If the price it pays for coffee beans continues to increase, the Coffe

Question

If the price it pays for coffee beans continues to increase, the Coffee Shoppe will have to increase its prices. In that case, either the Coffee Shoppe will begin selling noncoffee products or its coffee sales will decrease. But selling noncoffee products will decrease the Coffee Shoppe's overall profitability. Moreover, the Coffee Shoppe can avoid a decrease in overall profitability only if its coffee sales do not decrease.

Which one of the following statements follows logically from the statements above?

(A) If the Coffee Shoppe's overall profitability decreases, the price it pays for coffee beans will have continued to increase.
(B) If the Coffee Shoppe's overall profitability decreases, either it will have begun selling noncoffee products or its coffee sales will have decreased.
(C) The Coffee Shoppe's overall profitability will decrease if the price it pays for coffee beans continues to increase.
(D) The price it pays for coffee beans cannot decrease without the Coffee Shoppe's overall profitability also decreasing.
(E) Either the price it pays for coffee beans will continue to increase or the Coffee Shoppe's coffee sales will increase.

AndrewN · Accepted Answer

Hello,  Soumik28 . I enjoy providing an Expert response when no other such response has been offered, and I enjoyed working on this question, so I hope that by sharing my thoughts, I will help you as well as the larger community. When it comes to CR questions, I like to start with the question itself so that I can interpret the information in the passage through a certain lens as I go.

Our task is to supply the next link in a chain of logic. In general, CR questions ask us to do this anyway. You have to be careful to  stick to the exact phrasing of the passage , as well as the arrow of logic laid out, or you can quickly go wayward and end up downing way more time than you should to arrive at a guess. So what is this particular chain of logic?

Sentence 1 provides a conditional statement: if A, then B. Event A is the price of coffee beans increasing; the result, event B, is a price increase at the Coffee Shoppe.

Sentence 2 launches into the next conditional statement, but this one branches at the end: if B, then C  or  D. Notice that we are  not  starting with a separate condition here.  In that case  carries over the result from the previous sentence. If the Coffee Shoppe increases its prices, then one of two outcomes will result: event C, the business will shift into selling  noncoffee products ; or event D, the business will continue selling coffee, but  its coffee sales will decrease . Notice that in either case, the passage tells us what  will  (not may) happen. These are definite outcomes if event B is triggered.

Sentence 3 follows up on event C, providing yet another conditional statement: if C, then E. Selling noncoffee products will decrease  overall profitability , plain and simple.

Sentence 4 negates event D in a reversed conditional statement: if not D, then not F. That is, if  coffee sales do not decrease , then the business will not experience  a decrease in overall profitability . The double negatives may take a moment to sort out, but you will notice that we now have two pieces of information that tell us about the overall profitability of the Coffee Shoppe. (If you were wondering why I labeled the final outcome as event F, rather than the earlier E, it is because E is a direct result of C, while F is not.)

Our answer must fit with the chain of logic that we can map out in the following manner:

If A → B
If B → C or D
If C → E
If  D  →  F  (notice the strikethroughs)

This is a reversal from the passage. We know that  overall profitability  can decrease in one of two ways: 1) selling noncoffee products (event C); or 2) decreasing coffee sales (via D and F). You will notice that neither case mentions coffee beans. Event A serves as a  catalyst  for a negative outcome—raising prices—but we cannot say for certain that just because overall profitability decreases, it  must  be true that the price of coffee beans has continued to rise. It could be true that the Coffee Shoppe is not selling as much coffee as usual, regardless of the price it pays for beans.  Red light.

Remember, the entire chain of logic presented in the passage relies upon increasing the price of the products the Coffee Shoppe offers to customers (event B). It is  that  event that leads to events C or D. By removing that crucial link in B, we have broken our chain. Although tempting at first glance, this answer choice has a glaring omission.  Red light.

This is the very missing link in question from the previous answer, and we can be glad that we took note of the language used in the passage with all those instances of  will . The outcome is  guaranteed  by the passage if event B occurs. Again, either the business will resort to hawking noncoffee products (event C), a dead-in-the-water proposition (that ends in event E), or the Coffee Shoppe will sell less coffee (event D), the lifeblood of, well, the  coffee  shop, per the final line of the passage. In short, the Coffee Shoppe  must  sell coffee to  avoid a decrease in overall profitability . This is our answer.  Green light.

We can only speculate on what  could  happen to the price of coffee beans, since the arrow of logic points away from that condition from the start. There is no need to read beyond  cannot decrease  here, as nothing from the passage can be used to back up such a statement. Pure speculation does not deliver on what the question is asking us to do.  Red light.

There is no condition in the passage under which we are told that  coffee sales will increase . We are only informed as to what will cause a decrease. If you negate the last line from  only if its coffee sales  do not decrease   to  only if its coffee sales  increase  , then that is a logical misstep. For all we know,  do not decrease  could refer to breaking even, making the same number of sales, with no increase at all. Stick to what the passage says.  Red light.

I hope that helps clarify the question and answer choices. One final note: this is an official LSAT question, and those tend to be a little more nuanced than their GMAT™ counterparts. I would not recommend studying too many of these questions over others that will more likely be on the test you are planning to take. Learn what you can from such questions, but always center your studies on official GMAT™ questions. Like produces like.

Good luck with your preparation.

- Andrew

gonerias · Answer

IMO, "C".
(A) Cannot always be true. Consider case when shop starts selling non-coffee items, therefore decreasing profitability but it is no longer paying any increasing prices for coffee.
(B) and (C) have very subtle difference. (B) ignores any other possibility due to which profitability can get affected.
(C) is correct as it is the conclusion of the argument. If price it pays for coffee continues to increase, it will either sell non-coffee (decreased profitability) or have decrease in coffee sales (decreased profitability). either case --> decreased profit.
(D) Talks about illogical relationship since we are not given any reason behind decrease/increase of coffee prices
(E) Establishes mutually exclusive property in increase of coffee prices and sale of coffee which is not directly implied by the argument

Soumik28 · Answer

Could you pease help me understand this question with proper solution?

Ranasaymon · Answer

(A) If the Coffee Shoppe's overall profitability decreases, the price it pays for coffee beans will have continued to increase.(No, if the price it pays for coffee beans has continued to increase, then the Coffee Shoppe's overall profitability will decrease)

(B) If the Coffee Shoppe's overall profitability decreases, either it will have begun selling noncoffee products or its coffee sales will have decreased.( No, selling noncoffee products or decreasing sales have negative effect on overall profitability)
 
(C) The Coffee Shoppe's overall profitability will decrease if the price it pays for coffee beans continues to increase. Yes

(D) The price it pays for coffee beans cannot decrease without the Coffee Shoppe's overall profitability also decreasing. (No, actually the Coffee Shoppe's overall profitability can not decrease without the price it pays for coffee beans increases)

(E) Either the price it pays for coffee beans will continue to increase or the Coffee Shoppe's coffee sales will increase ( They can happen at the same time)

azamatboden · Answer

I think (C) is literally mentioned in the argument

beeblebrox · Answer

AndrewN : I could eliminate all but options (B) & (C). I understood why option (B) is incorrect. But I have a doubt regarding option (C). It was because of this doubt that I omitted option (C) and marked option (B).

My doubt is:   The Coffee Shoppe's overall profitability will decrease if the price it pays for coffee beans continues to increase.  : If the price it pays for coffee beans continues to increase & further if Coffee Shoppe cascade this hike to their coffee products & if the sales of the coffee products don't go down, then, in that case, Coffee Shoppe's profitability will not go down.

Is my inference correct? In the above case, there is no guarantee that profitability will go down for sure even if the prices of the coffee beans go up. Kindly clarify?

Your response is awaited. Regards.

AndrewN · Answer

Hello,  beeblebrox . I understand your real-world chain of logic here. But remember, both the GMAT™ and the LSAT employ airtight logic in their own bubbles, and we have to appreciate the vacuum. In that light, I have taken the liberty of  highlighting  the wayward direction within your thought process. The passage, within the first two lines, categorically dismisses the possibility that the coffee shop can both pay higher prices for coffee beans  and  continue selling as much coffee. It is an either/or proposition instead. (My   bold italics  .)

In this situation, we know the coffee shop will enter a downward spiral: sell noncoffee products at a loss, or sell less coffee, all based on the rising price of coffee beans.

One more thought on CR in general. It is better to get behind an answer you think is safer than to go with one you can definitely pin a doubt to. I know that sinking feeling of chasing an answer simply because I was unsure about something or other in another answer choice, only to find out my original answer was correct. Put into practice a firmer method, though, something you can apply to question after question, and accuracy will follow, even on these tough ones.

I hope that helps clarify the matter. Thank you for thinking to ask.

- Andrew

unfairpolarbear · Answer

First premise. I denoted it as, P-->Q. "If price it pays for coffee beans increase then the shop will increase its price"

Second premise denoted as, Q-->(R v S). 
"In case Q---the shop increasing its price----, then either R---shop will begin selling non-coffee products---or S--coffee sales will decrease."

Third premise. R-->T. "If shop sells non-coffee products then overall profitability will decrease."

Fourth premise. ~T-->~S. "shop can avoid decreasing profit only if its coffee sales do not decrease."

the ~ denotes a negation and key word, "only if" is the consequent of a conditional.

Just a quick recap on conditionals: there are 2 components, the antecedent and the consequent. 
the antecedent of a conditional is the "if" part of a conditional statement for example, "IF I go for a walk today, THEN it is sunny" 
and the term, "only if" is equivalent to "then" thus, the fourth premise is symbolically denoted as ~T-->~S.

Now let's take a look at each conclusion and see which ones are valid.

A) If overall profitability decreases, the price it pays for coffee beans will have continued to increase. 
 
This is symbolically equivalent to "If T then P".

Right away I can tell this is incorrect based on truth tables for conditional logic.

P --> Q 
T T T 
T F F
F T T
F T F

So the T's and F's represent true or false; it is binary and for a conditional, there are 4 total possible combinations of the validity for statement P and statement Q. 
I will not go into detail on truth tables, you can wikipedia it yourself to follow along. 
We see that in a conditional, there is only one instance that would make a conditional statement false, which is when the antecedent is true and the consequent 
is false. 
It basically means that when you have a conditional if the antecedent is true, then the consequent must necessarily follow. 
However, we see that the consequent can be True even if the antecedent is false. 
Where validity of P is False and validity for Q is true.

Now for conclusion A, we see that in order for T--"profit decrease" to even be valid, it requires the antecedent R---sells noncoffee products. And R requires the antecedent Q---increase sale of coffee beans. 
 
Q. Q ---> (R v S). R-->T.

And as we've seen, Q can occur even if P does not occur, so P---price it pays for coffee beans increase---can never be contingent on T---profit decrease.

For conclusin B) If the shops overall profitability decreases, either it will have begun selling non-coffee products or its cotton sales will have decreased.

T --> (R v S).

here we have the same problem as A. the antecedent and consequents are flipped and they are not equivalent. the only way a conditional is equal both ways is if it is a bi-conditional, the key term for bi-conditional is "if and only if"

conclusion C) the shops overall profit will decrease if the price it pays for coffee beans continues to increase.

P --> T.

Another way to word the conclusion is, "if the price it pays for coffee beans continue to increase, the shops overall profit will decrease".

So here, I will show you what is called a derivation. Basically its like accounting but for arguments. 
Premises: P--->Q. Q-->(R v S). R-->T. ~T-->~S. 
Conclusion: P-->T 
 
1) Prove P-->T -----------------> line 3, conditional proof

2) P Assume the conditional

3) Prove T -----------------> line 9, direct proof

4) ~T Assume the indirect

5) ~S line 4, Premise 4. Modus Ponens

6) Q line 2, Premise 1. Modus Ponens

7) R v S line 6, Premise 2. Modus Ponens

8) R line 5, line 7, Modus Tollendo Ponens (disjunctive syllogism)

9) T line 8, Premise 3. Modus Ponens

Now on line 3 we can provide our reasoning which is a direct proof of the consequent T. 
And finally, for line 1, we proved the conditional P-->T

logically speaking, conclusion C is valid, given the premises, therefore C is the correct answer.

Edit:

Sorry I do not know how to align properly in this text editor. i will post a screenshot of the derivation using a logic software.

thelastskybender · Answer

(A) If the Coffee Shoppe's overall profitability decreases, the price it pays for coffee beans will have continued to increase.  We can't say that---we don't know what will happen when Price of coffee beans decreases. It also might lead to decrease in overall profitability ]
(B) If the Coffee Shoppe's overall profitability decreases, either it will have begun selling noncoffee products or its coffee sales will have decreased.  Same reason: We can't say that---we don't know what will happen when Price of coffee beans decreases. It also might lead to decrease in overall profitability ]
(C) The Coffee Shoppe's overall profitability will decrease if the price it pays for coffee beans continues to increase.  Yes! look at the tree diagram; we can infer this one ] 
(D) The price it pays for coffee beans cannot decrease without the Coffee Shoppe's overall profitability also decreasing.
(E) Either the price it pays for coffee beans will continue to increase or the Coffee Shoppe's coffee sales will increase.

Below is the tree diagram, which you might find helpful.

VerbalBot · Answer

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