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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: 53
P, V and G had to paint three identical fences. On the  [#permalink]

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25 Nov 2019, 06:38
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Difficulty:

75% (hard)

Question Stats:

54% (03:14) correct 46% (03:00) wrong based on 57 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: 1301
Location: India
Re: P, V and G had to paint three identical fences. On the  [#permalink]

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25 Nov 2019, 09:23
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$$\frac{1}{m}+\frac{1}{m+5}=\frac{1}{m-4}$$

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

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, 20:43
[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: 10110
Location: Pune, India
Re: P, V and G had to paint three identical fences. On the  [#permalink]

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27 Nov 2019, 21:23
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
Veritas Prep GMAT Instructor

VP
Joined: 19 Oct 2018
Posts: 1301
Location: India
Re: P, V and G had to paint three identical fences. On the  [#permalink]

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28 Nov 2019, 04:10
1
Chaman51

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

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

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

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

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

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

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

$$(m-10)(m+2)=0$$
Director
Joined: 27 May 2012
Posts: 952
P, V and G had to paint three identical fences. On the  [#permalink]

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02 Jan 2020, 09:13
Chaman51 wrote:
nick1816 wrote:
$$\frac{1}{m}+\frac{1}{m+5}=\frac{1}{m-4}$$

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

m=10

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

Thanks

Hi Chaman51,

If you arrive at an equation that has only one variable, and the answer choices give you values for that variable. You could simply try substituting the values from the answer choices.

In this question, the equation:
$$\frac{1}{m}+\frac{1}{m+5}=\frac{1}{m-4}$$ will only be satisfied by m=10

Hope this helps.
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- Stne
P, V and G had to paint three identical fences. On the   [#permalink] 02 Jan 2020, 09:13
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