Question

A number 57a2b is divisible by 9 and36b2 is divisible by 11, where a and b are the missing digits. Which of these could be the relation between a and b? Option1: a= 2b
Option 2: b − a = 3
Option 3: ab
Option 4: a –b = 3

Answer 1

Answer:

Option 4: a – b = 3

Step-by-step explanation:

When solving 'b', we get b = 5

If 36b2 is divisible by 11, then b + 3 = 6 + 2

⇒ b = 6 + 2 – 3 = 3 + 2 = 5

∴ b = 5

And when b = 5, then when 57a2b is divisible by 9, then a = 8

the number is 57a25.

5 + 7 + a + 2 + 5 = a multiple of 9

⇒ a + 19 = mearest greater multiple of 9 = 27

⇒ a = 27 – 19 = 8

and when we see a relation b/w 'a' and 'b', a = 8 and b = 5

a – b = 8 – 5 = 3

∴ it is Option 4: a – b = 3

Hope it helps...

Answer 2

a - b = 3  if A number 57a2b is divisible by 9 and 36b2 is divisible by 11, where a and b are the missing digits

Given:

• A number 57a2b is divisible by 9
• A number 36b2 is divisible by 11
• a and b are missing digits

To Find:

• Relation between a and b from below options
• Option 1: a= 2b
• Option 2: b − a = 3
• Option 3: ab
• Option 4: a – b = 3

Solution:

Step 1:

A number is divisible by 9 if sum of digits is divisible by 9

57a2b

sum of digits = 5 + 7 + a + 2 + b

= 14 + a + b

a + b must be 4   or 13

as 14 + 4 = 18  and 14 + 13 = 27 is divisible by 9

a + b = 4

a + b = 13

Step 2:

A number is divisible by 11 if difference between digits at odd places and even places is divisible by 11

36b2

(3 + b) - (6 + 2)

= b - 5

b must be 5

as 5 - 5 = 0 is divisible by 11

Step 3:

a + b = 4 is not possible as b = 5

Hence a + b = 13

=> a + 5 = 13

=> a = 8

a = 8  and b = 5

=> a - b = 8 - 5 = 3

a - b = 3 is correct option

Option 4) a - b = 3