Question

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Answer 1

4.

Let the middle numbers be x, y and z.

Then it'll be 5, x, y, z and 6.

5xy = xyz = 6yz = 120

Consider 5xy = 6yz = 120

5x = 6z = 120 / y

On 5x = 6z, we can find that x/z = 6/5

∴ x : z = 6 : 5

Here we can understand that x and z are multiples of 6 and 5 respectively.

Let x and z be 6m and 5n respectively.

xyz = (6m)y(5n) = 30myn = 120

myn = 120 / 30 = 4

If x = 6 and z = 5, then myn = 1 x y x 1 = y = 4

So we can take the 5 numbers as,

5, 6, 4, 5, 6.

5.

Find the sum of digits of the number. If the sum is divisible by 3, the number is a multiple of 3. If the sum is divisible by 9, the number is divisible by 9. If the number is divisible by 9, it is also divisible by 3.

123456789 is divisible by both 3 and 9. The sum of its digits is 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45. 45 is divisible by 9.

546782543 is not divisible by 3 and 9. 5 + 4 + 6 + 7 + 8 + 2 + 5 + 4 + 3 = 44 is not divisible by 3.

389457986 is not divisible by both 3 and 9.

678458886 is divisible by 3, but not by 9.

189868437756 is divisible by both 3 and 9.

Hope these may be helpful.

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