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thelosthippie
GMAT 1: 730 Q49 V41
Posts: 39
03 May 2013, 03:08
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
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Question Stats:
37% (02:31) correct
63%
(02:38)
wrong
based on 759
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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.
(1) 44% of the left-handed gloves in the shipment were black.
(2) The shipment included 84 black, right-handed gloves.
03 May 2013, 05:01
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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?
Given: Black:Brown=6x:5x, so the # of black gloves is a multiple of 6 and # of brown gloves is a multiple of 5.
(1) 44% of the left-handed gloves in the shipment were black --> 44%=11/25 of left-handed gloves are black, thus the # of left-handed gloves is a multiple of 25. Not sufficient.
(2) The shipment included 84 black, right-handed gloves. Also not sufficient.
(1)+(2) We have the following matrix:
Notice that we have that \(84+\frac{11Y}{25}=6X\).
Now, since both 84 and 6x are multiples of 6, then \(\frac{11Y}{25}\) must also be a multiple of 6, which means that Y must be both multiple of 25 and 6, or a multiple of 150 (LCM of 25 and 6). Thus the least value of Y is 150. In this case \(84+\frac{11*150}{25}=150=6x\) --> \(X_{min}=25\) --> \(Total=6X+5X=11x=275>250\). Sufficient.
Answer: C.
Hope it's clear.
(1)+(2).png [ 4.44 KiB | Viewed 19193 times ]
Given: Black:Brown=6x:5x, so the # of black gloves is a multiple of 6 and # of brown gloves is a multiple of 5.
(1) 44% of the left-handed gloves in the shipment were black --> 44%=11/25 of left-handed gloves are black, thus the # of left-handed gloves is a multiple of 25. Not sufficient.
(2) The shipment included 84 black, right-handed gloves. Also not sufficient.
(1)+(2) We have the following matrix:
Notice that we have that \(84+\frac{11Y}{25}=6X\).
Now, since both 84 and 6x are multiples of 6, then \(\frac{11Y}{25}\) must also be a multiple of 6, which means that Y must be both multiple of 25 and 6, or a multiple of 150 (LCM of 25 and 6). Thus the least value of Y is 150. In this case \(84+\frac{11*150}{25}=150=6x\) --> \(X_{min}=25\) --> \(Total=6X+5X=11x=275>250\). Sufficient.
Answer: C.
Hope it's clear.
Attachment:
(1)+(2).png [ 4.44 KiB | Viewed 19193 times ]
03 May 2013, 05:10
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1) Not sufficient.As we don't know anything on right handed gloves.
2) Not sufficient.
Combining both :
Let the total no of gloves be 200x. 100x for left hand and 100x for right hand.
For right hand: black gloves = 84
brown gloves = 100x - 84.
For left hand : black gloves = 44x
brown gloves = 100x - 44x = 56x
So total no of black gloves = 84 + 44x
total no of brown gloves = 100x - 84 + 56x = 156x - 84.
Then, (84 + 44x)/(156x - 84) = 6/5
=> x = 924/716
=> 200x = 258
Ans : Option C.
----------------------------------------
Please press \(+1 Kudos\)if my post helps you.
2) Not sufficient.
Combining both :
Let the total no of gloves be 200x. 100x for left hand and 100x for right hand.
For right hand: black gloves = 84
brown gloves = 100x - 84.
For left hand : black gloves = 44x
brown gloves = 100x - 44x = 56x
So total no of black gloves = 84 + 44x
total no of brown gloves = 100x - 84 + 56x = 156x - 84.
Then, (84 + 44x)/(156x - 84) = 6/5
=> x = 924/716
=> 200x = 258
Ans : Option C.
----------------------------------------
Please press \(+1 Kudos\)if my post helps you.
