A conceptual Question

Question

Hello Everybody,

I saw the below question in a course on logical thinking. It's an interesting question that tests how precisely ones understands a statement, a critical skill tested heavily in the GMAT CR section. Data says that 70% of the people get the answer wrong.

Statement: If a card has a vowel on one side, then it has an even number on the other side.

Flipping which of the following cards will help you in verifying the correctness of the above statement? (Multiple cards may be helpful)

Attachment:

Picture2.jpg

I'll post the answer in a few hours.

arvany · Answer

I think flipping card with even number(ie, 8) will help to validate this statement. This is a sufficient condition statement, which says that if a vowel on one side then it will have even no on other side of the card. So, taking an analogy to this ques, this is similar to saying that if I take this route then I will reach Delhi. Now, even if I don't take this route that doesn't mean that I will not reach Delhi. But if I have reached Delhi then I must have taken this route. So, by this logic. If card is showing even number on its one face then it must have a vowel on other side.

Am I correct, CJ?

-Arvind

Posted from my mobile device

Am I correct, CJ?

-Arvind

Posted from my mobile device

PKN · Answer

If a card has a vowel on one side, then it has an even number on the other side.

a) If something is ON, "flip of something" is OFF.

OR

b) If something is BLACK, "flip of something" is WHITE.

Here, the cases to verify the correctness of the given statement could be:-

a) If a card has a vowel on one side, then it has an ODD number on the other side.
  A3

b) If a card has a CONSONANT on one side, then it has an even number on the other side.
  X8

Amankatyal · Answer

Answer is card showing Vowel "A". 
It is simple, Card has vowel, flipping the card should reveal an even number and if not then the statement doesn't hold.

Why i didn't choose 8, because the statement doesn't say :-
an even number on one side, will reveal a vowel on flipping ...!!!

Rest other are also wrong, using same reasoning !!!

tarunanandani · Answer

I think flipping the cards '3' and 'A' will help to evaluate the correctness of the statement.
Flipping '8' will not help because it is not mentioned that 'vowel on one side' is the only condition to have an even number on the other side. It is possible that both sides of the card have numbers.
Similarly, flipping 'X' also will not help because it is a possibility that a consonant on one side can also have an even number on the other side.
Flipping card '3' will confirm the statement if on its other side there isn't a vowel. Anything other than a vowel can have a odd number on the other side. So, flipping '3' will help to confirm whether its other side has a vowel.
Flipping 'A' will help to directly check the statement, i.e., it must have an even number on its other side for the validity of the statement.

Salsanousi · Answer

I think this probably follows conditional statement

Where sufficient > necessary?

If x then y

Not y then not x

Here if vowel then even

Not even then not vowel.

I think A and 3 will help

Posted from my mobile device

ChiranjeevSingh · Answer

Statement: If a card has a vowel on one side, then it has an even number on the other side.

First of all, we need to understand that the statement means the following:
1. Every card with a vowel on one side will have an even number on the other side.
2. A card which doesn't have an even number on one side cannot have a vowel on another side. (since if it had had a vowel on another side, it would have had an even number on the initial side)
3. No information is given about cards which don't have vowels on one side. They may have even numbers or odd numbers on the other side. (Assuming that each card has an alphabet on one side and an integer on another side.)
4. Based on points 1 and 3 above, we can say that a card with an even number on one side can have a vowel or a consonant on another side.

Thus, we can say that the statement doesn't make any conclusive statement about cards which have either a consonant or an even number on one side.

Thus, we'll not be able to verify the statement by flipping over X or 8.

However, the statement makes conclusive statements about cards which have either a vowel (must have an even number on another side) or an odd number on one side (cannot have a vowel on another side).

Thus, flipping over the card with A and the card with 3 will help us verify the truth value of the statement.

If we don't make the assumption made in point 3 above, flipping over the card with 'X' would also be helpful since per the statement, it cannot have a vowel on another side.

Hope it helps!

- CJ

arvany · Answer

Thanks CJ. Messed up point no 2.

Should have done it correctly. ques was quite doable.

A conceptual Question

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