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# A sporting goods store received a shipment of baseball glove

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03 May 2013, 03:08
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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.
[Reveal] Spoiler: OA

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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.

Hope it's clear.

[Reveal] Spoiler:
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(1)+(2).png [ 4.44 KiB | Viewed 3152 times ]

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Re: A sporting goods store received a shipment of baseball glove [#permalink]

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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
=> 200x = 258

Ans : Option C.

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Re: A sporting goods store received a shipment of baseball glove [#permalink]

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03 May 2013, 05:15
Expert's post
subhendu009 wrote:
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
=> 200x = 258

Ans : Option C.

----------------------------------------
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That's not correct.

First of all, we cannot get the exact number of the gloves in the shipment. Next, the # of gloves MUST be a multiple of 11, so the # of gloves cannot be 258.

Check here: a-sporting-goods-store-received-a-shipment-of-baseball-glove-152090.html#p1220135 The least # of gloves is 275.
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Re: A sporting goods store received a shipment of baseball glove [#permalink]

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03 May 2013, 07:40
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thelosthippie 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.

Bunuel,I feel this question is a bit out of place for GMAT, ONLY because it requires one to know that baseball glvoes don't come in pairs.Your take?
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Re: A sporting goods store received a shipment of baseball glove [#permalink]

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03 May 2013, 07:55
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vinaymimani wrote:
thelosthippie 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.

Bunuel,I feel this question is a bit out of place for GMAT, ONLY because it requires one to know that baseball glvoes don't come in pairs.Your take?

Yes, in baseball players wear only one glove, but not sure that this is a common knowledge, thus real GMAT question would probably make note about that.
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Re: A sporting goods store received a shipment of baseball glove [#permalink]

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14 Jun 2014, 12:14
Total Gloves have to be a multiple of 10k + 12k..including right + left for both the colors

Now A says it is a multiple of 25..so the least possible number where 22 and 25 meet (LCM) is above 250..A is suff

B is also suff---> 168 Black gloves + 168*5/6 = some number greater than or less than 250...suff

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Re: A sporting goods store received a shipment of baseball glove [#permalink]

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14 Jun 2014, 12:33
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JusTLucK04 wrote:
Total Gloves have to be a multiple of 10k + 12k..including right + left for both the colors

Now A says it is a multiple of 25..so the least possible number where 22 and 25 meet (LCM) is above 250..A is suff

B is also suff---> 168 Black gloves + 168*5/6 = some number greater than or less than 250...suff

From stem: the total # of gloves is a multiple of 11, not necessarily of 22.

From (1): the # of left-handed gloves is a multiple of 25, not the total # of gloves.

From (2): the shipment included 84 black, right-handed gloves. How does it follow from this that there are 168 black gloves?

Hope it helps.
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Re: A sporting goods store received a shipment of baseball glove [#permalink]

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14 Jun 2014, 12:50
Bunuel wrote:
JusTLucK04 wrote:
Total Gloves have to be a multiple of 10k + 12k..including right + left for both the colors

Now A says it is a multiple of 25..so the least possible number where 22 and 25 meet (LCM) is above 250..A is suff

B is also suff---> 168 Black gloves + 168*5/6 = some number greater than or less than 250...suff

From stem: the total # of gloves is a multiple of 11, not necessarily of 22.

From (1): the # of left-handed gloves is a multiple of 25, not the total # of gloves.

From (2): the shipment included 84 black, right-handed gloves. How does it follow from this that there are 168 black gloves?

Hope it helps.

I just went through the complete thread...I didn't have any clue about baseball stuff..
So there cant be 5 brown and 6 black gloves..as they have to be in pairs(My assumption)..Hence I deduced the 10 -12 logic
Same assumption for 2nd statement and you should get a D..
Not a GMAT type question..No body outside US follows baseball(I believe)
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Re: A sporting goods store received a shipment of baseball glove [#permalink]

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30 Jun 2014, 11:03
Hi Bunuel,

A is not sufficient since we don't know the exact number of the total left hand gloves.

for B if we know there are 84 right hand gloves, then there will be equivalent number of left hand side gloves.
hence the total will be 168. Also, its given the ration of Brown to black 5:6 ... hence 140 another gloves .... this makes the total more than 250 .. sufficient .

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Re: A sporting goods store received a shipment of baseball glove [#permalink]

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30 Jun 2014, 11:38
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GmatDestroyer2013 wrote:
Hi Bunuel,

A is not sufficient since we don't know the exact number of the total left hand gloves.

for B if we know there are 84 right hand gloves, then there will be equivalent number of left hand side gloves.
hence the total will be 168. Also, its given the ration of Brown to black 5:6 ... hence 140 another gloves .... this makes the total more than 250 .. sufficient .

Hope it helps.
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Re: A sporting goods store received a shipment of baseball glove [#permalink]

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23 Nov 2015, 13:14
Bunuel 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?

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.

Hope it's clear.

I thought I'd point out that Bunuel approach is sometimes known as the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of baseball gloves, and the two characteristics are:
-left-handed or right-handed
- black or brown

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

Cheers,
Brent
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Re: A sporting goods store received a shipment of baseball glove [#permalink]

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29 Nov 2015, 16:36
Expert's post
Hi All,

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.

[Reveal] Spoiler:
C

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30 Nov 2015, 05:38
Expert's post
EMPOWERgmatRichC wrote:
Hi All,

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.

[Reveal] Spoiler:
C

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

Hi Rich,

Although Fact 2 is insufficient, how could you use the original ratio in the prompt (5:6)? you have only the number of Right handed gloves 84, while the ration is about Total Brown to Total black. So the balk left handed gloves are missing.
A sporting goods store received a shipment of baseball glove   [#permalink] 30 Nov 2015, 05:38
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