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If a number 5x423y is completely divisible by 88 then find the value of 5x - 8y.
- a)16
- b)24
- c)32
- d)40
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
If a number 5x423y is completely divisible by 88 then find the value o...
Given Information:
The number is in the form 5x423y and is completely divisible by 88.
Divisibility Rule for 88:
A number is divisible by 88 if it is divisible by both 8 and 11.
A number is divisible by 8 if the last three digits of the number are divisible by 8.
A number is divisible by 11 if the difference between the sum of the digits at odd places and the sum of the digits at even places is either 0 or a multiple of 11.
Applying Divisibility Rules:
- Since the number is divisible by 88, it must be divisible by 8. Therefore, y must be 2 (since 4232 is divisible by 8).
- Now, we need to find x. For the number to be divisible by 11, the difference between the sum of digits at odd places and even places should be 0 or a multiple of 11.
Calculations:
Sum of digits at odd places = 5 + 4 + 2 = 11
Sum of digits at even places = x + 2 + 3 = x + 5
Now, (x + 5) - 11 = x - 6 must be 0 or a multiple of 11. Therefore, x = 6.
Calculating 5x - 8y:
Substitute x = 6 and y = 2 into the expression:
5(6) - 8(2) = 30 - 16 = 14
Therefore, the value of 5x - 8y is 14, which is not among the given options.
The number is in the form 5x423y and is completely divisible by 88.
Divisibility Rule for 88:
A number is divisible by 88 if it is divisible by both 8 and 11.
A number is divisible by 8 if the last three digits of the number are divisible by 8.
A number is divisible by 11 if the difference between the sum of the digits at odd places and the sum of the digits at even places is either 0 or a multiple of 11.
Applying Divisibility Rules:
- Since the number is divisible by 88, it must be divisible by 8. Therefore, y must be 2 (since 4232 is divisible by 8).
- Now, we need to find x. For the number to be divisible by 11, the difference between the sum of digits at odd places and even places should be 0 or a multiple of 11.
Calculations:
Sum of digits at odd places = 5 + 4 + 2 = 11
Sum of digits at even places = x + 2 + 3 = x + 5
Now, (x + 5) - 11 = x - 6 must be 0 or a multiple of 11. Therefore, x = 6.
Calculating 5x - 8y:
Substitute x = 6 and y = 2 into the expression:
5(6) - 8(2) = 30 - 16 = 14
Therefore, the value of 5x - 8y is 14, which is not among the given options.
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Community Answer
If a number 5x423y is completely divisible by 88 then find the value o...
Given:
If a number 5x423y is completely divisible by 88
Concept used:
Divisibility rule of 8 = Last three digit of any number should be divisible by 8 , then number is divisible by 8
Divisibility Rule of 88 = Number should be divisible by both 8 and 11.
Divisibility Rule of 11 = Sum of odd place digit - Sum of even digit place = 0 or multiple of 11
Calculation:
If a number 5x423y is completely divisible by 88
So, By using divisibility rule of 8
y = 2 because 232 is divisible by 8
Now, By using divisibility rule of 11
⇒ (x + 2 + 2) - (5+4+3) = 0
⇒ (x + 4) - (12) = 0
⇒ x = 8
The value of 5x - 8y = 40 - 16 = 24
∴ The required answer is 24
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