## June 2007, Logical Reasoning 2, Question 22

### Transcript

Question 23. When a question asks what follows logically from a set of facts, you're doing an inference question. On inference question, your job is to prove the answer true based on the facts that you've been given. So begin by taking stock of the information you've been given.

And this question, you're basically given a series of linked if then statements. The first, if the price that it pays for coffee beans goes up. The coffee shop is going to have to increase its prices. If it increases its prices, it'll either have to begin selling non coffee products or the coffee sales will go down. But if it sells non coffee products that's going to decrease its overall profitability.

And finally, the only way to avoid a decrease in overall profitability is also to make sure that the coffee sales don't decrease. Which you could flip around in your head to, if the coffee sales do decrease then it's going to decrease the overall profitability. It might be easier to take each of these and put them into formal logic in your notes.

So that the first sentence would become this, if the bean price goes up, the prices go up. The next sentence would become if the prices go up, then either they'll sell non coffee products or the sales will go down. If they sell non coffee products, the profits will go down. And if the sales go down, the profits will go down.

If you link these statements up, you can prove something which is probably gonna be the answer. If the beans go up, the prices go up which will have one or two effects. But both of those effects will lead to a decrease in profits. So in other words, if the price of beans keeps going up, their profits are definitely gonna go down.

Go to the answer choices looking for that. Answer choice A, well, this is the converse of what we're looking for. The answer we want is that an increase in beans is going to cause a decrease in profits. This answer choice is if you have a decrease in profits, you're going to have an increase in bean price.

Not what we're looking for, so go to answer choice B. Answer choice B is another converse, this time of one of the pieces of information that we were given and the original stimulus. The original stimulus told us that if either the non coffee products get sold or the sales go down, the profitability is gonna go down. This answer choice says if the profitability goes down, then one of those two things must have happened.

Answer choice C, of this is the one we wanted, if the beam price goes up, the profitability goes down. So a courtesy glance to see why the other answers are wrong. Answer choice D is wrong because it flips the decrease and increase. This says the price can't decrease without the profitability decreasing. We wanted that the price can't increase without the profitability decreasing.

And answer choice E is wrong because it creates an either or between two things coffee being price going up. And sales increasing those who things weren't linked in that way. So E is not our answer, the answer was C.