MBT - Conditional logic Question type

Do the right way

Hi Guys,
Can you please help with this question ?

Either A’s faction or B’s faction, but not both, will win control of the government. If A’s faction wins, the nation will suffer economically. If B’s faction wins, the nation will suffer militarily.

Given the statements in the passage, which one of the following statements must be true?

(A) It is possible, but not certain, that the nation will neither suffer economically nor suffer militarily.
(B) If the nation suffers economically, it is certain that A’s faction has won control of the government.
(C) It is certain that the nation will suffer either economically or militarily, and also certain that it will not suffer both.
(D) If the nation suffers militarily, it is possible, but not certain, that B’s faction has won control of the government.
(E) If the nation suffers both economically and militarily, it is certain that neither A’s faction nor B’s has won control of the government.

I tried to apply the conditional logic but still i am not able to figure it out.

AW - A's faction wins
BW - B's faction wins
NSE- Nation suffers economically
NSM- Nation suffers militarily

ST(1) : AW->/BW
BW->/AW

ST(2) : AW->NSE
/NSE->/AW

BW->NSM
/NSM->/BW

I am not able to derive D (Right AC) from this logical conditionals.

Source: Gmatclub
I hope it is rephrased correctly.

Thanks.

FixedDice

Either Perry’s faction or Tucker’s faction, but not both, will win. (P or T)
If Perry’s wins, the nation will suffer economically. (P -> E)
If Tucker’s wins, the nation will suffer militarily. (T -> M)

In other words, either E or M is bound to occur. Notice that the scenario precludes neither (P -> M) nor (T -> E); only (P -> E) and (T -> M) are certain. If the scenario really wanted to preclude (P -> M) and (T -> E), it would have presented the last two sentence as biconditionals.

Answer choices:

(A): Wrong. Either P or T has to occur, which means E (economic suffering) or M (military suffering). There is no way the nation will not suffer.

(B): Wrong. We are only given the necessary condition here. As mentioned above, (T -> E) is not precluded. So we don't know whether E resulted from P or T.

(C): Wrong. The first part is right. But as mentioned above, neither (P -> M) nor (T -> E) are precluded, meaning (P -> E and M) or (T -> E and M) is entirely possible. So it is not "certain that [the nation] will not suffer both."

(D): Correct. We are only given the necessary condition here. The stimulus indicates (T -> M), but as mentioned above (P -> M) too is possible. So from M, one can deduce that T may have occurred.

(E): Wrong. The stimulus implies that P or T has to occur, which means that the second part of the answer choice is false.

keets993

So if Perry wins then nation will suffer economically.
PW -> NSE
If Terry wins then nation will suffer militarially.
TW -> NSM

With ac A we don't know enough to support this. It's basically denying our conditionals. Because we know either Perry will win or Terry will win. And the answer choice is saying "possible not [NSE or NSM]" which I think might be the negation of the conditionals.

Answer choice B states in lawgic NSE ->PW. That's classic invalid argument form. It's affirming the necessary and as a result concluding the sufficient condition.

Answer choice C is tricky because it's asserting that PW or NSM will happen - which we can support 100% - but also claiming that it won't be both. We don't know that. It could be the case the Terry wins and the nation will suffer militarially but that effects the economy and so the nation suffers economically. It's the same with Perry. The nation suffering economically might cause the nation to suffer militarially as well because there might be less money to put into the military. We know it's either PW or TW and can't be both but the mistake is inferring that both NSE and NSM can't happen.

Answer choice D states that if NSM then maybe, but not certain that TW. It's not the same as stating NSM -> TW because that's 100%. Whereas it's saying that if we affirm the necessary it's possible that the sufficient condition happened. Like logic games when you have a conditional and the necessary has been affirmed and so the rule becomes irrelevant and the sufficient condition is free to float. It could be the case that the sufficient condition has been satisfied or it could fail.

And lastly, answer choice E is stating that if NSE and NSM -> /PW and /TW. Which is just condracticing what we've been told by the stimulus that one of them will win.

Hope that helped!

keets993

@FixedDice I swear we're always typing at the same time

FixedDice

@keets993 said:
@FixedDice I swear we're always typing at the same time

Great minds act alike!

FixedDice

Holy guacamole, this is a licensed GMAT question? Business school doesn't look as intimating and alien as it used to!

akistotle

@FixedDice said:
Holy guacamole, this is a licensed GMAT question? Business school doesn't look as intimating and alien as it used to!

Sorry, the note had a mistake. It's from The Official LSAT Prepkit published by LSAC in 1990, and it seems like the book has been used for GMAT prep by many. (I don't know why. I guess it's usedful for GMAT's CR section?)

Sorry @"Do the right way", any copyrighted content that infringe on copyright is prohibited on this Forum. (Copying and pasting something without a proper citation is plagiarism.) Please rephrase it like "Either A or B, but not both, will win...." and indicate where you found the question.

keets993

@akistotle
I was browsing a GMAT prep book - a friend of mine was thinking about taking it - and their reading component is basically LR and RC. You got your MBT, weaken, strengthen question types for LR and entire passages for RC with the same questions that we get tested on.

Holy guacamole, this is a licensed GMAT question? Business school doesn't look as intimating and alien as it used to!

The daunting part for me is that on top of all that they gotta do math too. With formulas and all that other good stuff.

Do the right way

@akistotle Sorry about the infringement. I have rephrased the question. I hope this will do. And
Thanks @keets993 and @FixedDice for your explanations. The explanations helped me. Thanks.