If rs ≠ 0, is 1/r + 1/s = 4 ? (1) r + s = 4rs (2) r = s

Hi guys,

Quick question, because it's a method I've been using and has seemed to work but I don't know if it is correct.

Could 1/r + 1/s =4 be rearranged to r + s = 1/4?

No, that's not correct. For example, \(\frac{1}{2} + \frac{7}{2} = 4\) but \(2 + \frac{2}{7} \neq{ \frac{1}{4}}\)

The correct way is:
\(\frac{1}{r}+\frac{1}{s}=4\);

\(\frac{r+s}{rs}=4\)

\(r+s=4rs\).

Hi Bunuel

I understand that statement 2 has several solutions for r and s - but why can't I just determine the value for r and s as as following:

(2) r = s
-> replace r by s: 1/s + 1/s = 4
-> multiply with s: 1 + 1 = 4s
-> divide by 4: 1/2 = s
-> replace s by 1/2: 1/ 1/2 + 1/ 1/2 = 4
-> multiply with 1/2: 1+1 = 2
-> this s = 1/2 is true, so r has to be 1/2 as well and 2nd statement is sufficient?

Thanks!
gentler

When you do all these manipulations with 1/r + 1/s = 4, you should not forget that it's not given as a fact. 1/r + 1/s = 4 is a question. We want to know whether 1/r + 1/s = 4. So, you don't get there that s = 1/2. when you substitute r = s into the question (1/r + 1/s = 4), the question becomes "does s = 1/2?".

Hope it's clear.

2) if we put r=s we get

1/r +1/r=4
r=1/2

We get r as 1/2 but this is not our intention.we need to find 1/r+1/s which we are not getting .
That's why this statement 2 is insufficient

Give kudos if it helps

Posted from my mobile device

Hi guys,

I was also in trouble with statement (2) and reading the answers I understood. Since I see there are some still with problems, I will try to explain with my words:

The question is x≠0, is 1/r + 1/s = 4? Since it has a question mark, this is not a statement and you can not use it to prove the point. The best thing is to rephrase the question. Since the question wants to no if 1/r plus 1/s equals to 4, a yes or no to this question would be enough. Therefore, you can rephrase as: r=? and s=? (you need to know both to know it they equal 4 in the equation).

(2) number 2 says r=s; but you still don’t know whether r=s=1 what would lead you to 1+1=2≠4 or r=s=1/2 leading to 2+2=4. Since there are cases where the answer is yes and others where the answer is no, statement 2 does not answer your question.

(1) one gives your question as a statement, so it answers

A

Solution:

Question Stem Analysis:

We need to determine whether 1/r + 1/s = 4, i.e., (r + s)/(rs) = 4.

Statement One Alone:

Since r + s = 4rs, we have (r + s)/(rs) = (4rs)/(rs) = 4. Statement one alone is sufficient.

Statement Two Alone:

Statement two is not sufficient. For example, if r = s = 1/2, 1/r + 1/s = 2 + 2 = 4. However, if r = s = 1, 1/r + 1/s = 1 + 1 = 2.

Answer: A

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