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
Both machines work for the same amount of time.
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
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.
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