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.

Learn more about 'numbers' here:

fist on the left goes with the third on the right. second on the left goes with the fourth on the right. third on the left goes with the second on the right. the fourth on the left goes with first on the right