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

Question

(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.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked. 
 B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked. 
 C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked. 
 D. EACH statement ALONE is sufficient to answer the question asked. 
 E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

chetan2u · Accepted Answer

Hi,

this has more to with logic than with pure maths.. 
let Rain in Baronia = X and Rain in Dukia = Y...
so we are looking for If X, then Y....
in these we can Negate the second and it will follow If NOT Y, then NOT X....

(1) Whenever it rains in Dukia, it also rains in Baronia. 
whenever Y, it is also X...
so it can be said - If Y, then X... But it is not the same as If X then Y..
Insuff

(2) If it does not rain in Dukia, it does not rain in Baronia. 
If NOT Y, then NOT X....
Negating it we get
If X, then Y
Suff
B

babuvgmat · Answer

Ans:-

1. It can rain in Baronia and doesnt rain in Dukia . So Not sufficient.

2. doesnt rain in dukia implies doesnt in rain Baronia. It is like X causes Y but we are not sure whether Y causes X i.e, if it rains in Baronia .. it can or cannot rain in Dukia.

This is almost similar to statement 1.

Ans E

Papist · Answer

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

atilasol · Answer

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

kdipayan · Answer

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

JaxTran · Answer

How come I don't see the list of options for answers. 
All I see is

"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."

Bunuel · Answer

This is a data sufficiency question. Options for DS questions are always the same and usually omitted on the site.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Hope this helps.

AkshayBhushan · Answer

Hello, 
Howcome its b?
Same as the first statement, it says if it does not rain in D, it does not rain in B, ideally to make it correct it shouln't be the other way round?

Bunuel · Answer

Statement (2) says:  No rain in Dukia means no rain in Baronia.

But we already know it  did  rain in Baronia.

So the “no rain in Dukia” case cannot be true. Therefore, it must have rained in Dukia.

Statement (1) does not give us that.

egmat · Answer

Hi AkshayBhushan,

You're spot-on that Statement 1 doesn't help, and I can see why Statement 2  looks  like the same thing. But there's one move that makes them behave in opposite ways: what happens when you negate  both  sides of a conditional.

Start with what each statement literally says: 
- Statement 1: rain in Dukia → rain in Baronia. (D → B)
- Statement 2: no rain in Dukia → no rain in Baronia. (¬D → ¬B)

We already know it rained in Baronia (B is true), and we want to know about Dukia.

Statement 1 (D → B):  Knowing B happened tells you nothing about D. Baronia could rain on its own, with Dukia dry.  Not sufficient  - you agree here.

Statement 2 is the key trick - read it "backwards":  A statement of the form ¬D → ¬B is exactly the same as B → D. This is the contrapositive: flip the  two  sides  and  negate them, and the truth is unchanged. So "no Dukia rain means no Baronia rain" is just another way of saying "if Baronia rained, Dukia rained." Since Baronia did rain,  Dukia must have rained .  Sufficient .

So the two statements are  not  the same: Statement 1 gives D → B, Statement 2 gives B → D. Only the second one points the arrow the way we need.

Feel it with an everyday version: 
- "If it's not raining, the ground is not wet" is the same as "If the ground is wet, it's raining."
- But "If it's raining, the ground is wet" does  not  let you conclude it's raining just because the ground is wet (a sprinkler could have done it).

Same  two  shapes as your statements - one lets you work backward, the other doesn't. That's why the answer is  B .

Answer: B

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

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GMAT Data Sufficiency (DS) Questions

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

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