deepesh.gupta wrote:To avoid economic collapse, Russia must increase its GNP by 20%. However, due to the structure of its economy, if the 20% threshold is reached, then a 40% increase in GNP is achievable.
Assuming that the above statements are true, which one of the following must also be true?
(A) If ethnic strife continues in Russia, then a 20% increase in GNP will be unattainable.
(B) If a 40% increase in Russia's GNP is impossible, its economy will collapse.
(C) If Russia's GNP increases by 40%, its economy will not collapse.
(D) If the 20% threshold is reached, then a 40% increase in GNP is achievable and a 60% increase is probable.
(E) If Russia's economy collapses, then it will not have increased its GNP by 40%.
This is certainly an LSAT (or LSAT-like) question. You could get something like this on the GMAT, but the chances are quite slim. The first sentence yields the following conditonal statement:
If Russia avoids economic collapse,
then it increases GNP by 20%.
(avoid ec. coll.----> increase GNP 20%)
The second sentence yields:
if it increases GNP by 20%,
then 40% is possibe.
(increase GNP 20%----> 40% possible)
Note that the right hand side of the first conditional statement is also the left-hand side of the second. Thus:
if Russia avoids economic collapse,
then 40% is possible,
whose contrapositive is:
if 40% is NOT possible (ie, IS impossible),
then Russia will NOT avoid economic collapse (ie, WILL collapse).
Which, of course, is a perfect match to choice B.
(Choices A and D are outside the scope while chioces C and E involve mixing up sufficient and necessary conditions, which is the same thing as making a mistake in contraposing).
Now, we could also had just reasoned it through verbally as Becky did. For any fomal logic that appers on the GMAT, if you are a good reasoner, then that will be sufficient; no need to write down if-then statements (although you certainly can if you find it helps). Again, this must be an LSAT question; wrong answers on the GMAT would never test your technical contraposing skills this vigorously.
_______________________
When it comes to formal logic on the LSAT, there are exactly four sub-skills we have to have nailed down:
-identifying (in the first place, we need to identify that a sentence can yield a formal logic relationship)
-translating (we can translate the Englsh sentence into an algebraic one)
-contraposing (for every conitional statement, there is always exactly one other way of stating it; a
contrary way of expressing the same
positive information--the contrapositive)
-connecting (if the right hand side of one conditional statement is the left hand side of another, we can connect the two)
Note that I applied all four of these skills to prove that choice B must be true.