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# If rs#0, is 1/r + 1/s = 4 ?

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Director
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If rs#0, is 1/r + 1/s = 4 ? [#permalink]

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11 Jun 2007, 22:19
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73% (01:48) correct 27% (00:49) wrong based on 109 sessions

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If rs#0, is 1/r + 1/s = 4 ?

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-rs-0-is-1-r-1-s-102597.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 23 Feb 2014, 02:29, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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11 Jun 2007, 22:26
St1:
r = 4rs-s = s(4r-1)

Insufficient.

St2:
1/r + 1/s = 2/r or 2/s. Insufficient.

Using both, we have, 2s = 4s^2
2s(1-2s) = 0
s = o (invalid) or s = 1/2 = r. So we can answer the question now. Sufficient.

Ans C
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11 Jun 2007, 22:26
ggarr wrote:
if rs is not equal to 0, is 1/r + 1/s = 4?

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

1) (r+s) / rs = 4
=> (r/rs) + (s/rs) = 4
=> (1/r) + (1/s) = 4
SUFFICIENT

2) plug in r=s=1/2, you get 4=4. But plug in r=s=1, you get 2=4. INSUFFICIENT.
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11 Jun 2007, 22:27
bkk145 wrote:
ggarr wrote:
if rs is not equal to 0, is 1/r + 1/s = 4?

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

1) (r+s) / rs = 4
=> (r/rs) + (s/rs) = 4
=> (1/r) + (1/s) = 4
SUFFICIENT

2) plug in r=s=1/2, you get 4=4. But plug in r=s=1, you get 2=4. INSUFFICIENT.

gar!! failed to see that...
Manager
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11 Jun 2007, 22:55
For me the answer is A
r+s=4rs
dividing both sides by rs
r/rs+s/rs=4
1/r+1/s=4 (Sufficient)
r=s
Different values of r or s suggest that 1/r+1/s may or may not be =4 thus insufficient
Director
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11 Jun 2007, 23:36
ywilfred wrote:
bkk145 wrote:
ggarr wrote:
if rs is not equal to 0, is 1/r + 1/s = 4?

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

1) (r+s) / rs = 4
=> (r/rs) + (s/rs) = 4
=> (1/r) + (1/s) = 4
SUFFICIENT

2) plug in r=s=1/2, you get 4=4. But plug in r=s=1, you get 2=4. INSUFFICIENT.

gar!! failed to see that...
why can't we just answer this question w/the info provided in the stem? did we really need additional info to figure that out? 1/r + 1/s = 4 => s/rs + r/rs = 4 => 1/r + 1/s = 4

does this make sense?
Manager
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11 Jun 2007, 23:49
Well we could certainly have done it that way Fig if the stem had told us that 1/r+1/s is indeed equal to 4. The stem is asking whether the expression is a true equation or not. And to validate the stem we are provided with two different sets of information which are statements A & B.
Actually this is how i had made D the correct option by putting r=s in the stem. But as u see, stem is not stated to be true, it is asked wherther it is true or not.
I hope this explains ur question.
Director
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11 Jun 2007, 23:56
it does. thanks. I made this more difficult than I should have. why are you calling me Fig?
Manager
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12 Jun 2007, 00:20
sorry dude
u see when the boss is just around the corner, then such mistakes are bound to happen. Especially when ur boss is more like a blood hound, who only wnats ur blood instead of ur sweat.
And yes u did make it more difficult. It happens to me too. simple solution is in fornt of me, but i start making complex equations.
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12 Jun 2007, 00:47
ggarr wrote:
it does. thanks. I made this more difficult than I should have. why are you calling me Fig?

Because I'm the one who will do such thing

By the way, I'm also with (A) ...... because neither r nor s could be equal to 0..... We can thus divide the equation by rs.
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12 Jun 2007, 02:18
ggarr wrote:
if rs is not equal to 0, is 1/r + 1/s = 4?

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

From the stem we have that (r+s)/rs = 4

1) (r+s)/rs= 4rs/rs = 4, SUF
2) r=s, from the stem => 1/r, but since we do not know how much does r worth we also do not know how much 1/r worths, INSUF.

A
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Re: if rs is not equal to 0, is 1/r + 1/s = 4? 1) r+s = 4rs 2) r [#permalink]

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22 Feb 2014, 22:19
why is (1) sufficient? if r = 0.3 and s = 0.2, 4rs = 0.24. s+r = 0.5. The question didn't state that r and s are integers.
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Re: if rs is not equal to 0, is 1/r + 1/s = 4? 1) r+s = 4rs 2) r [#permalink]

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22 Feb 2014, 23:43
r+s=4 rs or (r+s)/rs=4 or (r/rs)+(s/rs)=4 or 1/r+1/s=4 . so sufficient .

statements 2 is clearly out .

if this portion of the question " rs is not equal to 0 " is not given , then ? what would happen ?

Posted from my mobile device
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Re: if rs is not equal to 0, is 1/r + 1/s = 4? 1) r+s = 4rs 2) r [#permalink]

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23 Feb 2014, 02:32
shiblee wrote:
r+s=4 rs or (r+s)/rs=4 or (r/rs)+(s/rs)=4 or 1/r+1/s=4 . so sufficient .

statements 2 is clearly out .

if this portion of the question " rs is not equal to 0 " is not given , then ? what would happen ?

Posted from my mobile device

If rs#0, is 1/r + 1/s = 4 ?

Question: is $$\frac{1}{r}+\frac{1}{s}=4$$ --> is $$\frac{r+s}{rs}=4$$ --> is $$r+s=4rs$$?

(1) $$r+s=4rs$$, directly answers the question. Sufficient.

(2) $$r = s$$, the question becomes: is $$\frac{1}{r}+\frac{1}{r}=4$$ ? --> is $$r=\frac{1}{2}$$? but we dont' know whether $$r=\frac{1}{2}$$. Not sufficient.

As for your question: if rs#0 were not given, then r=s=0 would be possible and in this case 1/r + 1/s would be undefined.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-rs-0-is-1-r-1-s-102597.html
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Re: if rs is not equal to 0, is 1/r + 1/s = 4? 1) r+s = 4rs 2) r   [#permalink] 23 Feb 2014, 02:32
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