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Confusing

by [email protected] » Thu Jan 30, 2014 7:49 pm
A sporting goods store received a shipment of baseball gloves that included 5 brown gloves for every 6 black gloves. If left-handed and right-handed gloves are sold and ordered individually, 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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Source: — Data Sufficiency |

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by [email protected] » Thu Jan 30, 2014 11:31 pm
Hi shibsriz,

This DS question revolves around a ratio. In these situations, it's important to remember that ratio questions often come down to "multiples."

We're given a starting ratio of Brown gloves to Black gloves = 5/6. We're told that Left-handed and Right-handed gloves are ordered individually (which means that there's NO ratio governing the number of Left or Right). We're asked if the total number of gloves is at least 250? This is a YES/NO question.

From the prompt, we KNOW that the number of Brown gloves MUST be a multiple of 5 and the number of Black gloves MUST be a multiple of 6...

Fact 1: 44% of left-handed gloves are Black.

44/100 = 11/25 left-handed gloves are Black, so the minimum number of this type = 11

This means....

56/100 = 14/25 left-handed gloves are Brown, so the minimum number of this type = 14

We don't know the number (or color) of Right-handed gloves, which is a significant missing piece of information, so we could have ANY NUMBER of Right-handed Black and Right-handed Brown gloves (as long as those number properly complete the given ratio). For example:

Brown Left = 14
Black Left = 11
Brown Right = 1
Black Right = 7
Total = 33 and the answer to the question is NO

Brown Left = 14
Black Left = 11
Brown Right = 101
Black Right = 127
Total = 253 and the answer to the question is YES

Fact 1 is INSUFFICENT

Fact 2: 84 Black Right-handed Gloves

Using the original ratio, this info tells us that there are a MINIMUM of 70 Brown gloves, so the MINIMUM TOTAL = 154 (answer is NO), but the total could be higher (e.g. in the 1000s, so the answer is YES.
Fact 2 is INSUFFICIENT

Combined, we know:
Black Right-handed = 84
Brown Rightt-handed = ???
Black Left-handed = multiple of 11
Brown Left-handed = multiple of 14
Total Brown = multiple of 5
Total Black = multiple of 6

Here's where things get a bit more complex:

Since the Total Black must be a multiple of 6....84 + (multiple of 11) = (multiple of 6)

The MINIMUM multiple of 11 that "fits" this factoid would be 66, so we'd have 84 + 66 = 150 Black gloves AT THE MINIMUM

With those 150 Black gloves, we'd have to match the ratio in the prompt, so the Total number of Brown gloves would be 125 AT THE MINIMUM.

So, we end up with a MINIMUM of 275 gloves; the answer to the question is ALWAYS YES.

Final Answer: C

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by sanju09 » Fri Jan 31, 2014 4:02 am
[email protected] wrote:A sporting goods store received a shipment of baseball gloves that included 5 brown gloves for every 6 black gloves. If left-handed and right-handed gloves are sold and ordered individually, 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 the store receive 5x brown gloves and 6x black gloves, so that a total of 11x gloves are received by the store, where x is some positive integer. The rephrased question is:

Is 11x ≥ 250?

One thing is certain that 11x cannot be equal to 250 because x is a positive integer, hence the refined question is:

Is 11x > 250? Or

Is x > 22?

(1) Since the question is number specific, percentages alone won't serve any purpose. Insufficient

(2) The shipment included 84 black, right-handed gloves. How many black, left-handed gloves? We don't know. If we know that, we'd have known all the missing things in order to answer the target question. Insufficient

Taking together, we know that 56% of black gloves = 84, hence total black can be known, and then total brown may also be known. [spoiler]Sufficient

Pick C[/spoiler]
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by maximiliano » Tue Sep 09, 2014 5:50 am
sanju09 wrote:
[email protected] wrote:A sporting goods store received a shipment of baseball gloves that included 5 brown gloves for every 6 black gloves. If left-handed and right-handed gloves are sold and ordered individually, 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 the store receive 5x brown gloves and 6x black gloves, so that a total of 11x gloves are received by the store, where x is some positive integer. The rephrased question is:

Is 11x ≥ 250?

One thing is certain that 11x cannot be equal to 250 because x is a positive integer, hence the refined question is:

Is 11x > 250? Or

Is x > 22?

(1) Since the question is number specific, percentages alone won't serve any purpose. Insufficient

(2) The shipment included 84 black, right-handed gloves. How many black, left-handed gloves? We don't know. If we know that, we'd have known all the missing things in order to answer the target question. Insufficient

Taking together, we know that 56% of black gloves = 84, hence total black can be known, and then total brown may also be known. [spoiler]Sufficient

Pick C[/spoiler]
I think that may be there is an error when you are taking the statements together. The first statement says that "44% of the left-handed gloves were black". This means that 56% of the left handed gloves were brown. And the 2nd statement refers to the black, right handed gloves, not to the brown gloves. Therefore, we don´t know if 56%=84. However, you are deducing that 56%=84. Am I right?
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by GMATGuruNY » Tue Sep 09, 2014 6:08 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.
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 smallest multiple of 6 -- and thus the least possible 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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