Percent Topic Concept - Increase By Problems

GRE Quant Problem Solving
1

I am not understanding when a question states increase by → when should i place a 1+% increase and when not to.
For example
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The explanation was the following :
when you increase a number by 250%, you are NOT simply multiplying it by 2.5. Rather, you are finding
250% (or 2.5 times) that number and then adding it back to the original, Thus, to increase a number by 250%, you are adding 100% to 250% for a total of 350%. Therefore, multiply by 3.5

However, in this example:

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image987×182 23.6 KB

doesn’t this also mean increases by 50% so it is (0.5)(2.5)(x) rather than (0.5)(1.5)(x)?

2

Let me explain-
Let’s assume the original value be 100.
It’s loses half of its value => value is now 50
It then increases by 50% => (1 + 0.5) 50 = 75
By doing 2.5 you are increasing it by 150%, that is where you are wrong