Mary has qualified to become a police officer. Has Albert qualified

Interesting to see a logical question!

As Chetan has already explained, suppose you are given a FACT, which is:

If A, then B (or if cause, then effect)... then there is one more conclusion that you can draw from this, which is:
If not B, then not A (if no effect, then no cause).

Probably it will be more clear as we go with the statements.

(1) If A becomes officer, them M will become officer.

But this doesn't mean that M will become officer only if A becomes officer. M can be officer without A being an officer too. This also implies that M becoming an officer doesn't guarantee that A must have become an officer (as just explained, M can be officer without A being an officer too). So we cannot guarantee that A has become an officer. Not Sufficient.

(2) This statement can also simply be read as, "M cannot become officer unless A has already become an officer". So if we add this information to the info in the question that M has become an officer, then there is no doubt that A also must have become an officer. (else how will M become). This statement is sufficient.
we can also use the logic explained previously. If (A is not officer), then (M is not officer)
If we read above as 'If X, then Y' then we can draw another conclusion: 'If not Y, then not X'. Thus If (M is officer), it means (A is officer)

Hence B answer

I'm sorry but I don't understand explanation from Both above experts....

Let me tell u why............

Question stem = M is Police AT PRESENT , Has A become Police yet?

1) IF A becomes Police THEN M will(CERTAINLY) (IN FUTURE) be police as well

So ITS CERTAIN THAT M will be Police if A becomes a police

So This certainty shows that M is POLICE which means A is already a POLICE IN PAST

2) IF A doesn't become Police , then M will(Certainity) not become Police

SO M is dependent on A ...If A cant do it then M also cant

Hence If M has done it its SURE THAN A has done it already


HOW CAN D not be an answer?

Hi..
You are absolutely correct till So ITS CERTAIN THAT M will be Police if A becomes a police
..
But it is not certain that if M is police officer, A will also be police officer..

Let me explain you with circles/sets..
If A then B means A is a subset of B, that is B is a larger circle while A is a smaller circle completely inside it...
Now there will be areas in bigger circle B, where A is not there..
So it is possible that B is there but A is not there..
Draw it and you will understand.

Hi

Please refer to the highlighted part once again. If you are given a universal truth of this type:
If 'Cause', then 'Effect'.

So if a certain cause takes place, then a particular effect will also take place.
But does this above statement also make it mandatory that this particular cause only will lead to this particular effect? That is not necessary, because this effect could have been due to some other cause too.

Say if we know for certain that:- 'If Government releases memo, Democrats will protest'. Consider for a moment this statement to be truth.

If memo is released, Demos will protest. But does this statement also mean that 'Democrats will protest only if Government releases memo'.. Not necessary. Democrats could protest for a number of other reasons too.
So If we are given that memo is released, we can be sure that Democrats will protest. But if instead we are given that Democrats have protested, we cannot be sure that memo has been released - Democrats could have protested for some other reason also.

Lets now try to apply same logic in this question - statement 1. If A becomes police, M will become police.
So if we know that A has become police, we can be sure that M will be police.
But if we know that M has become police, we cannot be sure that A has also become police; as A becoming police was not the only condition for M to have become police.

Wow , a CR question in Data Sufficiency.

Contrapositive rules !

if A -> B
Contrapositive: ~B -> ~A

Question: (Albert qualified) ?

Statement 1:
Mistaken reversal case
if A -> B, then if B -> Need not be A.
similiarly, if Albert qualified -> Mary is qualified
then if Mary is qualifed, does not mean Albert is qualifed -> insuff

Statement 2:
If Albert does not qualify to become a police officer, then Mary will not qualify to become a police officer.
if ~Albert -> ~Mary
taking contrapositive: Mary -> Albert, so Albert is qualified, as Mary is qualified => sufficient

(B)

This is question where we have see the dependency of one event over other called Causality

Statement 1: If Albert qualifies to become a police officer, then Mary will qualify to become a police officer.

This statement ensures that Mary is qualified if Albert qualifies
BUT
It doesn't take into account what happens if Albery fails. Hence, the conclusion is that mary may or may not qualify if albert fails

Hence
Mary may qualify alongwith qualification of Albert as well as Albert's disqualification hence

NOT SUFFICIENT

Statement 2: If Albert does not qualify to become a police officer, then Mary will not qualify to become a police officer.

This states that mary can't qualify if albert fails therefore it becomes necessary that Albert qualifies if Mary has to qualify

The given premise is that mary qualifies hence Albert must be qualified as well hence

SUFFICIENT

Answer: option B