Find a 2-digit number smaller than 50, the sum of whose digits does not change after being multiplied by a number greater than 1

The only 2-digit number that is lesser than 50 and the sum of its digits remain unaffected despite being multiplied by a number < 1 would be '18.'

To prove, we will look at some situations:

If we add up the two digits of 18. We get,

And we multiply 18 by 2 which is greater than 1. We get,

×

The sum remains the same i.e.

Similarly,

If 18 is multiplied to 3(greater than 1), the sum of the two digits comprising the number still remains the same;

×

where (5 + 4 = 9)

Once more,

Even if 18 is multiplied to 4 or 5(greater than 1), the sum of its digits will still be 9.

  ×

×

Thus, 18 is the answer.

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