Question

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

Answer 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,

$1 + 8 = 9$

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

$18$ × $2 = 36$

The sum remains the same i.e. $3 + 6 = 9$

Similarly,

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

$18$ × $3 = 54$

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.

 $18$ × $4 = 72$

$(7 + 2 = 9)$

$18$ × $5 = 90$

$(9 + 0 = 9)$

Thus, 18 is the answer.

Learn more about 'numbers' here: brainly.com/question/1624562