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A sufficient condition can be defined as an event or

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A sufficient condition can be defined as an event or  [#permalink]

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New post 11 Apr 2013, 22:31
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A sufficient condition can be defined as an event or circumstance whose occurrence indicates that a necessary condition must also occur.
A necessary condition can be defined as an event or circumstance whose occurrence is required in order for a sufficient condition to
Occur.

If a sufficient condition occurs, it means that the necessary condition MUST occur. But if a necessary condition occurs, then it is possible but not certain that the sufficient condition will occur.
The assumption underlying a conditional statement is that the necessary condition must occur in order for the sufficient condition to occur.

Can somebody explain the meaning of highlighted sentence in the light of 3 statements mentioned above. If possible, kindly explain with proper examples.

Fame
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Re: Necessary Condition  [#permalink]

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New post 11 Apr 2013, 23:22
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fameatop wrote:
A sufficient condition can be defined as an event or circumstance whose occurrence indicates that a necessary condition must also occur.
A necessary condition can be defined as an event or circumstance whose occurrence is required in order for a sufficient condition to
Occur.

If a sufficient condition occurs, it means that the necessary condition MUST occur. But if a necessary condition occurs, then it is possible but not certain that the sufficient condition will occur.

Can somebody explain the meaning of highlighted sentence in the light of 3 statements mentioned above. If possible, kindly explain with proper examples.

Fame


@fameatop.
I'm happy to help.

Just a small example to understand NECESSARY condition & SUFFICIENT condition.

EXAMPLE:

If you want to be a CPA, you must pass CPA exams (1)
If you want to sit for CPA exams, you need at least 150 college credits. (2)

(1) is the Sufficient condition, it means you will be a CPA ONLY IF you pass CPA exams.
(2) is the Necessary condition, it means that you're eligible for taking CPA exams ONLY IF you earned 150 college credits.

ANALYSIS:

If sufficient condition occurs - you pass CPA exams, it means that necessary condition MUST occur - you MUST have 150 college credits. If you do not have 150 college credit, you're not eligible for taking CPA exams.

On the other hand, If necessary condition occurs - you earned 150 college credits, then it is possible but not certain that sufficient condition will occur - you MAY or MAY NOT PASS CPA exams.

Hope it's clear
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Re: Necessary Condition  [#permalink]

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New post 11 Apr 2013, 23:48
Let me take a shot :o
A necessary condition can be defined as an event or circumstance whose occurrence is required in order for a sufficient condition to
Occur.

Example: When I run for a mile or more, I get breathless. I don't get breathless any other time.

Necessary - To run for a mile or more..
Sufficient - To know that I was breathless..implying I must have run a mile or more..

The assumption underlying a conditional statement is that the necessary condition must occur in order for the sufficient condition to occur.

Example: People who work very hard score well on the GMAT. Rick scored a 700+ on the GMAT, so he must have worked hard.

Sufficient: 700+ on the GMAT
Necessary: worked hard

Assumption is that Rick worked hard to get his GMAT 700+ score..

Let me know if it makes sense ... I am a retake junkie who aspires to get better at CR :D
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Re: Necessary Condition  [#permalink]

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New post 12 Apr 2013, 17:19
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fameatop wrote:
A sufficient condition can be defined as an event or circumstance whose occurrence indicates that a necessary condition must also occur.
A necessary condition can be defined as an event or circumstance whose occurrence is required in order for a sufficient condition to
Occur.

If a sufficient condition occurs, it means that the necessary condition MUST occur. But if a necessary condition occurs, then it is possible but not certain that the sufficient condition will occur.
The assumption underlying a conditional statement is that the necessary condition must occur in order for the sufficient condition to occur.

Can somebody explain the meaning of highlighted sentence in the light of 3 statements mentioned above. If possible, kindly explain with proper examples.

Fame

I'm happy to help. :-)

First of all, keep in mind that "necessary & sufficient are complementary conditions -----
If A is necessary for B, then B is sufficient for A.
Let A = the car has gas in its tank
B = one can turn this car on and drive it from place to place
OR
A = polygon is a rectangle
B = polygon is a square
OR
A = I am in California
B = I am in San Francisco, CA

Now, your sentence: "If a sufficient condition occurs, it means that the necessary condition MUST occur. But if a necessary condition occurs, then it is possible but not certain that the sufficient condition will occur."
If the car moves, then it must have gas. If all you know is that the car has gas, it may or may not turn on (what if the battery is missing?)
If the polygon is square, it is definitely a rectangle as well. If the polygon is a rectangle, then it may or may not be a square.
If I am in SF, I'm definitely in CA, but if I'm in CA, I could be a number of places other than SF ---- LA, San Diego, Lake Tahoe, Yosemite, etc etc.

The terms "necessary" and "sufficient" are alternate ways of phrasing "if-then" statements. The following four statements all say the same thing:
(1) If P, then Q
(2) Only if Q, then P.
(3) P is necessary for Q
(4) Q is sufficient for P

Incidentally, this is why "J if and only if K" is equivalent to "J is necessary and sufficient for K".

Does all this make sense?

Mike :-)
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Re: A sufficient condition can be defined as an event or  [#permalink]

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New post 21 Oct 2019, 04:37
mikemcgarry wrote:
fameatop wrote:
A sufficient condition can be defined as an event or circumstance whose occurrence indicates that a necessary condition must also occur.
A necessary condition can be defined as an event or circumstance whose occurrence is required in order for a sufficient condition to
Occur.

If a sufficient condition occurs, it means that the necessary condition MUST occur. But if a necessary condition occurs, then it is possible but not certain that the sufficient condition will occur.
The assumption underlying a conditional statement is that the necessary condition must occur in order for the sufficient condition to occur.

Can somebody explain the meaning of highlighted sentence in the light of 3 statements mentioned above. If possible, kindly explain with proper examples.

Fame

I'm happy to help. :-)

First of all, keep in mind that "necessary & sufficient are complementary conditions -----
If A is necessary for B, then B is sufficient for A.
Let A = the car has gas in its tank
B = one can turn this car on and drive it from place to place
OR
A = polygon is a rectangle
B = polygon is a square
OR
A = I am in California
B = I am in San Francisco, CA

Now, your sentence: "If a sufficient condition occurs, it means that the necessary condition MUST occur. But if a necessary condition occurs, then it is possible but not certain that the sufficient condition will occur."
If the car moves, then it must have gas. If all you know is that the car has gas, it may or may not turn on (what if the battery is missing?)
If the polygon is square, it is definitely a rectangle as well. If the polygon is a rectangle, then it may or may not be a square.
If I am in SF, I'm definitely in CA, but if I'm in CA, I could be a number of places other than SF ---- LA, San Diego, Lake Tahoe, Yosemite, etc etc.

The terms "necessary" and "sufficient" are alternate ways of phrasing "if-then" statements. The following four statements all say the same thing:
(1) If P, then Q
(2) Only if Q, then P.
(3) P is necessary for Q
(4) Q is sufficient for P

Incidentally, this is why "J if and only if K" is equivalent to "J is necessary and sufficient for K".

Does all this make sense?

Mike :-)


Hi mikemcgarry,

Sorry for digging up such an old thread. I was reading this post and I think there is an error here. From what I understand, If (Sufficient Condition), then (Necessary Condition). Meaning P = Sufficient Condition and Q = Necessary Condition.

Then, shouldn't (3) be Q is necessary for P and (4) P is sufficient for Q. I spent nearly 20 mins trying to understand that and then googled it. Here is what I found on Wikipedia. ""If P then Q", Q is necessary for P, because P cannot be true unless Q is true. Similarly, "P is sufficient for Q" because P being true always implies that Q is true, but P not being true does not always imply that Q is not true." Here is the link to the article: https://en.wikipedia.org/wiki/Necessity_and_sufficiency

Let me know if I'm mistaken. Thank you.

Best, Aditya
GMAT Club Bot
Re: A sufficient condition can be defined as an event or   [#permalink] 21 Oct 2019, 04:37
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