Mo2men wrote:A sporting goods store received a shipment of baseball gloves that included 5 brown gloves for every 6 black gloves. Did the store receive at least 250 gloves in the shipment?
(1) 44% of the left-handed gloves in the shipment were black.
(2) The shipment included 84 black, right-handed gloves.
Source: Veritas
Organize the information in a MATRIX.
A sporting goods store received a shipment of baseball gloves that included 5 brown gloves for every 6 black gloves.
Since black/brown = 6x/5x, the following matrix is yielded:
Did the store receive at least 250 gloves in the shipment?
In the matrix above, the total number of gloves = 11x.
Question stem, rephrased:
Is 11x ≥ 250?
Statement 1: 44% of the left-handed gloves in the shipment were black.
Let the total number of left-handed gloves = y, implying that the number of black left-handed gloves = (44/100)y = (11/25)y.
The following matrix is yielded:
Since (11/25)y must be an INTEGER VALUE, y must be a MULTIPLE OF 25.
If y=25, then it's possible that 11x < 250.
If y=2500, then 11x > 250.
INSUFFICIENT.
Statement 2: The shipment included 84 black, right-handed gloves.
The following matrix is yielded:
If 6x = 84, then 11x < 250.
If 6x = 840, then 11x > 250.
INSUFFICIENT.
Statements combined:
The leftmost column indicates the following equation:
84 + (11/25)y = 6x.
(11/25)y = 6x - 84 = (multiple of 6) - (multiple of 6) = multiple of 6.
Since (11/25)y must be a multiple of 6, and y must be a multiple of 25, the least possible value for y = 6*25 = 150.
Substituting y=150 into 84 + (11/25)y = 6x, we get:
84 + (11/25)(150) = 6x
150 = 6x
x = 25.
Since the least possible value for x is 25, 11x > 250.
SUFFICIENT.
The correct answer is
C.
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