Can someone help me with this critical thinking problem?

[bandie89]

Okay so this is one of those lateral puzzle questions that I’m having trouble finding an answer with.

Chocolate Demographics: suppose 1/2 of all people are chocolate eaters and 1/2 of all people are women does it follow that 1/4 of all people are women chocolate eaters? Does it follow that 1/2 of all men are chocolate eaters.

please explain your reasoning.

 

[Deleted member 4993]

Okay so this is one of those lateral puzzle questions that I’m having trouble finding an answer with.

Chocolate Demographics: suppose 1/2 of all people are chocolate eaters and 1/2 of all people are women does it follow that 1/4 of all people are women chocolate eaters? Does it follow that 1/2 of all men are chocolate eaters.

please explain your reasoning.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

 

[bandie89]

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

Here are the directions for it and I did answer it but I'm just not sure if this is the correct answer or if it's detailed enough. right now the answer is "No, because we don’t know the split among the chocolate eaters. It could be all men are the chocolate eaters since they are half of the population."

 

[Deleted member 4993]

Here are the directions for it and I did answer it but I'm just not sure if this is the correct answer or if it's detailed enough. right now the answer is "No, because we don’t know the split among the chocolate eaters. It could be all men are the chocolate eaters since they are half of the population."

I would accept your answer as correct and logical.

 

[JeffM]

Okay so this is one of those lateral puzzle questions that I’m having trouble finding an answer with.

Chocolate Demographics: suppose 1/2 of all people are chocolate eaters and 1/2 of all people are women does it follow that 1/4 of all people are women chocolate eaters? Does it follow that 1/2 of all men are chocolate eaters.

please explain your reasoning.

There is no formula about this. You are being asked to think, and there is nothing lateral about it.

What numbers dont we know

p = number of people
a = number of people who are woman
b = number of people who are men
m = number of people who like chocolate
u = number of women who like chocolate
v = number of men who like chocolate

What do we want to know

u / m
v / m

What do we know to start with

a + b = p
a = p/2
m = p/2
u + v = m

Do we have enough equations?

 

[Dr.Peterson]

Chocolate Demographics: suppose 1/2 of all people are chocolate eaters and 1/2 of all people are women does it follow that 1/4 of all people are women chocolate eaters? Does it follow that 1/2 of all men are chocolate eaters.

"No, because we don’t know the split among the chocolate eaters. It could be all men are the chocolate eaters since they are half of the population."

What you said can be thought of as a counterexample, which is a good way to show that something is not (always) true. If half the population are male chocolate eaters and the other half are female non-chocolate eaters, then both premises are true (1/2 of all people are chocolate eaters and 1/2 of all people are women), but the conclusions are both false, so they can't follow from the premises. Of course, there are many other possibilities, but only one counterexample is needed.

That's actually very good reasoning.

 

[JeffM]

I actually tried to rewrite my answer after I saw the OP's second post, but time had expired.

Your reasoning is fine. You should simply see that there is an alternative way to look at it using algebra.