Question

for how many positive integer values of 'n' are both n/3 and 3n three digit whole number is …
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Answer 1

Answer:

The correct option is 1.

Step-by-step explanation:

We have to find the positive integer values of 'n' for which both n/3 and 3n three digit whole number.

The three digits are from 100 to 999.

It is clear that

$\frac{n}{3}<3n$

$\frac{n}{3}=100$

$n=300$

The first value of n is 300.

$3n=999$

$n=333$

So the value of n are from 300 to 333. The number must be divided by 3, it means the value of n should be multiple of 3.

The value of n are

300, 303, 306, 309, 312, 315, 318, 321, 324, 327, 330, 333

The are total 12 possible values of n, therefore option 1 is correct.

Answer 2

"Answer: option A  

Three digits number are starting from 100 to 999

Form the above question, $(\frac { n }{ 3 } )<3n$

We can take  

$\frac { n }{ 3 } \quad =\quad 100$

           $n\quad =\quad 100\times 3\quad =\quad 300$

               3n = 999

               $n\quad =\quad \frac { 999 }{ 3 } \quad =\quad 333$

So the values of n are from 300 to 333. The number must be divisible by 3

The values of n between 300 to 333 are 300, 303, 306, 309, 312, 315, 318, 321, 324, 327, 330, 333

There are total 12 possible values of n

Therefore, option A is correct"