If 653xy is exactly divisible by 80, then find the value of (x + y) .

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answer is D.

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Detailed Solution

The number is shown as three digits with two variables. 80 is given; divide it into the product of two numbers. Take a look at both numbers' division rules now. For a number to be divisible by their product, which is 80, it must be divisible by both of these numbers. The value of x and y can be obtained in 2 circumstances using these criteria. In light of the two rules. Simply add the values of x and y to determine their sum after obtaining the values of x and y. The last three digits of a number must be a multiple of 8 in order for it to be divisible by 8, according to the rule of 8.
The "Rule of Ten" states that a number must have a units digit of zero in order to be divisible by 10.
It is necessary that the given integer can be divided by 80.
We can write 80 as the result of 8, 10, and 20. 80 = (8) (10) .
So, if a number can be divided by 8, 10, and 80, it can also be divided by 80.
To demonstrate that the number is divisible by 80, we must now use the divisibility rules of 8 and 10.
The number mentioned in the query can be expressed as follows: -
653xy
The unit digits of 653xy must be 0 in order for it to be divisible by 10.
Applying the aforementioned criterion results in the value of y being:
y = 0 – (1)
The number 53x must divide by 8 in order for the number 653x to be divisible by 8.
Applying the aforementioned criterion, the value of x is obtained as;
53x must be divisible by 8.
53x can be written as = 5×100+3×10+x
As, 500=62×8+4
30=8×3+6
By substituting these into above, we get
(62×8+4) +(8×3+6) +x=(65×8) +(10+x)
0≤x≤90≤x≤9
Since x = 6 and y = 0, it follows that x + y = 6.
Hence, the correct option is 4) 6
ExamType: CBSE

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