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# If rs ≠ 0, does 1/r + 1/s = 5 ?

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Math Expert
Joined: 02 Sep 2009
Posts: 42560

Kudos [?]: 135317 [0], given: 12686

If rs ≠ 0, does 1/r + 1/s = 5 ? [#permalink]

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02 Oct 2017, 04:45
00:00

Difficulty:

65% (hard)

Question Stats:

40% (00:27) correct 60% (01:08) wrong based on 40 sessions

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If rs ≠ 0, does 1/r + 1/s = 5 ?

(1) rs > 1
(2) s < –r
[Reveal] Spoiler: OA

_________________

Kudos [?]: 135317 [0], given: 12686

Director
Joined: 25 Feb 2013
Posts: 619

Kudos [?]: 304 [2], given: 39

Location: India
GPA: 3.82
If rs ≠ 0, does 1/r + 1/s = 5 ? [#permalink]

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02 Oct 2017, 04:54
2
KUDOS
Bunuel wrote:
If rs ≠ 0, does 1/r + 1/s = 5 ?

(1) rs > 1
(2) s < –r

$$\frac{1}{r}+\frac{1}{s}=5$$ or $$\frac{(r+s)}{rs}=5$$. we need to find the values of r & s to verify the equation.

Statement 1: from this we know $$rs>1$$ but we cannot find the value of r & s. Hence Insufficient.

Statement 2: $$s<-r$$ or $$r+s<0$$. again value of $$r$$ & $$s$$ cannot be calculated. Insufficient

Combining 1 & 2 we know that $$rs>0$$ and $$r+s<0$$ hence $$\frac{(r+s)}{rs}$$ will be negative so it cannot be equal to 5. Hence sufficient

Option C

Last edited by niks18 on 14 Oct 2017, 20:30, edited 3 times in total.

Kudos [?]: 304 [2], given: 39

Manager
Joined: 12 Feb 2017
Posts: 71

Kudos [?]: 28 [2], given: 46

If rs ≠ 0, does 1/r + 1/s = 5 ? [#permalink]

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02 Oct 2017, 22:39
2
KUDOS
niks18 wrote:
Bunuel wrote:
If rs ≠ 0, does 1/r + 1/s = 5 ?

(1) rs > 1
(2) s < –r

$$\frac{1}{r}+\frac{1}{s}=5$$ is only possible when both $$r$$ and $$s$$ are fractions for eg $$r=1$$ and $$s=\frac{1}{4}$$ or $$r=\frac{1}{2}$$ and $$s=\frac{1}{3}$$, if $$r$$ & $$s$$ are integers then LHS will has a value less than $$1$$.

Statement 1: from this we know $$rs>1$$ this implies that r and s are not a proper fraction because the multiplication is greater than 1. Hence LHS cannot be equal to RHS. Sufficient.

Statement 2: $$s<-r$$ or $$r+s<0$$. again value of $$r$$ & $$s$$ cannot be calculated. Insufficient

Option A

both r and s not necessarily be fractions or integers.
eg r=5 and s= 5/24
then rs= 25/24 ----> rs>1
and 1/5 +1/(5/24) = 1/5 + 24/5 = 5

Hence Statement 1 is not sufficient.

stmt 2 says s< -r
that means s+r <0
stmt 2 also gives nothing hence insufficient.

Combining stmt 1 and 2 we get rs>1 means rs is positive, and r+s<0 means r+s is negative
1/r + 1/s
=(r+s)/rs
=negative / positive
so in any case 1/r + 1/s will not be equal to 5.
Hence Both statements together are sufficient.

Kudos if it helps.

Kudos [?]: 28 [2], given: 46

Director
Joined: 25 Feb 2013
Posts: 619

Kudos [?]: 304 [0], given: 39

Location: India
GPA: 3.82
Re: If rs ≠ 0, does 1/r + 1/s = 5 ? [#permalink]

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03 Oct 2017, 02:07
niks18 wrote:
Bunuel wrote:
If rs ≠ 0, does 1/r + 1/s = 5 ?

(1) rs > 1
(2) s < –r

$$\frac{1}{r}+\frac{1}{s}=5$$ is only possible when both $$r$$ and $$s$$ are fractions for eg $$r=1$$ and $$s=\frac{1}{4}$$ or $$r=\frac{1}{2}$$ and $$s=\frac{1}{3}$$, if $$r$$ & $$s$$ are integers then LHS will has a value less than $$1$$.

Statement 1: from this we know $$rs>1$$ this implies that r and s are not a proper fraction because the multiplication is greater than 1. Hence LHS cannot be equal to RHS. Sufficient.

Statement 2: $$s<-r$$ or $$r+s<0$$. again value of $$r$$ & $$s$$ cannot be calculated. Insufficient

Option A

both r and s not necessarily be fractions or integers.
eg r=5 and s= 5/24
then rs= 25/24 ----> rs>1
and 1/5 +1/(5/24) = 1/5 + 24/5 = 5

Hence Statement 1 is not sufficient.

stmt 2 says s< -r
that means s+r <0
stmt 2 also gives nothing hence insufficient.

Combining stmt 1 and 2 we get rs>1 means rs is positive, and r+s<0 means r+s is negative
1/r + 1/s
=(r+s)/rs
=negative / positive
so in any case 1/r + 1/s will not be equal to 5.
Hence Both statements together are sufficient.

Kudos if it helps.

thanks for highlighting the mistake . initially i had solved correct but then got swayed by the fraction Great work in identifying that unique fraction 5/24

Kudos [?]: 304 [0], given: 39

Re: If rs ≠ 0, does 1/r + 1/s = 5 ?   [#permalink] 03 Oct 2017, 02:07
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