Last visit was: 17 Jul 2025, 11:15 It is currently 17 Jul 2025, 11:15
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
Close
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
Your Progress

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
 1   2   3   
avatar
HongHu
avatar
Joined: 03 Jan 2005
Last visit: 25 Apr 2011
Posts: 966
Own Kudos:
793
 [54]
Posts: 966
Kudos: 793
 [54]
Since we have been working on some logical reasoning Updated on: 30 Mar 2005, 09:56
Originally posted by HongHu on 02 Mar 2005, 10:35.
Last edited by HongHu on 30 Mar 2005, 09:56, edited 4 times in total.
15
Kudos
Add Kudos
39
Bookmarks
Bookmark this Post
Since we have been working on some logical reasoning questions I'm going to try to collect the principles I'm following here for everybody's reference. Please feel free to discuss and add more. :)

If X then Y
This is the equivalent of: If non Y then non X.
Example: If it rains, then I will take an umbrella with me. I don't have a umbrella with me. That must mean it is not raining.

This is NOT equivalent to: If Y then X, or If Y then non X, or if non Y then X. In fact, if we know "If X then Y" and Y occurred, X may or may not happen.
Example. If it rains, then I will definitely take an umbrella with me. I have a umbrella with me today. Is it raining? It may or may not be raining. I said if it rains I will take an umbralla with me. But I could also take an umbralla with me just for the sake of it, even if it doesn't rain. By the same token, if it is not raining, do I have an umbralla with me? I may or may not have.

Using symbals:
X->Y<nonY>nonX
These two below are the same thing:
nonX->Y<nonY>X
X->nonY <Y>non X

Y if and only if X
This is the equivalent of: If X then Y, AND if Y then X. Also, if non X then non Y. If non Y then non X.

Example:
I will take an umbralla with me if and only if it rains. If it rains, then I have the umbralla with me. If I have the umbralla, then it must be raining. If I don't have the umbralla, then it mustn't be raining. If it isn't raining, then I don't have the umbralla with me.

Y unless X
This is the equivalent of: If non X then Y. Also, if non Y then X.

Example:
I will take an umbralla with me unless it is sunny. If it is not sunny, I will take an umbralla with me. If I don't have an umbralla with me, it must mean that it is sunny. However, if it is sunny, I may or may not take an umbralla with me. If I have my umbralla with me, it may or may not be sunny.
User avatar
prep_gmat
User avatar
Joined: 13 Oct 2004
Last visit: 11 Sep 2005
Posts: 113
Own Kudos:
56
 [1]
Posts: 113
Kudos: 56
 [1]
Since we have been working on some logical reasoning 02 Mar 2005, 12:52
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
This is sticky material!!.
Abstracting the info given in the stem is the way to attack the formal logic/paraellism questions. I was trying to keep all the information straight in my head and do the saurya's campaign stop q under 2 mins and got it wrong. I will internalize this, thanks.
User avatar
banerjeea_98
User avatar
Joined: 18 Nov 2004
Last visit: 17 May 2012
Posts: 676
Own Kudos:
199
 [8]
Posts: 676
Kudos: 199
 [8]
Since we have been working on some logical reasoning Updated on: 02 Mar 2005, 13:38
Originally posted by banerjeea_98 on 02 Mar 2005, 13:18.
Last edited by banerjeea_98 on 02 Mar 2005, 13:38, edited 1 time in total.
5
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
Good job....to put this in our heads mathematically, u can deduce these.


----> just like we inverse inequality sign when we multiply -ve, we can perhaps do the same for X---> Y

1) For X--> Y......-ve on both sides will give.....(non Y ----> non X)...note the relation is reversed i.e. Y to X now

2) For (non X ----> Y)......multiply-ve on both sides.....(non Y ----> X)

3) For (X----> non Y).....multiply-ve on both sides.....(Y-----> non X)

Just a thought on mathematical approach for easier recollection.
avatar
HongHu
avatar
Joined: 03 Jan 2005
Last visit: 25 Apr 2011
Posts: 966
Own Kudos:
793
 [1]
Posts: 966
Kudos: 793
 [1]
Since we have been working on some logical reasoning 02 Mar 2005, 13:26
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Good strategy! I'm making this sticky.
User avatar
Paul
User avatar
Joined: 15 Dec 2003
Last visit: 10 Nov 2012
Posts: 2,708
Own Kudos:
1,607
Posts: 2,708
Kudos: 1,607
Since we have been working on some logical reasoning 02 Mar 2005, 21:03
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Great post Honghu, it is often not easy to verbalize such abstract concepts :good
avatar
HongHu
avatar
Joined: 03 Jan 2005
Last visit: 25 Apr 2011
Posts: 966
Own Kudos:
793
 [12]
Posts: 966
Kudos: 793
 [12]
Since we have been working on some logical reasoning 03 Mar 2005, 11:19
5
Kudos
Add Kudos
7
Bookmarks
Bookmark this Post
Necessary conditions:

If A is a necessary condition of B, that means A must happen for B to happen. In other words, if B happened, A must be true. If A is not true, then B can't happen.

In summary: If B then A. If non A then non B.

Example: I will take my umbralla with me only if it rains.
Raining is a necessary condition for my taking the umbralla with me.
If it is not raining, you can be sure that I don't have my umbralla with me.

Sufficient conditions:

If A is a sufficient condition of B, that means if A happens B must happen. In other words, if B did not happen, A must be false.

In summary: If A then B. If non B then non A.

Example: I will take my umbralla with me if it rains.
Raining is a sufficient condition for me to take the umbralla with me.
If it is not raining, you are not sure whether I have my umbralla with me. But if I don't have my umbralla with me, you can be sure that it is not raining.

Necessary and sufficient
If A is a necessary and sufficient condition for B, that means if A happen B must happen, and if A does not happen, B does not happen. In other words, A=B. It is equivalent with B if and only if A.

In summary: If A then B. If B then A. If non B then non A. If non A then non B.

Example: I will take my umbralla if and only if it rains.
If it is raining, you can be sure I have the umbralla. If it is not raining, I don't have the umbralla. If I have my umbralla with me, you can be sure that it is raining. If I don't have it with me, it mustn't be raining.
User avatar
Rupstar
User avatar
Joined: 15 Feb 2005
Last visit: 12 Apr 2007
Posts: 116
Own Kudos:
13
Location: Rockville
Posts: 116
Kudos: 13
Since we have been working on some logical reasoning 03 Mar 2005, 12:27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
This is seriously an awesome post, our forum here is worth more than any kaplan course!:read
You guys are awesome!
:banana
User avatar
ywilfred
User avatar
Joined: 07 Jul 2004
Last visit: 06 Mar 2012
Posts: 1,989
Own Kudos:
2,014
Location: Singapore
Posts: 1,989
Kudos: 2,014
Since we have been working on some logical reasoning 05 Mar 2005, 18:27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Thanks Honghu, just what I was looking for ever since we've been working on logical reasoning CR question types, recently. :cool
avatar
HongHu
avatar
Joined: 03 Jan 2005
Last visit: 25 Apr 2011
Posts: 966
Own Kudos:
793
 [3]
Posts: 966
Kudos: 793
 [3]
Since we have been working on some logical reasoning 07 Mar 2005, 09:43
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
We have to be careful about sometimes, always, and never.

If A = always doing something
then non A = not doing something sometimes

If A = never doing something
then non A = doing something sometimes

If A = doing something sometimes
then non A = never doing something

If A = not doing something sometimes
then non A = always doing something

For example:

Birds sing sometimes. A never sings. Therefore A is not a bird.
Birds don't sing sometimes. A always sings. Therefore A is not a bird.

Compare to:

Birds always sing. A doesn't sing sometimes. Therefore A is not a bird.
Birds never sing. A sings sometimes. Therefore A is not a bird.

Compare to:
Birds sing sometimes. A sings sometimes. Is A a bird? We don't know. A may be a person who sings sometimes.
Birds sing sometimes. A doesn't sing sometimes. Is A not a bird? We don't know. A maybe a bird who sings sometimes and doesn't sing the other times.
User avatar
swath20
User avatar
Joined: 25 Oct 2004
Last visit: 05 Apr 2007
Posts: 141
Own Kudos:
296
Posts: 141
Kudos: 296
Since we have been working on some logical reasoning 07 Mar 2005, 16:47
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hong Thanks for the post its really awesome!!!
User avatar
Vijo
User avatar
Joined: 01 Jan 2005
Last visit: 11 Jul 2005
Posts: 76
Own Kudos:
8
Location: NJ
Posts: 76
Kudos: 8
Since we have been working on some logical reasoning 13 Mar 2005, 12:38
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Oh this is a gr8 post :circle
Thx Hong...
User avatar
chunjuwu
User avatar
Joined: 26 Apr 2004
Last visit: 01 Aug 2005
Posts: 541
Own Kudos:
4,741
Location: Taiwan
Posts: 541
Kudos: 4,741
Since we have been working on some logical reasoning 21 Mar 2005, 01:42
Kudos
Add Kudos
Bookmarks
Bookmark this Post
HongHu
Necessary conditions:

If A is a necessary condition of B, that means A must happen for B to happen. In other words, if B happened, A must be true. If A is not true, then B can't happen.

In summary: If B then A. If non A then non B.

Example: I will take my umbralla with me only if it rains.
Raining is a necessary condition for my taking the umbralla with me.
If it is not raining, you can be sure that I don't have my umbralla with me.

.


Hi, HongHu, first thanks for your great post.
I have a question. We often heard about a necessary condition is not a sufficient condition.

Does that mean it rains, but I may take or not take an umbrella?
avatar
HongHu
avatar
Joined: 03 Jan 2005
Last visit: 25 Apr 2011
Posts: 966
Own Kudos:
793
Posts: 966
Kudos: 793
Since we have been working on some logical reasoning 21 Mar 2005, 06:50
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Yes, that's very good. If raining is the necessary condition of me bringing the umbrella, then if I have the umbrella you know that it must be raining. However, if it is raining, I may or may not take the umbrella with me.
User avatar
Hjort
User avatar
Joined: 17 Jul 2004
Last visit: 06 Mar 2011
Posts: 3,248
Own Kudos:
517
Posts: 3,248
Kudos: 517
Since we have been working on some logical reasoning 25 Mar 2005, 01:27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
In the admissions context:

An undergraduate degree is a necessary condition for admission to Business School X

however

Holding an undergrad degree is not a sufficient condition for admission to School X since only 20% of applicants with undergraduate degrees are accepted each year
User avatar
ywilfred
User avatar
Joined: 07 Jul 2004
Last visit: 06 Mar 2012
Posts: 1,989
Own Kudos:
2,014
Location: Singapore
Posts: 1,989
Kudos: 2,014
Since we have been working on some logical reasoning 30 Mar 2005, 00:42
Kudos
Add Kudos
Bookmarks
Bookmark this Post
HongHu
Since we have been working on some logical reasoning questions I'm going to try to collect the principles I'm following here for everybody's reference. Please feel free to discuss and add more. :)

If X then Y
This is the equivalent of: If non Y then non X.
Example: If it rains, then I will take an umbrella with me. I don't have a umbrella with me. That must mean it is not raining.

This is NOT equivalent to: If Y then X, or If Y then non X, or if non Y then X. In fact, if we know "If X then Y" and Y, X may or may not happen.
Example. If it rains, then I will definitely take an umbrella with me. I have a umbrella with me today. Is it raining? It may or may not be raining. I said if it rains I will take an umbralla with me. But I could also take an umbralla with me just for the sake of it, even if it doesn't rain. By the same token, if it is not raining, do I have an umbralla with me? I may or may not have.

Using symbals:
X->Y<=>nonY->nonX
These two below are the same thing:
nonX->Y<=>nonY->X
X->nonY <=>Y->non X

Y if and only if X
This is the equivalent of: If X then Y, AND if Y then X. Also, if non X then non Y. If non Y then non X.

Example:
I will take an umbralla with me if and only if it rains. If it rains, then I have the umbralla with me. If I have the umbralla, then it must be raining. If I don't have the umbralla, then it mustn't be raining. If it isn't raining, then I don't have the umbralla with me.

Y unless X
This is the equivalent of: If non X then Y. Also, if non Y then X.

Example:
I will take an umbralla with me unless it is sunny. If it is not sunny, I will take an umbralla with me. If I don't have an umbralla with me, it must mean that it is sunny. However, if it is sunny, I may or may not take an umbralla with me. If I have my umbralla with me, it may or may not be sunny.


Hi Honghu,
for the if x then y section, you have this sentence: "This is NOT equivalent to: If Y then X, or If Y then non X, or if non Y then X. In fact, if we know "If X then Y" and Y, X may or may not happen. "

I think you meant: "In fact, if we know "If X then Y", then X may not or may not happen if Y occurs (y->not sure)"

Is that right ?
avatar
HongHu
avatar
Joined: 03 Jan 2005
Last visit: 25 Apr 2011
Posts: 966
Own Kudos:
793
Posts: 966
Kudos: 793
Since we have been working on some logical reasoning 30 Mar 2005, 09:55
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Yes, I meant If X then Y and if we know that Y occurs, X may or may not happen. I'll add the word "occurs" in the text for easy understanding. Thanks.
User avatar
jpv
User avatar
Joined: 05 Jul 2004
Last visit: 10 Jan 2012
Posts: 374
Own Kudos:
227
Posts: 374
Kudos: 227
Since we have been working on some logical reasoning 11 Apr 2005, 17:04
Kudos
Add Kudos
Bookmarks
Bookmark this Post
1. My Dog Dylan loves being brushed. At the moment, he is not a happy doggie, so I can't have just brushed him.

If X, then Y => Not Y, then Not X
if I brush my Dog, he will love it => He is not happy, I can't have brushed him
CORRECT LOGIC.

2. Dylan barks loudly when he is alarmed or frightened. One night I woke up when he barked fiercely. I concluded that he must have been either alarmed or frightened, so I tiptoed down the stairs expecting to find a burglar in the house. Was my conclusion a logical one?

When Dylan is alarmed or frightened ==> Dylan barks loudly
Dylan barked loudly ==> alarmed or frightened.

Wrong Logic

Correct logic is :
If X, Then Y ==>
a) X then Y or
b) Not Y, Not X

Please correct me if I am wrong.
User avatar
jpv
User avatar
Joined: 05 Jul 2004
Last visit: 10 Jan 2012
Posts: 374
Own Kudos:
227
Posts: 374
Kudos: 227
Since we have been working on some logical reasoning 11 Apr 2005, 17:05
Kudos
Add Kudos
Bookmarks
Bookmark this Post
1. Whenever the red light is on and the green light is off, it means that the protection shields are no longer in place covering the uranium core. The protection shields are covering the uranium core, yet the green light is off. This means that the red light must be off also.

Logic:
(A)
If a, then b => Not b, Not a

(B)
If Not(X and Y) ==> (X is true, Not Y) or (Y is true, Not X): Correct Logic
If Not(X and Y) ==> (X is Not true, Y true) or (Y is Not true, X): Wrong Logic

So, in the question:
(red is on) and (green is off) ==> (No Protection shield)
using (A)
(There is Protection shield) ==> Not((red is on) and (green is off))

Now we have for second Part (using B):
Not((red is on) and (green is off)) ==> (green is off), (red is off) [x, not y]
So logically Correct.

2. My biology text book tells me that no birds are mammals. I conclude that no mammals are birds.
No birds are mammals.
=> X (no birds) -> Y(mammals)
=> No Y [no (mammals)] -> No X [no (no birds)]
=> no mammals -> birds
Logically Correct.


3. Our leisure centre had a budget of £100,000 last year to be spent on a swimming pool costing £60,000 or a gymnasium costing £55,000. We went ahead and ordered the swimming pool to be built. Therefore we did not spend any money on having a gymnasium built last year.
Logic:
(X or Y) == Not(X and Y) => (X is true, Not Y) or (Y is true, Not X): Correct Logic
(spent 60k on swimming pool) or (spent 55k in gymnasium) => (spent 60k on swimming pool), Not (spent 55k in gymnasium)
So statement is Logically correct

Please correct me if I am wrong.
avatar
smjohn
avatar
Joined: 03 Jun 2005
Last visit: 21 Dec 2005
Posts: 12
Own Kudos:
3
Posts: 12
Kudos: 3
Since we have been working on some logical reasoning 03 Jun 2005, 16:38
Kudos
Add Kudos
Bookmarks
Bookmark this Post
HongHu
Since we have been working on some logical reasoning questions I'm going to try to collect the principles I'm following here for everybody's reference. Please feel free to discuss and add more. :)

If X then Y
This is the equivalent of: If non Y then non X.
Example: If it rains, then I will take an umbrella with me. I don't have a umbrella with me. That must mean it is not raining.

This is NOT equivalent to: If Y then X, or If Y then non X, or if non Y then X. In fact, if we know "If X then Y" and Y occurred, X may or may not happen.
Example. If it rains, then I will definitely take an umbrella with me. I have a umbrella with me today. Is it raining? It may or may not be raining. I said if it rains I will take an umbralla with me. But I could also take an umbralla with me just for the sake of it, even if it doesn't rain. By the same token, if it is not raining, do I have an umbralla with me? I may or may not have.


I didn't Understand this.
First, You said that 'if it rains, then I will take an umbrella with me.' The 'If/then' here is a condition that implies that you will take an umbrella "only" if it is raining. Does GMAT have such devious logic?
avatar
HongHu
avatar
Joined: 03 Jan 2005
Last visit: 25 Apr 2011
Posts: 966
Own Kudos:
793
Posts: 966
Kudos: 793
Since we have been working on some logical reasoning 03 Jun 2005, 22:27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Yes, GMAT tests this kind of logic all the time.

If x then y is NOT equivalent to Y only if X. In if x then y, x is the sufficient condition of y. In Y only if X, X is the necessary condition of Y.
 1   2   3   
Moderators:
GMATNinja
GMAT Club Verbal Expert
7359 posts
GMATNinjaTwo
GMAT Club Verbal Expert
235 posts
Sajjad1994
GRE Forum Moderator
15854 posts