Question

Find the greatest five-digit number, which is divisible by 279 is,
A.99603
B.99837
C.99882
D.None

Answer 1

Hint: In the given question, we have been asked what is the largest five-digit number which is divisible by 279. To solve any kind of such question, involving of finding the greatest n-digit number divisible by an integer m, we first take the largest number of n-digit (which is \[{10^n} - 1\]), then we divide it by m, then if we get a remainder, we subtract the remainder from the largest n-digit number and that gives us our answer, and if we do not get a remainder, then the largest n-digit number itself is the answer.

Complete step-by-step answer:
We have to find the largest five-digit number which is divisible by \[279\]. So, we are going to solve it by dividing the largest five-digit number \[\left( {99999} \right)\] by the given number and applying the remainder rule.
\[279\mathop{\left){\vphantom{1\begin{array}{l}{\rm{ 99999}}\\\dfrac{{{\rm{ - }}837}}{{{\rm{ }}1629}}\\\dfrac{{{\rm{ - 1395}}}}{\begin{array}{l}{\rm{ 2349}}\\{\rm{ }}\dfrac{{{\rm{2232}}}}{{117}}\end{array}}\end{array}}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{\begin{array}{l}{\rm{ 99999}}\\\dfrac{{{\rm{ - }}837}}{{{\rm{ }}1629}}\\\dfrac{{{\rm{ - 1395}}}}{\begin{array}{l}{\rm{ 2349}}\\{\rm{ }}\dfrac{{{\rm{2232}}}}{{117}}\end{array}}\end{array}}}}
\limits^{\displaystyle\,\,\, {358}}\]
Now, remainder, \[R = 117\].
To get the answer, we subtract R from \[99999\].
Hence, the required number is \[99999 - 117 = 99882\].
Thus, the correct option is C.

Note: For solving these types of questions we think about the formulae which contain the known and the unknown and pick the one which is the most suitable and the most effective for finding the answer of the given question. Then we put in the knowns into the formula, evaluate the answer and find the unknown. It is really important to follow all the steps of the formula to solve the given expression very carefully and in the correct order, because even a slightest error is going to make the whole expression awry and is going to give us an incorrect answer.