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# If Machine X can produce 80 widgets in 4 hours, how long would it take

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Math Expert
Joined: 02 Sep 2009
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If Machine X can produce 80 widgets in 4 hours, how long would it take  [#permalink]

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17 Feb 2016, 02:39
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5% (low)

Question Stats:

91% (01:00) correct 9% (01:23) wrong based on 116 sessions

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If Machine X can produce 80 widgets in 4 hours, how long would it take machine X and Y working together, to produce 500 widgets?

(1) Machine Y works at 3/4 the speed of machine X
(2) If Machine Y's speed doubled, it would produce 120 widgets in 4 hours

Kudos for correct solution.

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Re: If Machine X can produce 80 widgets in 4 hours, how long would it take  [#permalink]

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19 Feb 2016, 07:48
1
(1) Machine Y works at 3/4 the speed of machine X
(2) If Machine Y's speed doubled, it would produce 120 widgets in 4 hours

As, X can produce 80 widgets in 4 hours
So, X can produce 20 widgets in 1 hours

Statement 1: Sufficient.

Y works at 3/4 the speed of machine X
So, Y can produce 15 widgets in 1 hours (3/4 of 20)

X and Y together can produce 35 widgets in 1 hours.
X and Y together can produce 500 widgets in (500/35) = 14 Hours 17 mins

Statement 2: Sufficient.

Machine Y's speed doubled, it would produce 120 widgets in 4 hours
Machine Y's speed doubled, it would produce 30 widgets in 1 hours
Machine Y's at normal speed, it would produce 15 widgets in 1 hours

X and Y together can produce 35 widgets in 1 hours.
X and Y together can produce 500 widgets in (500/35) = 14 Hours 17 mins

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Re: If Machine X can produce 80 widgets in 4 hours, how long would it take  [#permalink]

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23 Feb 2016, 05:06
Bunuel wrote:
If Machine X can produce 80 widgets in 4 hours, how long would it take machine X and Y working together, to produce 500 widgets?

(1) Machine Y works at 3/4 the speed of machine X
(2) If Machine Y's speed doubled, it would produce 120 widgets in 4 hours

Kudos for correct solution.

Given: Machine X can produce 80 widgets in 4 hours
Required: How long would it take machine X and Y working together, to produce 500 widgets

Statement 1: Machine Y works at 3/4 the speed of machine X
Rate of Machine X = 20 widgets per hour
Therefore rate of machine Y = 20*(3/4) = 15 widgets per hour.
Hence we can find out the time needed by machine X and Y together to produce 500 widgets
SUFFICIENT

Statement 2: If Machine Y's speed doubled, it would produce 120 widgets in 4 hours
Normal speed of machine Y = 60 widgets in 4 hours or 15 widgets/hour
Hence we can find out the time needed by machine X and Y together to produce 500 widgets
SUFFICIENT

Option D
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Re: If Machine X can produce 80 widgets in 4 hours, how long would it take  [#permalink]

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29 Feb 2016, 18:15
Bunuel wrote:
If Machine X can produce 80 widgets in 4 hours, how long would it take machine X and Y working together, to produce 500 widgets?

(1) Machine Y works at 3/4 the speed of machine X
(2) If Machine Y's speed doubled, it would produce 120 widgets in 4 hours

Kudos for correct solution.

X rate - 20W/hr

A) Y rate 3*20/4=15W/hr
Rx+Ry=R(total).
500/Rtotal = total time working together. /
Sufficient

B) 120/4hr ----> 60/4hr----> 15W/hr. Same info as A.
Sufficient.

D.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6955
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If Machine X can produce 80 widgets in 4 hours, how long would it take  [#permalink]

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01 Mar 2016, 23:55
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If Machine X can produce 80 widgets in 4 hours, how long would it take machine X and Y working together, to produce 500 widgets?

(1) Machine Y works at 3/4 the speed of machine X
(2) If Machine Y's speed doubled, it would produce 120 widgets in 4 hours

In the original condition, it gives power of X and 500 widgets. So you need to figure out power of Y, which makes 1 variable. In order to match with the number of equations, you need 1 equation. However, for 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), power of Y=power of (3/4)X=(3/4)(80widgets/4hrs)=15widgets/1hr, which is unique and sufficient.
For 2), power of 2Y=120widgets/4hrs. Then, power of Y is 13widgets/1hr, which is unique and sufficient.

 For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Re: If Machine X can produce 80 widgets in 4 hours, how long would it take  [#permalink]

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17 Oct 2018, 09:22
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Re: If Machine X can produce 80 widgets in 4 hours, how long would it take   [#permalink] 17 Oct 2018, 09:22
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