Math Destroyer question

[babytomato]

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In Math Destroyer Test 10 #25, the solutions say to subtract 10 from both 24 and 35. I thought you're supposed to add 24+35 and then subtract 10 to get the answer? Test 1 #25 and Test 3 #12 are done that way.

 

[lwergod]

what is the question asking? if it's A or B but not both, then it's A+ B -2(overlap %).

 

[babytomato]

24 people in one category, 35 in another, 10 in both. It's asking how many people are in only one of the categories. The answer is 39 but I thought it would be 49.

 

[lwergod]

draw a venn diagram, see if that helps

 

[artist2022]

So let's make it like this:
24 people like tennis
35 people like baseball
10 people like tennis AND baseball
How many people like ONLY tennis or ONLY baseball?

24 people like tennis = this includes the people that like ONLY tennis + the people that like tennis AND baseball
35 people like baseball = this includes the people that like ONLY baseball + the people that like tennis AND baseball

We want to find the green and the red numbers, and add them together.
Green = 24 - 10 = 14
Red = 35 - 10 = 25

Add them together! 39 is your answer 🙂

Sorry for the blinding colors! A Venn Diagram might be easier to understand but too much for me to draw right now haha. Hope it makes sense though.

 

[babytomato]

It makes sense the way you explained it. I'm confused then on the other two problems like it, where the numbers are given as percentages of a population and it asks for the probability of choosing either one or the other. For those problems, the solutions say to add the two percentages and subtract the percentage of people with both qualities from the sum, not from each percentage.