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# X, Y and Z together can complete a job in 10 days. The rate of work of

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Math Expert
Joined: 02 Sep 2009
Posts: 55716
X, Y and Z together can complete a job in 10 days. The rate of work of  [#permalink]

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18 Jun 2019, 00:23
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67% (01:39) correct 33% (02:59) wrong based on 12 sessions

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X, Y and Z together can complete a job in 10 days. The rate of work of X is three times that of Y, which, in turn is twice that of Z. What is the time taken by Z alone to complete the job?

A. 30 days
B. 60 days
C. 90 days
D. 120 days
E. 180 days

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Manager
Joined: 16 Jan 2019
Posts: 158
Location: India
Concentration: General Management, Strategy
WE: Sales (Other)
Re: X, Y and Z together can complete a job in 10 days. The rate of work of  [#permalink]

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18 Jun 2019, 00:34
(z+2z+6z)*10=1
z=1/90

So z can complete the job alone in 90 days

Hit Kudos if this helped!
Senior Manager
Joined: 22 Nov 2018
Posts: 289
Location: India
GMAT 1: 640 Q45 V35
GMAT 2: 660 Q48 V33
Re: X, Y and Z together can complete a job in 10 days. The rate of work of  [#permalink]

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18 Jun 2019, 00:47
1
Bunuel wrote:
X, Y and Z together can complete a job in 10 days. The rate of work of X is three times that of Y, which, in turn is twice that of Z. What is the time taken by Z alone to complete the job?

A. 30 days
B. 60 days
C. 90 days
D. 120 days
E. 180 days

Through rate 1/x+1/y+1/z=1/10; since rate of z=2*rate of y and 6*rate of x from the stem 1/z+2/z+6/z=1/10;Z=90 IMO C
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CEO
Joined: 18 Aug 2017
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Concentration: Sustainability, Marketing
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Re: X, Y and Z together can complete a job in 10 days. The rate of work of  [#permalink]

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18 Jun 2019, 05:30
Bunuel wrote:
X, Y and Z together can complete a job in 10 days. The rate of work of X is three times that of Y, which, in turn is twice that of Z. What is the time taken by Z alone to complete the job?

A. 30 days
B. 60 days
C. 90 days
D. 120 days
E. 180 days

giveb
x+y+x/xyz=1/10
and
x=2/z
y=2*3/z ; 6/z
so total ; 9/z= 1/10
z=90
IMO C
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Senior Manager
Joined: 20 Jul 2017
Posts: 263
Re: X, Y and Z together can complete a job in 10 days. The rate of work of  [#permalink]

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18 Jun 2019, 07:30
Bunuel wrote:
X, Y and Z together can complete a job in 10 days. The rate of work of X is three times that of Y, which, in turn is twice that of Z. What is the time taken by Z alone to complete the job?

A. 30 days
B. 60 days
C. 90 days
D. 120 days
E. 180 days

Given, 1/X + 1/Y + 1/Z = 1/10

The rate of work of X is three times that of Y, which, in turn is twice that of Z
—> X takes 1/3rd time of Y, which in turn takes half the time of Z
—> X = Y/3 & Y = Z/2
—> X = Z/6

1/X + 1/Y + 1/Z = 1/10
—> 6/Z + 2/Z + 1/Z = 1/10
—> 9/Z = 1/10
—> Z = 90 days

IMO Option C

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Re: X, Y and Z together can complete a job in 10 days. The rate of work of   [#permalink] 18 Jun 2019, 07:30
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