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# P, V and G had to paint three identical fences. On the

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Manager
Joined: 18 Jul 2019
Posts: 54
P, V and G had to paint three identical fences. On the  [#permalink]

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25 Nov 2019, 07:38
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Difficulty:

55% (hard)

Question Stats:

63% (03:19) correct 38% (03:19) wrong based on 24 sessions

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P, V and G had to paint three identical fences. On the first day, only P turned up for work and he completed the work only on the first fence, taking m hours. On the second day, all three of them turned up for work and they completed the work only on the second fence, taking (m –4) hours. On the third day, V and G turned up and they completed the work on the third fence, taking (m+ 5) hours. What is the value of m?

a) 6
b) 8
c) 9
d) 10
e) 12
VP
Joined: 19 Oct 2018
Posts: 1151
Location: India
Re: P, V and G had to paint three identical fences. On the  [#permalink]

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25 Nov 2019, 10:23
1
$$\frac{1}{m}+\frac{1}{m+5}=\frac{1}{m-4}$$

$$m^2-8m-20=0$$

m=10

CaptainLevi wrote:
P, V and G had to paint three identical fences. On the first day, only P turned up for work and he completed the work only on the first fence, taking m hours. On the second day, all three of them turned up for work and they completed the work only on the second fence, taking (m –4) hours. On the third day, V and G turned up and they completed the work on the third fence, taking (m+ 5) hours. What is the value of m?

a) 6
b) 8
c) 9
d) 10
e) 12
Intern
Joined: 01 Aug 2019
Posts: 1
Re: P, V and G had to paint three identical fences. On the  [#permalink]

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27 Nov 2019, 21:43
[quote="nick1816"]$$\frac{1}{m}+\frac{1}{m+5}=\frac{1}{m-4}$$

$$m^2-8m-20=0$$

m=10

Could you provide more detail on how you resolve this equation?

Thanks
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9850
Location: Pune, India
Re: P, V and G had to paint three identical fences. On the  [#permalink]

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27 Nov 2019, 22:23
CaptainLevi wrote:
P, V and G had to paint three identical fences. On the first day, only P turned up for work and he completed the work only on the first fence, taking m hours. On the second day, all three of them turned up for work and they completed the work only on the second fence, taking (m –4) hours. On the third day, V and G turned up and they completed the work on the third fence, taking (m+ 5) hours. What is the value of m?

a) 6
b) 8
c) 9
d) 10
e) 12

Since P takes m hrs to complete one fence, his rate of work = 1/m fence/hr = p
P, V and G take (m - 4) hrs to complete one fence so their rate of work = 1/(m - 4) fence/hr = p + v + g
V and G take (m + 5) hrs to complete one fence so their rate of work = 1/(m + 5) = v + g

1/m + 1/(m+5) = 1/(m - 4)

Now just try to plug in the options to see which value of m works.
Note that m = 6 gives 11 in the second denominator on left hand side. It is a big prime number and seeing that on right hand side, we will have 1/2, m = 6 will not work. Same logic works for 8 and 9 too.

The first option you should actually try is m = 10 which works.

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Karishma
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VP
Joined: 19 Oct 2018
Posts: 1151
Location: India
Re: P, V and G had to paint three identical fences. On the  [#permalink]

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28 Nov 2019, 05:10
1
Chaman51

$$\frac{1}{m}+\frac{1}{m+5}=\frac{1}{m-4}$$

$$\frac{m+5+m}{m(m+5)}=\frac{1}{m-4}$$

$$\frac{2m+5}{m^2+5m}=\frac{1}{m-4}$$

$$(2m+5)(m-4)=m^2+5m$$

$$2m^2-3m-20=m^2+5m$$

$$m^2-8m-20=0$$

$$m^2-10m+2m-20=0$$

$$(m-10)(m+2)=0$$
Re: P, V and G had to paint three identical fences. On the   [#permalink] 28 Nov 2019, 05:10
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# P, V and G had to paint three identical fences. On the

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