Question

If the eight-digit number 5668x25y is divisible by 48, find the least value of x+y.we want the answer 1

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Answer 1

Answer:

$given -$

Eight digit no. 5668x25y is divisible by 48

$to \: find -$

The least value of x+y

$solution -$

The factors of 48 are 3 and 16

For divisible by 3: Sum of the digits must be divisible by 3

⟹5+6+6+8+x+2+5+y=32+x+y must be divisible by 3

We know that x and y are digits and hence 0≤x,y≤9⟹x+y≤18

32+x+y is divisible by 3 when x+y=1,4,7,10,13,16

For the entire number to be divisible by 16, the last 4 digits must be divisible by 16

⟹ last 3 digits must necessarily be divisible by 8 ⟹25y to be divisible by 8, the last 3 digits must be 256 and it is the only possibility.

That leaves us to find the value of x

Since y=6 and x+y≥6⟹x+y=7,10,13⟹x=1,4,7

The last 4 digits would be 1256,4256,7256

Out of these only 4256 is divisible by 16⟹x=4,y=6

⟹x+y=10

Answer 2

Answer:

thanks for free points.

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