Question

M(x, y, z) denote the number of multiples of 'x' that are less than 'z' and greater than 'y'. what
is m(93, 94, 96)?​

Answer 1

SOLUTION

GIVEN

M(x, y, z) denote the number of multiples of 'x' that are less than 'z' and greater than 'y'.

TO DETERMINE

The value of $\sf{M( {9}^{3} , {9}^{4} , {9}^{6}) }$

EVALUATION

Here it is given that M(x, y, z) denote the number of multiples of 'x' that are less than 'z' and greater than 'y'.

We have to find the value of

$\sf{M( {9}^{3} , {9}^{4} , {9}^{6}) }$

So we have

$\sf{x = {9}^{3} \: , \: y = {9}^{4} \: , \: z = {9}^{6}}$

Now it is given that y < x < z

Which is satisfied

Now

$\sf{ {9}^{4} = 9 \times {9}^{3} }$

$\sf{ {9}^{6} = {9}^{3} \times {9}^{3} = 729 \times {9}^{3} }$

So multiples of 'x' that are less than 'z' and greater than 'y' are

$\sf{10 \times {9}^{3} ,11 \times {9}^{3},12\times {9}^{3},..,728 \times {9}^{3}}$

So the required number of multiples

= 728 - 10 + 1

= 719

FINAL ANSWER

$\boxed{ \: \: \sf{ M( {9}^{3} , {9}^{4} , {9}^{6}) = 719 } \: \: }$

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