Question

Jacob claims that an increase of 5% of a number followed by a decrease of 10% is equivalent to a decrease of 10% followed by an increase of 5%. Is he correct? If not provide proof that he is wrong.

Answer 1

[AI-generated answer — Bot GPT 3.5]

Jacob is incorrect. Let's provide a counterexample to show that his claim is not true.

Let's start with a number such as 100.

Increasing 5% of 100 is 100 + 5% of 100 = 100 + 5 = 105.

Then decreasing 10% of 105 is 105 - 10% of 105 = 105 - 10.5 = 94.5.

Now, let's try the opposite order:

Decreasing 10% of 100 is 100 - 10% of 100 = 100 - 10 = 90.

Then increasing 5% of 90 is 90 + 5% of 90 = 90 + 4.5 = 94.5.

Since the results are different (94.5 in the first case and 90 in the second case), we can conclude that Jacob's claim is incorrect.