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Fraction-Please help me with my logic

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Fraction-Please help me with my logic

by zazoz » Wed May 29, 2013 10:56 pm
if rs isn't 0, is (1/r)+(1/s)=4

1)r+s=4rs
2)r=s

I think it's a simple problem. I wonder, why statement 2 is insufficient? When I plug statement 2 into the original equation, the only answer it gives me is r=s=1/2 and the equation will be correct, so why statement 2 is insufficient? Please explain me where I went wrong?
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by srcc25anu » Wed May 29, 2013 11:45 pm
st2: r=s
if r = s = 1, 1/r + 1/s = 2 (not 4) but if r = s = 1/2, them 1/r + 1/s = 4
hence insufficient

and when you put r = s in the original equation it solves r = s = 1/2 but that does not mean r = s are actually 1/2 each. r and s could assume many other values and the only restriction is that either r or s is not 0.
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by zazoz » Thu May 30, 2013 12:51 am
srcc25anu wrote:st2: r=s
if r = s = 1, 1/r + 1/s = 2 (not 4) but if r = s = 1/2, them 1/r + 1/s = 4
hence insufficient

and when you put r = s in the original equation it solves r = s = 1/2 but that does not mean r = s are actually 1/2 each. r and s could assume many other values and the only restriction is that either r or s is not 0.
Thats alright. But if we put statement 2 into original one why it gives us just one answer? I know i am thinking badly, but i cannot figure it out where my logic is wrong.
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by Brent@GMATPrepNow » Thu May 30, 2013 4:23 am
zazoz wrote:if rs isn't 0, is (1/r)+(1/s)=4

1)r+s=4rs
2)r=s

I think it's a simple problem. I wonder, why statement 2 is insufficient? When I plug statement 2 into the original equation, the only answer it gives me is r=s=1/2 and the equation will be correct, so why statement 2 is insufficient? Please explain me where I went wrong?
Just because (1/r)+(1/s)=4 when r=s=1/2, does not mean that we can definitely say that (1/r)+(1/s) must equal 4.
For example, when r=s=1, then (1/r)+(1/s) does not equal 4.

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by Brent@GMATPrepNow » Thu May 30, 2013 4:25 am
zazoz wrote:if rs isn't 0, is (1/r)+(1/s)=4

1)r+s=4rs
2)r=s
Target question: Is 1/r + 1/s = 4?

This one is a great candidate for rephrasing the target question
Let's add 1/r + 1/s to create one rational expression.
Find common denominator: s/rs + r/rs
Add numerators: (s+r)/rs
So, 1/r + 1/s = (s+r)/rs

So, rather than ask "Does 1/r + 1/s = 4?" we can ask "Does (s+r)/rs = 4?"

Even better, we can cross multiply the equation to get: "Does s+r = 4sr?"

Statement 1: r + s = 4rs
This is exactly what one of our rephrased target questions asks.
So, statement 1 is SUFFICIENT

Statement 2: r = s
Knowing that r=s does not help us determine whether s+r = 4sr
So, statement 2 is NOT SUFFICIENT

Answer: A

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by zazoz » Thu May 30, 2013 5:27 am
Brent@GMATPrepNow wrote:
zazoz wrote:if rs isn't 0, is (1/r)+(1/s)=4

1)r+s=4rs
2)r=s
Target question: Is 1/r + 1/s = 4?

This one is a great candidate for rephrasing the target question
Let's add 1/r + 1/s to create one rational expression.
Find common denominator: s/rs + r/rs
Add numerators: (s+r)/rs
So, 1/r + 1/s = (s+r)/rs

So, rather than ask "Does 1/r + 1/s = 4?" we can ask "Does (s+r)/rs = 4?"

Even better, we can cross multiply the equation to get: "Does s+r = 4sr?"

Statement 1: r + s = 4rs
This is exactly what one of our rephrased target questions asks.
So, statement 1 is SUFFICIENT

Statement 2: r = s
Knowing that r=s does not help us determine whether s+r = 4sr
So, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent
Thank you Brent; I would like to show how I solve this an how I reach to sufficient!! I know its incorrect. I know that if I consider r=s=3 it will show me that's insufficient.

Statement 2: I said to myself "Plug r=s into the question" then I reached to r=1/2 so s=1/2. After that, I, once again put r=s=1/2 into the question and reach to yes, it is sufficient. I said to myself that this method gives me just one answer nothing more. At first place can I plug r=s into the question or it is a wrong way because we want to improve that is the equation equals 4 or not? I think maybe I am not allowed to plug statement into the equation? Sorry for asking again
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by Brent@GMATPrepNow » Thu May 30, 2013 11:55 am
zazoz wrote:if rs isn't 0, is (1/r)+(1/s)=4

1)r+s=4rs
2)r=s

Thank you Brent; I would like to show how I solve this an how I reach to sufficient!! I know its incorrect. I know that if I consider r=s=3 it will show me that's insufficient.

Statement 2: I said to myself "Plug r=s into the question" then I reached to r=1/2 so s=1/2. After that, I, once again put r=s=1/2 into the question and reach to yes, it is sufficient. I said to myself that this method gives me just one answer nothing more. At first place can I plug r=s into the question or it is a wrong way because we want to improve that is the equation equals 4 or not? I think maybe I am not allowed to plug statement into the equation? Sorry for asking again
Sure, it's okay that you plugged r=s into the target question. HOWEVER, it's important to note that when you do this, you are essentially assuming that the answer to the target question is YES, even though your job is to the answer to the target question with certainty.

So, when you assumed that the answer to the target question is YES, you reached the conclusion that r = s = 1/2. This part is not necessarily true. It's POSSIBLE that, given statement 2, r = s = 1/2, in which case the answer to the target question is YES.

However, being told that r = s, does not mean that r = s = 1/2.
It could also be the case that r = s = 3, in which case the answer to the target question is NO.

Once we have two conflicting answers to the target question, we can conclude that statement 2 is not sufficient.

Cheers,
Brent
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by zazoz » Thu May 30, 2013 12:18 pm
Brent@GMATPrepNow wrote:
zazoz wrote:if rs isn't 0, is (1/r)+(1/s)=4

1)r+s=4rs
2)r=s

Thank you Brent; I would like to show how I solve this an how I reach to sufficient!! I know its incorrect. I know that if I consider r=s=3 it will show me that's insufficient.

Statement 2: I said to myself "Plug r=s into the question" then I reached to r=1/2 so s=1/2. After that, I, once again put r=s=1/2 into the question and reach to yes, it is sufficient. I said to myself that this method gives me just one answer nothing more. At first place can I plug r=s into the question or it is a wrong way because we want to improve that is the equation equals 4 or not? I think maybe I am not allowed to plug statement into the equation? Sorry for asking again
Sure, it's okay that you plugged r=s into the target question. HOWEVER, it's important to note that when you do this, you are essentially assuming that the answer to the target question is YES, even though your job is to the answer to the target question with certainty.

So, when you assumed that the answer to the target question is YES, you reached the conclusion that r = s = 1/2. This part is not necessarily true. It's POSSIBLE that, given statement 2, r = s = 1/2, in which case the answer to the target question is YES.

However, being told that r = s, does not mean that r = s = 1/2.
It could also be the case that r = s = 3, in which case the answer to the target question is NO.

Once we have two conflicting answers to the target question, we can conclude that statement 2 is not sufficient.

Cheers,
Brent
Thank you very much Brent, now I completely realized my misunderstanding. Thank you very much again.
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