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Working independently at their respective constant rates, machines X 25 Feb 2020, 03:26
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

15% (low)

Question Stats:

81% (00:58) correct 19% (01:14) wrong based on 256 sessions

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Working independently at their respective constant rates, machines X and Y took 15 minutes to fill an order. What fraction of the order was filled by machine X?

(1) Working alone at its constant rate, machine X would have taken 60 minutes to fill the order.
(2) Working alone at its constant rate, machine Y would have taken 20 minutes to fill the order.
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D
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Working independently at their respective constant rates, machines X 25 Feb 2020, 06:20
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Bunuel
Working independently at their respective constant rates, machines X and Y took 15 minutes to fill an order. What fraction of the order was filled by machine X?

(1) Working alone at its constant rate, machine X would have taken 60 minutes to fill the order.
(2) Working alone at its constant rate, machine Y would have taken 20 minutes to fill the order.
Show more

Solution

Step 1: Analyse Question Stem


    • Let \(x\) and \(y\) be the rate of doing work of \(X\) and \(Y\), respectively.
      o X and Y together take \(15\) minutes to fill an order.
We need to find the fraction of the order was filled by X.
    • The fraction of work done by machine X = \(\frac{x}{(x+y)}\), we need to find the value of \(x\) and \(x+y\) or their ratio.

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE


Statement 1: Working alone at its constant rate, machine X would have taken \(60\) minutes to fill the order.
    • Let the total work be \(LCM(15, 60)=60\) units
      o \(x = \frac{60}{60}=1\) unit
      o \(x + y = \frac{60}{15}=4\) units
         \(\frac{x}{(x+y)}=\frac{1}{4}\)
      o We can find the fraction of work done by machine X.
Hence, statement 1 is sufficient, we can eliminate answer options B, C, and E.
Statement 2: Working alone at its constant rate, machine Y would have taken \(20\) minutes to fill the order.
    • Let the total work be LCM(15, 20)=60 units
      o \(y = \frac{60}{20}=3\) unit
      o \(x + y = \frac{60}{15}=4\) units
         \(x = 4-y = 4- 3= 1\)
      o \(\frac{x}{(x+y)}=\frac{1}{4}\).
    • We can find the fraction of work done by machine X.
Hence, statement 2 is also sufficient, the correct answer is Option D.
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Working independently at their respective constant rates, machines X 28 Feb 2020, 11:15
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Bunuel
Working independently at their respective constant rates, machines X and Y took 15 minutes to fill an order. What fraction of the order was filled by machine X?

(1) Working alone at its constant rate, machine X would have taken 60 minutes to fill the order.
(2) Working alone at its constant rate, machine Y would have taken 20 minutes to fill the order.
Show more

Analyzing the question:
Let x and y represent rates for machines X and Y. Then we have \(x + y = \frac{1}{15}\), then we need either x or y to find the asked ratio as any of them solves for the other.

Statement 1:
Gives x, sufficient.

Statement 2:
Gives y, sufficient.

Ans: D
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Working independently at their respective constant rates, machines X 29 Feb 2020, 11:44
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Bunuel
Working independently at their respective constant rates, machines X and Y took 15 minutes to fill an order. What fraction of the order was filled by machine X?

(1) Working alone at its constant rate, machine X would have taken 60 minutes to fill the order.
(2) Working alone at its constant rate, machine Y would have taken 20 minutes to fill the order.
Show more


Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

Assume x and y are numbers of minutes that machines X and Y take to fill the order, respectively.
Then we have \(\frac{1}{15} = \frac{1}{x} + \frac{1}{y}\).

Since we have 2 variable and 1 equations, D is most likely to be the answer. So, we should consider each condition on its own first.

Condition 1)
We have \(\frac{1}{15} = \frac{1}{60} + \frac{1}{y}\) or \(\frac{1}{15} - \frac{1}{60} = \frac{1}{20} = \frac{1}{y}\).
Then we have \(y = 20\).
Thus, \(\frac{1}{x+y}/\frac{1}{x}= \frac{1}{80}/\frac{1}{20} = \frac{1}{4}\).


Since condition 1) yields a unique solution, it is sufficient.

Condition 2)
We have \(\frac{1}{15} = \frac{1}{x} + \frac{1}{20}\) or \(\frac{1}{15} - \frac{1}{20} = \frac{1}{x}\).
Then we have \(x = 60\).
Thus, \(\frac{1}{x+y}/\frac{1}{x}= \frac{1}{80}/\frac{1}{20} = \frac{1}{4}\).

Since condition 2) yields a unique solution, it is sufficient.

Therefore, D is the answer.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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Working independently at their respective constant rates, machines X 17 Jul 2022, 17:56
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Work problems can be solved by the rate - work/time concept.
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Working independently at their respective constant rates, machines X 05 Jan 2026, 13:12
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