If A, then B. If B, then C....

figs wrote:If A, then B.
If B, then C.
If C, then D.

If all of the statements above are true, which of the following must also be true?
A. If D, then A
B. If not B, then not C
C. If not D, then not A
D. If D, then E
E. If not A, then not D

I would like to think of all the three statements independent and represent below:

A->B
B->C
C->D

A) It cannot be true.
C) It cannot be true.
D) Out of scope.
E) It cannot be true.
B) If not B then not C is true.

The answer is B.

IMO B

would go for C

If A, then B.
If B, then C.
If C, then D

=>if A then D
=>if not D, then not A

figs wrote:If A, then B.
If B, then C.
If C, then D.

If all of the statements above are true, which of the following must also be true?
A. If D, then A
B. If not B, then not C
C. If not D, then not A
D. If D, then E
E. If not A, then not D

My answer: None of the above.

B sounds like a plausible choice at first, but not B doesn't necessarily imply not C.
If it rains tomorrow, I will have hot chocolate.
If it doesn't rain tomorrow, I will also have hot chocolate (or I may not).

figs wrote:If A, then B.
If B, then C.
If C, then D.

If all of the statements above are true, which of the following must also be true?
A. If D, then A
B. If not B, then not C
C. If not D, then not A
D. If D, then E
E. If not A, then not D

Figs can you post the OA pls?

KICKGMATASS123 wrote:

figs wrote:If A, then B.
If B, then C.
If C, then D.

If all of the statements above are true, which of the following must also be true?
A. If D, then A
B. If not B, then not C
C. If not D, then not A
D. If D, then E
E. If not A, then not D

Figs can you post the OA pls?

The OA is C

This is a logic problem and we shouldn't be expecting this as part of the GMAT. I am going to show how we can get it from truth table.

(-> is then) From the given information, we can conclude that A->D is true. I will construct the truth table using https://en.wikipedia.org/wiki/Truth_tabl ... mplication
T= TRUE
F=FALSE

Please look at the file attached.

A->D and ~D->~A have the same truth table and hence is the right answer.

Another (slightly simplified) way of seeing this is as follows:

A implies B
B implies C
C implies D

all together imply that A implies D. By the contrapositive (not converse!), we have that not D implies not A. Generally, for ALL statements, if A implies B, then "not B" implies " not A".

For example, if you're a human, you have a brain. If you don't have a brain, you're not a human.

Cannot decide between A and B. Can anyone brake down these two choices for me please

Hello


would you explain more?

I thought in this way:

a: staying hungry
b: getting sick
c: leaving work
d: no money!

then if A doesn't happen, D will not happen
but D can happen independently
am I wrong??