Machine M, working alone at its constant rate, produces x widgets every 4 minutes. Machine N, working alone at its constant rate, produces y widgets every 5 minutes. If machines M and N working simultaneously at their respective constant rates for 20 minutes, does machine M produce more widgets than machine N in that time ?
1) x > 0.8y
2) y = x + 1
GPREP DS -1
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Machine M produces x widgets in 4 minutesabhasjha wrote:Machine M, working alone at its constant rate, produces x widgets every 4 minutes. Machine N, working alone at its constant rate, produces y widgets every 5 minutes. If machines M and N working simultaneously at their respective constant rates for 20 minutes, does machine M produce more widgets than machine N in that time ?
1) x > 0.8y
2) y = x + 1
Machine M produces x/4 widgets in 1 minutes
Machine N produces y widgets in 5 minutes
Machine N produces y/5 widgets in 1 minutes
Both Machines Together in 1 minute Produce = (x/4)+(y/5) = (5x+4y)/20
Both Machines Together in 1 minute Produce = (x/4)+(y/5) = (5x+4y)/20
Both Machines Together in 20 minute Produce = (x/4)+(y/5) = (5x+4y)
Question : Does M produce more widgets than Machine N?
Question Rephrased : Is 5x>4y ? i.e. IS x > (4/5)y? i.e. Is x > 0.8y ?
Statement 1) x > 0.8y
SUFFICIENT
Statement 1) y = x + 1
i.e. 0.8y = 0.8x + 0.8 but this can't be compared with x therefore
INSUFFICIENT
Answer: Option A
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Both machines work for the same amount of time.abhasjha wrote:Machine M, working alone at its constant rate, produces x widgets every 4 minutes. Machine N, working alone at its constant rate, produces y widgets every 5 minutes. If machines M and N working simultaneously at their respective constant rates for 20 minutes, does machine M produce more widgets than machine N in that time ?
1) x > 0.8y
2) y = x + 1
To produce more widgets than N, M must work faster than N.
Question rephrased:
Is M faster than N?
Statement 1: x > 0.8y
Let y=10, implying that x>8.
Since y=10, N produces 10 widgets every 5 minutes, implying that N's rate = 10/5 = 2 widgets per minute.
Since x>8, M produces MORE than 8 widgets every 4 minutes, implying that M's rate = (more than 8)/4 = MORE than 2 widgets per minute.
Thus, M is faster than N.
SUFFICIENT.
Statement 2: y = x+1
Case 1: x=1, y=2
Since y=2, N produces 2 widgets every 5 minutes, implying that N's rate = 2/5 widget per minute.
Since x=1, M produces 1 widget every 4 minutes, implying that M's rate = 1/4 widget per minute.
In this case, N is faster than M.
Case 2: x=100, y=101
Since y=101, N produces 101 widgets every 5 minutes, implying that N's rate = 101/5 ≈ 20 widgets per minute.
Since x=100, M produces 100 widgets every 4 minutes, implying that M's rate = 100/4 = 25 widgets per minute.
In this case, M is faster than N.
Since N is faster than M in Case 1 but slower than M in Case 2, INSUFFICIENT.
The correct answer is A.
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Alternate approach:
Since M produces x widgets every 4 minutes, M's rate = x/4 widgets per minute.
Since N produces y widgets every 5 minutes, N's rate = y/5 widgets per minute.
Since M and N work for the same amount of time, M will produce more widgets than N if M's rate is greater than N's rate.
For M's rate to be greater than N's rate, the following must be true:
x/4 > y/5
x > (4/5)y.
Question stem, rephrased: Is x > (4/5)y?
Statement 1: x > (0.8)y
Thus, x > (4/5)y.
SUFFICIENT.
Statement 2: y = x+1
If x=1 and y=2, then (4/5)y = 8/5.
In this case, x < (4/5)y.
If x=100 and y=101, then (4/5)y ≃ 80.
In this case, x > (4/5)y.
INSUFFICIENT.
The correct answer is A.
Since M produces x widgets every 4 minutes, M's rate = x/4 widgets per minute.
Since N produces y widgets every 5 minutes, N's rate = y/5 widgets per minute.
Since M and N work for the same amount of time, M will produce more widgets than N if M's rate is greater than N's rate.
For M's rate to be greater than N's rate, the following must be true:
x/4 > y/5
x > (4/5)y.
Question stem, rephrased: Is x > (4/5)y?
Statement 1: x > (0.8)y
Thus, x > (4/5)y.
SUFFICIENT.
Statement 2: y = x+1
If x=1 and y=2, then (4/5)y = 8/5.
In this case, x < (4/5)y.
If x=100 and y=101, then (4/5)y ≃ 80.
In this case, x > (4/5)y.
INSUFFICIENT.
The correct answer is A.
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\[M\,\,\, - \,\,\,4\,\,{\text{min}}\,\,\, - \,\,\,x\,\,{\text{widgets}}\,\,\,\,\, \Rightarrow \,\,\,\,\,\,M\,\,\, - \,\,\,20\,{\text{min}}\,\,\, - \,\,\,5x\,\,{\text{widgets}}\]abhasjha wrote:Machine M, working alone at its constant rate, produces x widgets every 4 minutes. Machine N, working alone at its constant rate, produces y widgets every 5 minutes. If machines M and N working simultaneously at their respective constant rates for 20 minutes, does machine M produce more widgets than machine N in that time ?
1) x > 0.8y
2) y = x + 1
\[N\,\,\, - \,\,\,5\,\,{\text{min}}\,\,\, - \,\,\,y\,\,{\text{widgets}}\,\,\,\,\, \Rightarrow \,\,\,\,\,N\,\,\, - \,\,\,20\,{\text{min}}\,\,\, - \,\,\,4y\,\,{\text{widgets}}\]
\[5x\mathop > \limits^? \,4y\]
\[\left( 1 \right)\,\,\,x > \frac{4}{5}y\,\,\,\,\,\,\mathop \Rightarrow \limits^{ \cdot \,5} \,\,\,\,\,5x > 4y\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \]
\[\left( 2 \right)\,\,\,\,y = x + 1\,\,\,\,\left\{ \begin{gathered}
\,\,{\text{Take}}\,\,\left( {x,y} \right) = \left( {1,2} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle \,\,\,\,\, \hfill \\
\,\,{\text{Take}}\,\,\left( {x,y} \right) = \left( {5,6} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\,\,\, \hfill \\
\end{gathered} \right.\]
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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