Question

The number of digits in the smallest number which when multiplied by 7 yields all nines is

• A. 3
• B. 4
• C. 5
• D. 6

Answer 1

Answer: (D)

6

$\text{we have to find out number od digits in the smallest number which when multiplied by 7 yields all nines}$

$i.e$

$\Rightarrow x\times 7=\mathrm{9999......}$

$\Rightarrow x=\frac{\mathrm{9999.......}}{7}$

$\text{divide 99999....by 7 and check whether is completely divisible or not, if not then add one more 9 over 99999....}$

$\text{and check divisibility again.continue this until 99999....is completely divisible by 7}$

finally, we get $142857$ which when multiplied by 7 yields all nines

$i.e$

$\Rightarrow 142857\times 7=999999$

thus $\text{the number of digits is 6}$