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If the seven-digit number 161x208 is divisible by 11 and the four-digit number 953y is divisible by 9, then, what is the value of (x+y)?
- a)7
- b)8
- c)12
- d)10
Correct answer is option 'A'. Can you explain this answer?
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If the seven-digit number161x208is divisible by11and the four-digit nu...
Given:
The seven-digit number 161x208 is divisible by 11 and the four-digit number 953y is divisible by 9,
Divisibility rule for 11 = Find the sum of the digits in the even places and the sum of the digits in the odd places. If the difference between the two sums is 0 or a multiple of 11, then the given number would be divisible by 11.
Divisibility law of 9= A number divisible by 9 if the sum of its digit is divisible by 9.
(i) The seven-digit number 161x208 is divisible by 11.
⇒ (1+1+2+8)−(6+x+0)
⇒ 12−(6+x)
⇒ (6−x)
If we put x=6, then the difference become zero.
⇒ x = 6
(ii) The four digit number 953y is divisible by 9.
⇒ 9+5+3+y
⇒ 17+y
If we put y = 1, the number become 18 which is divisible by 9.
⇒ y = 1
According to question,
(x+y) = (6+1) = 7
∴ The value of (x+y) is 7.
The seven-digit number 161x208 is divisible by 11 and the four-digit number 953y is divisible by 9,
Divisibility rule for 11 = Find the sum of the digits in the even places and the sum of the digits in the odd places. If the difference between the two sums is 0 or a multiple of 11, then the given number would be divisible by 11.
Divisibility law of 9= A number divisible by 9 if the sum of its digit is divisible by 9.
(i) The seven-digit number 161x208 is divisible by 11.
⇒ (1+1+2+8)−(6+x+0)
⇒ 12−(6+x)
⇒ (6−x)
If we put x=6, then the difference become zero.
⇒ x = 6
(ii) The four digit number 953y is divisible by 9.
⇒ 9+5+3+y
⇒ 17+y
If we put y = 1, the number become 18 which is divisible by 9.
⇒ y = 1
According to question,
(x+y) = (6+1) = 7
∴ The value of (x+y) is 7.
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