Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 20 Jul 2019, 15:36 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If A, then B. If B, then C. If C, then D. If all of the statements abo

Author Message
TAGS:

### Hide Tags

Intern  Joined: 24 Jun 2010
Posts: 7
If A, then B. If B, then C. If C, then D. If all of the statements abo  [#permalink]

### Show Tags

1
16 00:00

Difficulty:   65% (hard)

Question Stats: 42% (01:02) correct 58% (01:05) wrong based on 532 sessions

### HideShow timer Statistics 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.

Why is the official answer C ?

For example, choice B could be correct too. If not B then not C.

Originally posted by kimakim on 07 Sep 2010, 04:32.
Last edited by Bunuel on 01 Oct 2018, 22:24, edited 1 time in total.
Renamed the topic and edited the question.
Manager  Joined: 06 Aug 2010
Posts: 167
Location: Boston
Re: If A, then B. If B, then C. If C, then D. If all of the statements abo  [#permalink]

### Show Tags

9
2
utin wrote:
TehJay wrote:
kimakim 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.

Why is the official answer C ?

For example, choice B could be correct too. If not B then not C.

We're given A -> B, B -> C, and C -> D, and told they're all true. Since they're all true, you can say A -> D. Then by the law of contrapositive, ~D -> ~A. The answer is (C).

(B) isn't correct - this is the inverse of B -> C and does not have the same truth table.

CAN'T UNDERSTAND STILL!!! Ok, consider a simple example:

If I eat dinner now, I will eat dessert later. (A -> B)

You're told this is a TRUE statement - in other words, eating dinner absolutely, positively, no question about it, 100% results in eating dessert after. There's no possible situation that can exist where I will eat dinner now and then NOT eat dessert later.

Now consider the below statements:

If don't eat dessert later, I didn't eat dinner now. (contrapositive: ~B -> ~A)

Since we KNOW FOR A FACT that eating dinner now results in eating dessert later, we can conclude without a doubt that if I don't eat dessert, I most definitely did not eat dinner (because if I had eaten dinner, I would have eaten dessert). This is called the contrapositive and is logically equivalent to the original statement. (This is answer C)

If I don't eat dinner now, I won't eat dessert later. (inverse: ~A -> ~B)

We know for a fact that eating dinner will lead to eating dessert. However, we know absolutely nothing about the result of NOT eating dinner. I didn't say to you that I would ONLY eat dessert if I eat dinner first - only that I would definitely eat it after eating dinner. This statement is not logically equivalent to the original. This is called the inverse, and is answer B.

Does this help?
##### General Discussion
Manager  Joined: 06 Aug 2010
Posts: 167
Location: Boston
Re: If A, then B. If B, then C. If C, then D. If all of the statements abo  [#permalink]

### Show Tags

5
2
kimakim 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.

Why is the official answer C ?

For example, choice B could be correct too. If not B then not C.

We're given A -> B, B -> C, and C -> D, and told they're all true. Since they're all true, you can say A -> D. Then by the law of contrapositive, ~D -> ~A. The answer is (C).

(B) isn't correct - this is the inverse of B -> C and does not have the same truth table.
Intern  Joined: 24 Jun 2010
Posts: 7
Re: If A, then B. If B, then C. If C, then D. If all of the statements abo  [#permalink]

### Show Tags

TehJay wrote:
kimakim wrote:

We're given A -> B, B -> C, and C -> D, and told they're all true. Since they're all true, you can say A -> D. Then by the law of contrapositive, ~D -> ~A. The answer is (C).

(B) isn't correct - this is the inverse of B -> C and does not have the same truth table.

Yes, the logic is right, if we assume that ALL of the statement should be exist at the same time.
But consider if there is only C. Then C->D, and we don;t need A or B to come up with D. Hence if "not D" doesn't imply "not A".

On the other hand answer B "If not B then not C" is right, when we assume that all statements can exist independently of each other.

So, I am still confused Manager  Joined: 06 Aug 2010
Posts: 167
Location: Boston
Re: If A, then B. If B, then C. If C, then D. If all of the statements abo  [#permalink]

### Show Tags

3
kimakim wrote:
TehJay wrote:
kimakim wrote:

We're given A -> B, B -> C, and C -> D, and told they're all true. Since they're all true, you can say A -> D. Then by the law of contrapositive, ~D -> ~A. The answer is (C).

(B) isn't correct - this is the inverse of B -> C and does not have the same truth table.

Yes, the logic is right, if we assume that ALL of the statement should be exist at the same time.
But consider if there is only C. Then C->D, and we don;t need A or B to come up with D. Hence if "not D" doesn't imply "not A".

On the other hand answer B "If not B then not C" is right, when we assume that all statements can exist independently of each other.

So, I am still confused You're told that all of them are true, so you can't just take them independently and pretend that A doesn't exist. Also, irregardless of whether you're looking at A or not, (B) cannot be correct. This is the logical inverse, which is a fallacy. In logic, when dealing with implications, p -> q is equivalent to ~q -> ~p, but not equivalent to ~p -> ~q (inverse) or q -> p (converse). To see this, you can draw up the truth tables:

Attachment: Truth Table.jpg [ 59.45 KiB | Viewed 11182 times ]
Retired Moderator Joined: 02 Sep 2010
Posts: 755
Location: London
Re: If A, then B. If B, then C. If C, then D. If all of the statements abo  [#permalink]

### Show Tags

1
the statement "if A then B" is exactly the mathematical equation (A or not(B))

the three statements together, are three simultaneous equations which solve to give (A or (not(D)) [which logical deduction can tell you]

and finally :

(A or Not(D)) = (not(not(A)) or not(D)) = (not(D) or not(not(A))) = "if not D then not A"
_________________
Manager  Joined: 04 Apr 2009
Posts: 50
Location: United Kingdom
Schools: Cornell
Re: If A, then B. If B, then C. If C, then D. If all of the statements abo  [#permalink]

### Show Tags

2
I learned this today (forgot the original poster but kudos to him). His/her quote went as
If A then B , could be rephrased as if Not B then Not A and if B then may be A.

Take the example of: If I am in France, I am in Europe

If I am not in Europe, I am not in France. ( Not B then Not A)

If I am in Europe, I may be in France ( B then may be A).

All other violate this logical rule or add extra information.

So in the given example by reversing all the signs we get....
~D => ~C
~C => ~B
~B => ~A
Thus simply substituting....
~D => ~A
Retired Moderator Joined: 20 Dec 2010
Posts: 1733
Re: If A, then B. If B, then C. If C, then D. If all of the statements abo  [#permalink]

### Show Tags

1
1
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 saw the OA in the mail but C does make sense.

(A) If D, then A
A will definitely result in D doesn't mean someone else can't trigger D. Maybe Z can spawn D. So, we can have D by Z. A is nowhere in the picture.

(B) If not B, then not C.
Same logic as before. C is triggered by B doesn't mean ONLY B can trigger C. GHOST may trigger C. So, we have GHOST and C., and no B. This becomes false.

(C) If not D, then not A.
Definitely true. If we don't see D, it means there CAN't be A. Know this. As soon as A appears, at least B,C,D also appear. Thus, if don't see D, there can't be any A. However, if we see D, there is no guarantee that A is there. CORRECT.

(D) If D, then E.
What is E.

(E)If not A, then not D.
As I said in option "C", D can be spawned by something else. Say GHOST->C->D
Not true.

Ans: "C"
_________________
Manager  Joined: 04 Jun 2011
Posts: 141
Re: If A, then B. If B, then C. If C, then D. If all of the statements abo  [#permalink]

### Show Tags

ok here's a simpler way, if you are good with quant inequalities

if A -- > B, if B -- C , If C -- >

which implies if A -- > D

if you negate, then it becomes the opposite ~D -- > ~A which is C
Manager  Joined: 16 May 2011
Posts: 171
Concentration: Finance, Real Estate
GMAT Date: 12-27-2011
WE: Law (Law)
Re: If A, then B. If B, then C. If C, then D. If all of the statements abo  [#permalink]

### Show Tags

1
viks4gmat wrote:
ok here's a simpler way, if you are good with quant inequalities

if A -- > B, if B -- C , If C -- >

which implies if A -- > D

if you negate, then it becomes the opposite ~D -- > ~A which is C

well i love the Qyant approach: did you mean to say something like:

IF (POSITIVE) A>B>C>D THEN THE IF NOT (NEGATIVE) WILL BE LIKE MULTIPLYING BY -(1) WHICH REVERSES THE INEQUALITY TO IF NOT D>NOT C> NOT B> NOT A
Manager  Joined: 04 Jun 2011
Posts: 141
Re: If A, then B. If B, then C. If C, then D. If all of the statements abo  [#permalink]

### Show Tags

1
dimri10 wrote:
viks4gmat wrote:
ok here's a simpler way, if you are good with quant inequalities

if A -- > B, if B -- C , If C -- >

which implies if A -- > D

if you negate, then it becomes the opposite ~D -- > ~A which is C

well i love the Qyant approach: did you mean to say something like:

IF (POSITIVE) A>B>C>D THEN THE IF NOT (NEGATIVE) WILL BE LIKE MULTIPLYING BY -(1) WHICH REVERSES THE INEQUALITY TO IF NOT D>NOT C> NOT B> NOT A

yup thats pretty much what i intend to say !!!

if A> B> C > D then negating/ NOT-ing the components simply changes the direction of the sign
-A < -B < -C < -D (or -D> -C > -B > -A whichever way you are comfortable reading the equation from )
Manager  Status: mba here i come!
Joined: 07 Aug 2011
Posts: 200
Re: If A, then B. If B, then C. If C, then D. If all of the statements abo  [#permalink]

### Show Tags

good question. i have an even better trick for such questions. i solved the question in 1:17; i could've done that even earlier. here's the trick.

a->b

to find what else can be true, reverse the order of a,b and make them logical negations of themselves.

a->b= b'->a'
"if A, then B" = "if not B, then not A"

e.g. if it is cloudy, it will rain.
if it is not cloudy, then it will not rain (incorrect. we're not sure)
if it is raining, then it is cloudy (incorrect. again may be it also rains when there are no clouds. we don't know)

if it is not raining, then it is not cloudy (bingo! correct ans)
_________________
press +1 Kudos to appreciate posts
Intern  B
Joined: 21 Jan 2017
Posts: 32
Re: If A, then B. If B, then C. If C, then D. If all of the statements abo  [#permalink]

### Show Tags

kimakim 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.

Why is the official answer C ?

For example, choice B could be correct too. If not B then not C.

This question requires a good calculation in the background. One thing to remember is "if A then B does not imply the presence of B is only by A". It only implies that "if A is present, then B must be present".

Option A is incorrect because D might not necessarily imply that C is present and so B and A.
Option B is incorrect as if not B , there are chances of C to be present. Not necessarily true.
Option C is correct as if not D then no C.There is no B without C. There is no A without B.
Option D is irrelevant
Option E is also incorrect as if not A, there can be B. So with C and D.

Thanks,
Uma
Senior Manager  P
Joined: 26 Jun 2017
Posts: 404
Location: Russian Federation
Concentration: General Management, Strategy
WE: Information Technology (Other)
Re: If A, then B. If B, then C. If C, then D. If all of the statements abo  [#permalink]

### Show Tags

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.
------

Known one.

Why C is right. Because if D did not happen than A did not happen.
Because we know if A were true than D would become true
Director  P
Joined: 02 Oct 2017
Posts: 727
Re: If A, then B. If B, then C. If C, then D. If all of the statements abo  [#permalink]

### Show Tags

Concept of Negation

IF A =B
then Not B=Not A not vice versa
therefore applying the same rule

we can deduce C to be correct answer
_________________
Give kudos if you like the post
Manager  B
Joined: 28 Jun 2018
Posts: 74
Re: If A, then B. If B, then C. If C, then D. If all of the statements abo  [#permalink]

### Show Tags

With all due respect, I think this question is BS.
Non-Human User Joined: 01 Oct 2013
Posts: 4816
Re: If A, then B. If B, then C. If C, then D. If all of the  [#permalink]

### Show Tags

Hello from the GMAT Club VerbalBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: If A, then B. If B, then C. If C, then D. If all of the   [#permalink] 07 Jul 2019, 11:56
Display posts from previous: Sort by

# If A, then B. If B, then C. If C, then D. If all of the statements abo  