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DS Tough one from Veritas

by aaggar7 » Tue Jun 11, 2013 6:35 am
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.
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by GMATGuruNY » Tue Jun 11, 2013 9:24 am
aaggar7 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.
Let BR = total brown, BL = total black, L = total left, LBL = left black, and RBL = right black.

Statement 1: 44% of the left-handed gloves in the shipment were black.
LBL = (44/100)L = (11/25)L.
If L = 25, then LBL = 11.
If L = 50, then LBL = 22.
The examples above illustrate that LBL = multiple of 11.
No way to determine whether the total number of gloves is greater than 250.
INSUFFICIENT.

Statement 2: The shipment included 84 black, right-handed gloves.
If none of the black gloves are left-handed, then BL = 84.
This is the MINIMUM value of BL.
Since the question stem indicates that BL : BR = 6:5 = 84:70, the MINIMUM value of BR = 70.
If BL = 84 and BR = 70, then the total number of gloves = 84+70 = 154, which is less than 250.
If BL = 168 and BR = 140, then the total number of gloves = 168+140 = 308, which is greater than 250.
INSUFFICIENT.

Statements combined:
According to statement 2, RBL = 84.
According to statement 1, LBL must be a multiple of 11.
According to the question stem, BL : BR = 6:5, implying that BL = multiple of 6.

Since RBL + LBL = BL, we get:
84 + multiple of 11 = multiple of 6.

To determine the minimum value of BL, add multiples of 11 to 84 until a multiple of 6 is yielded:
95, 106, 117, 128, 139, 150.
The least multiple of 6 -- and thus the least value of BL -- is the value in red.

Since the minimum value of BL = 150, and BL : BR = 6:5 = 150:125, the minimum value of BR = 125.
Thus, the minimum possible total = BL + BR = 150+125 = 275, which is greater than 250.
SUFFICIENT.

The correct answer is C.
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by aaggar7 » Tue Jun 11, 2013 11:41 pm
Thanks Mitch.Do you feel this problem was of 700+ level?
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by bubbliiiiiiii » Wed Jun 12, 2013 4:36 am
Statement 2: The shipment included 84 black, right-handed gloves.
If none of the black gloves are left-handed, then BL = 84.
Hi Mitch,

Since gloves is something dealt in pairs, isn't it implicit to assume that if there are 84 right handed black gloves then there will be equivalent no. of left handed gloves too?

Having said that, I would have considered RBL=84 instead of BL=84!

Moreover, is question GMAT like? If it is, then I have a long way to go! :)

Please suggest.
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by GMATGuruNY » Wed Jun 12, 2013 7:31 am
bubbliiiiiiii wrote:
Statement 2: The shipment included 84 black, right-handed gloves.
If none of the black gloves are left-handed, then BL = 84.
Hi Mitch,

Since gloves is something dealt in pairs, isn't it implicit to assume that if there are 84 right handed black gloves then there will be equivalent no. of left handed gloves too?

Having said that, I would have considered RBL=84 instead of BL=84!

Moreover, is question GMAT like? If it is, then I have a long way to go! :)

Please suggest.
Avoid making assumptions.
BASEBALL gloves are not sold in pairs.
A baseball player requires only one type of glove: either right-handed (if the player catches with his right hand) or left-handed (if the player catches with his left hand).
For this reason, right-handed and left-handed gloves are sold separately.

This problem is more difficult than what you're likely to encounter on test day.
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