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If rs = rs + r + s, then for what value of s is r s equal to r for a

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HKD1710
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If rs = rs + r + s, then for what value of s is r s equal to r for a [#permalink] New post  13 Dec 2018, 07:27
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If \(r☉s = rs + r + s\), then for what value of \(s\) is \(r☉s\) equal to \(r\) for all values of \(r\)?

(A) –1
(B) 0
(C) 1
(D) \(\frac{1}{r+1}\)
(E) \(r\)
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BrentGMATPrepNow
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Re: If rs = rs + r + s, then for what value of s is r s equal to r for a [#permalink] New post  13 Dec 2018, 07:36
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HKD1710 wrote:
If \(r☉s = rs + r + s\), then for what value of \(s\) is \(r☉s\) equal to \(r\) for all values of \(r\)?

(A) –1
(B) 0
(C) 1
(D) \(\frac{1}{r+1}\)
(E)\(r\)


We want: \(r☉s = r\)

In other words: \(rs + r + s = r\)

Subtract r from both sides: \(rs + s = 0\)

Factor the left side: \(s(r + 1) = 0\)

So, either s = 0, or r = -1

So, \(r☉s = r\) when s = 0, or r = -1

The question asks about the value of s, so the correct answer is B.

Cheers,
Brent
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Re: If rs = rs + r + s, then for what value of s is r s equal to r for a [#permalink] New post  13 Dec 2018, 22:00
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We want: r☉s=r
Hence rs+r+s=r
Subtract r from both sides: rs+s=0
Taking s common: s(r+1)=0
So, either s = 0, or r = -1

But in the question, find s for all values of r .
Hence r can be any real number not only -1 . So s=0 .

IMO B.

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Re: If rs = rs + r + s, then for what value of s is r s equal to r for a [#permalink] New post  10 Feb 2019, 23:57
HKD1710 wrote:
If \(r☉s = rs + r + s\), then for what value of \(s\) is \(r☉s\) equal to \(r\) for all values of \(r\)?

(A) –1
(B) 0
(C) 1
(D) \(\frac{1}{r+1}\)
(E)\(r\)

Project PS Butler : Question #75


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what a subtle change in the question.

what value of \(s\) ???

\(r☉s = rs + r + s\) = r

rs + s = 0
s (r+1) = 0

r= -1, will make s = 0

s = 0

B
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Re: If rs = rs + r + s, then for what value of s is r s equal to r for a [#permalink] New post  18 Feb 2024, 11:42
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If rs = rs + r + s, then for what value of s is r s equal to r for a [#permalink]
18 Feb 2024, 11:42
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