Question

If the eight digit number 2575d568 is divisible by 54 and 87, the value of the digit 'd' is:

a) 4
b) 7
c) 0
d) 8


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Answer 1

Factors of 54=2×3×3×3

                87=3×29

=>The eight digit number 25,75d,568 must be divisible by 2×3³×29.

Since it is even it is always divisible by 2.

25,75d,568

=25,750,568+d(1,000)

=25,750,548+20+d(999+1)

=27(953,724)+20+d(27×37)+d

If 25,75d,568 is divided by 27, then 20+d must also be divided by 27.

Therefore,

d=7

Now,

$\frac{25,757,568}{54} = 476,9992$

Thus,

d=7

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