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# A factory has three types of machines – A, B, and C – each of which wo

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Math Expert
Joined: 02 Sep 2009
Posts: 52161
A factory has three types of machines – A, B, and C – each of which wo  [#permalink]

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21 Jul 2016, 03:42
2
9
00:00

Difficulty:

85% (hard)

Question Stats:

49% (02:00) correct 51% (02:06) wrong based on 368 sessions

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A factory has three types of machines – A, B, and C – each of which works at its own constant rate. How many widgets could one machine A, one Machine B, and one Machine C produce in one 8-hour day?

(1) 7 Machine As and 11 Machine Bs can produce 250 widgets per hour

(2) 8 Machine As and 22 Machine Cs can produce 600 widgets per hour

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Re: A factory has three types of machines – A, B, and C – each of which wo  [#permalink]

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22 Nov 2016, 06:02
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Top Contributor
1
Bunuel wrote:
A factory has three types of machines – A, B, and C – each of which works at its own constant rate. How many widgets could one machine A, one Machine B, and one Machine C produce in one 8-hour day?

(1) 7 Machine As and 11 Machine Bs can produce 250 widgets per hour

(2) 8 Machine As and 22 Machine Cs can produce 600 widgets per hour

Target question: How many widgets could one machine A, one Machine B, and one Machine C produce in one 8-hour day?

Statement 1: 7 Machine A's and 11 Machine B's can produce 250 widgets per hour
NOT SUFFICIENT

Statement 2: 8 Machine A's and 22 Machine C's can produce 600 widgets per hour
NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1: 7 Machine A's and 11 Machine B's can produce 250 widgets per hour
Statement 2: 8 Machine A's and 22 Machine C's can produce 600 widgets per hour

Hmmm, I see that we're given info about 11 Machine Bs and 22 Machine Cs. Perhaps we might gain some useful information, if we create an EQUIVALENT statement such that Machines B and C produce the SAME number of widgets.

Take statement 2 and HALVE everything to get: 4 Machine As and 11 Machine Cs can produce 300 widgets per hour
Combine this new (equivalent) info with statement 1 to see we have two useful pieces of info:

7 Machine A's and 11 Machine B's can produce 250 widgets per hour
4 Machine As and 11 Machine Cs can produce 300 widgets per hour

So, if we ADD all of the machines we get:
11 Machine A's, 11 Machine B's and 11 Machine C's can produce 550 widgets per hour

Now divide everything by 11 to get: 1 Machine A, 1 Machine B and 1 Machine C can produce 50 widgets per hour
So, 1 Machine A, 1 Machine B and 1 Machine C can produce 400 widgets in 8 hours
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

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Re: A factory has three types of machines – A, B, and C – each of which wo  [#permalink]

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21 Jul 2016, 05:43
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6
Require both the options.
(7A+11B) = 250 widgets per hr
Multiple by 2
14A+22B = 500 widgets per hr ---(1)
Using 2nd statement
8A+22C= 600 widgets per hr ---(2)

22A+22B+22C=1100
A+B+C= 50 widgets per hr.

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##### General Discussion
Manager
Joined: 14 Oct 2012
Posts: 165
A factory has three types of machines – A, B, and C – each of which wo  [#permalink]

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11 Nov 2016, 18:35
Hello Friends,
Bunuel, Vyshak, VeritasPrepKarishma, msk0657 and others
Shouldn't this question mention: Working together how many widgets could one machine A, one Machine B, and one Machine C produce in one 8-hour day?

Math Expert
Joined: 02 Sep 2009
Posts: 52161
Re: A factory has three types of machines – A, B, and C – each of which wo  [#permalink]

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12 Nov 2016, 02:37
manishtank1988 wrote:
Hello Friends,
Bunuel, Vyshak, VeritasPrepKarishma, msk0657 and others
Shouldn't this question mention: Working together how many widgets could one machine A, one Machine B, and one Machine C produce in one 8-hour day?

This is exactly what the question is asking. No need to over-complicate...
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Joined: 14 Oct 2012
Posts: 165
Re: A factory has three types of machines – A, B, and C – each of which wo  [#permalink]

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14 Nov 2016, 17:54
Bunuel wrote:
manishtank1988 wrote:
Hello Friends,
Bunuel, Vyshak, VeritasPrepKarishma, msk0657 and others
Shouldn't this question mention: Working together how many widgets could one machine A, one Machine B, and one Machine C produce in one 8-hour day?

This is exactly what the question is asking. No need to over-complicate...

Thanks Bunuel for clarifying.
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Posts: 9415
Re: A factory has three types of machines – A, B, and C – each of which wo  [#permalink]

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06 Feb 2018, 11:37
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Re: A factory has three types of machines – A, B, and C – each of which wo &nbs [#permalink] 06 Feb 2018, 11:37
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