Q. 172

Make the greatest and the smallest 5 - digit numbers using different digits in which 5 appears at ten’s place.

Answer :

Here, the ten’s place is fixed( = 5).


For the rest of the digits; Let’s use the digits in this way:


To minimize the number, the smaller digits will be used in left side;


And, to maximize the number, larger digits are used in left side. [As the left side digits contributes more towards the value of the number: Any number, say, ”anan - 1an - 2….a1a0 can be expanded as :


= an × 10n + an - 1 × 10n - 1 + an - 2 × 10n - 2 + an - 3 × 10n - 3 + … + a1 × 101 + a0]


The greatest number = 99959


The smallest number = 10050


[note, as we can not start a number with 0, we are taking the 2nd smallest digit available (here, 1) to start with while forming the least number.]


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