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Bunuel
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Bunuel
Yesterday it rained in Baronia. Did it rain in Dukia?

(1) Whenever it rains in Dukia, it also rains in Baronia.
(2) If it does not rain in Dukia, it does not rain in Baronia.

This question is a great reminder that the GMAT is a reasoning test, not a Math/English test.

S1: If it rains in Dukia it must be raining in Baronia but there is no reason it cannot rain in Baronia independently. NOT SUFFICIENT.

S2: In other words, if there is no rain in Dukia there is no rain in Baronia. Since there is rain in Baronia, there must be rain in Dukia. SUFFICIENT.

ANSWER: B
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According to the logical equivalences,
  • p -> q IS NOT EQUIVALENT TO q -> p
  • However, IT IS EQUIVALENT TO ~q -> ~p

let's define the following variables:

B: It rains in Baronia
D: It rains in Dukia
~B: It does not rain in Baronia
~D: It does not rain in Dukia

We want to know if B -> D

1) D -> B is not equivalent to B -> D: NOT SUFFICIENT
2) ~D -> ~B is equivalent to B -> D: SUFFICIENT

Answer: B
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Use Contrapositive logic:

Statement 1:- If it rains in Dukia, then it rains in Baronia
Contrapositive: If it does not rain in Baronia, then it does not rain in Dukia
Does not answer our question - If it rained in Baronia, did it rain in Dukia
Insufficient

Statement 2:- If it does not rain in Dukia, it does not rain in Baronia
Contrapositive: If it rains in Baronia, then it rains in Dukia. (negative of negative - positive)
Answers our question - If it rained in Baronia, did it rain in Dukia
Sufficient

(B) Statement (2) alone sufficient, statement (1) alone not sufficient


Bunuel
Yesterday it rained in Baronia. Did it rain in Dukia?

(1) Whenever it rains in Dukia, it also rains in Baronia.
(2) If it does not rain in Dukia, it does not rain in Baronia.
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