Logical Reasoning - Logical Problems - Discussion

The logic problems in this set present you with three true statements: Fact 1, Fact 2, and Fact 3. Then, you are given three more statements (labeled I, II, and III), and you must determine which of these, if any, is also a fact. One or two of the statements could be true; all of the statements could be true; or none of the statements could be true. Choose your answer based solely on the information given in the first three facts.


Fact 1: Mary said, "Ann and I both have cats."
Fact 2: Ann said, "I don't have a cat."
Fact 3: Mary always tells the truth, but Ann sometimes lies.
If the first three statements are facts, which of the following statements must also be a fact?
I: Ann has a cat.
II: Mary has a cat.
III: Ann is lying.

[A]. I only
[B]. II only
[C]. I and II only
[D]. All the statements are facts.

Answer: Option D


If Mary always tells the truth, then both Ann and Mary have cats (statements I and II), and Ann is lying (statement III). So all the statements are facts.

Tash said: (Aug 1, 2013)  
If Mary always tells the truth, then both Mary and Ann have cats.

But if Ann sometimes tells the truth, we are uncertain as to whether Ann has a cat or not because she could either be telling the truth or a lie.

Therefore answer is B.

101 said: (Sep 25, 2013)  
In my opinion option [A] Ann lied because Marry said that she and Ann have a cat + Marry always tells the truth.

Whoever said: (Nov 12, 2014)  
What if Ann lied to Mary?

Then she said the truth that she has no cats.

Logicman said: (Mar 22, 2015)  
@Tash - But it is a given that all of the first 3 statements are facts. So Ann is lying and all of the 3 other statements are facts.

Sharala said: (Jun 5, 2015)  

But it has also said "Sometime and lies" sometimes doesn't indicate she is lying. So I agree with @Tash.

Vincent said: (Sep 1, 2015)  
All three are facts. If Ann has a cat 1 and 3 are true. If Ann does not have a cat three could not be a fact. Therefore, D is true. This is elementary logic.

Purusottam said: (Oct 10, 2017)  
You are absolutely right @Vincent.

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