Gloves

[manik11]

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.

I can see why statement 1 and 2 are insufficient on their own, but can't figure out how combining them would answer the target question.

OA : C
Source : Veritas prep

[MartyMurray]

The trick here is noticing two things.

The first is that gloves have to be whole gloves. You wouldn't order .2 gloves or 1/2 of a glove.

Statement 1 say that 44% of the left handed gloves are black. So because you only have whole gloves, there have to actually be some number of black left handed gloves that can be 44%, and by the way, there also have to be some number of left handed gloves that can be 56%. The 44% and 56% can be broken down to 22 and 28 and then 11 and 14. So the smallest number of black left handed gloves is 11.

The other thing to notice is that the question says that there for every six black gloves there are five brown gloves. So the gloves have to number in multiples of 6 and 5.

Statement 2 says that there are 84 black right handed gloves.

We know of at least 84 + 11 black gloves. 84 + 11 = 95.

Let's try dividing 95 by 6. That gives us 15 5/6.

That doesn't work. The black gloves have to number in some multiple of 6.

So the total black gloves is at least 84 + (N x 11) such that the total is a multiple of 6.

84 is divisible by 6 and 11 is prime. So the smallest number of black gloves possible is

84 + (6 x 11) = 150

Now to find the minimum number of brown gloves we divide 150/6 = 25 and then multiply 25 x 5, to get to a minimum total of 275. So we have our answer.

(There is an issue with this question though. We can divide 84 by 6 without a remainder. So there could be 0 left handed gloves 44% of which is 0 and 56% of which is also 0.

So if you want to get technical, the answer is actually E. I am going to forward this to Veritas so that they fix it.)

[GMATGuruNY]

I posted an explanation here:

https://www.beatthegmat.com/ds-tough-one ... 63904.html

[manik11]

I posted an explanation here:

https://www.beatthegmat.com/ds-tough-one ... 63904.html

Thanks Mitch...If a question like this comes up on the test I guess I'll just pick an option and move on. There's no way I can do that much thinking under 2 minutes.

[MartyMurray]

I posted an explanation here:

https://www.beatthegmat.com/ds-tough-one ... 63904.html

Thanks Mitch...If a question like this comes up on the test I guess I'll just pick an option and move on. There's no way I can do that much thinking under 2 minutes.

manik11, the truth is that while you may see a question like this on the test, the question you might see would not likely have so many angles. To get the answer to this one you have to see that gloves have to be whole, that the black left handed gloves are in multiples of 11, and that the two colors of gloves are in multiples of 6 and 5. Then you have to use all that information together to generate an answer.

On the actual GMAT a question like this one would likely require you to see maybe two of those angles, maybe that the gloves have to be counted in integers and that they are in multiples of 6 and 5.

So if you see a question like this one, I suggest you don't automatically skip it. It might actually be pretty easy, especially now that you see in general how they work.

[[email protected]]

Hi manik11,

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

GMAT assassins aren't born, they're made,
Rich