$.

Using the above equation, for a = 0, 2, 4, 6, 8, we get the values of b as 1, 5, 9, and 13, respectively.

∴, The possible order pairs (a, b) = $(0, 1), (2, 1), (4, 5), (6, 9), (8, 13).$

The possible number of order pair (a, b) = 5.

Hence, the possible number of order pair (a, b), if N = 1234ab56a is divisible by 22 is 5.

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