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According to a certain estimation, the total number of black cats is 2

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According to a certain estimation, the total number of black cats is 2  [#permalink]

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New post 20 May 2015, 12:09
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A
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E

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According to a certain estimation, the total number of black cats is 25% greater than the number of black male cats, and the number of all female cats is 5 times the number of black female cats. If the male cats are 50% of all cats, then what percent of male cats are black?

A. 10
B. 20
C. 40
D. 50
E. 80

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Re: According to a certain estimation, the total number of black cats is 2  [#permalink]

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New post 20 May 2015, 17:05
With percent problems like this it is almost always easiest to just pick a number (100, because it is dealing with percents) and then go from there. Here, if you pick 100 for the number of black male cats, then that means that the total number of black cats is 125 (25% more), and therefore the number of black female cats is 25. The total number of female cats is 5x the number of black female cats, so that is 125. Male cats are 50% of the cats, and because there are 125 female cats, then there must also be 125 male cats. 100 black male cats / 125 total male cats = 80%, or answer choice E. Trying to do this problem conceptually, rather than just picking the number 100 and then carefully moving from one piece of information to the next like I did here, would be confusing.

I hope this helps!
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Re: According to a certain estimation, the total number of black cats is 2  [#permalink]

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New post 20 May 2015, 20:05
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Hi reto,

TESTing VALUES (the approach Brandon used) is a great way to deal with this question (as it puts all of the unknowns in terms of real-world numbers). As it stands, you can also answer this question with Algebra. The question is written with the information in the perfect order to translate as you read....

According to a certain estimation, the total number of black cats is 25% greater than the number of black male cats.....

Black Male Cats = X
Total Black Cats = 1.25X

From this, we can figure out the number of Black FEMALE Cats....

Black Female Cats = 1.25X - X = 0.25X

.....and the number of all female cats is 5 times the number of black female cats....

Black Female Cats = 0.25X
Total Female Cats = 5(0.25X) = 1.25X

....If the male cats are 50% of all cats.....

Since Total Male Cats = 50% of all cats, then the other 50% of the cats have to be female (and we already know that the Total Female Cats = 1.25X)....

Total Female Cats = 50% of ALL Cats = 1.25X
Total Male Cats = 50% of ALL Cats = 1.25X

The question then asks what percent of MALE cats are BLACK?

Total Male Cats = 1.25X
Black Male Cats = X

X/1.25X = 4/5 = .8 = 80%

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According to a certain estimation, the total number of black cats is 2  [#permalink]

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New post 20 May 2015, 21:55
This is a pure ratio problem, so the answer will be the same for any numbers we use, and we might as well use the simplest ones.

the total number of black cats is 25% greater than the number of black male cats - if one value is 25% more than another, then the values are in a 5 to 4 ratio. So for every 4 black male cats, there are 5 black cats in total, and since that total is just males+females, we must have 1 black female cat for every 4 black male cats. So we can just pretend we have:

4 black male cats
1 black female cat

then since the number of all female cats is 5 times the number of black female cats, we have 5 female cats in total. Since the male cats are 50% of all cats, we also have 5 male cats in total, 4 of which are black, so the answer is 4/5 = 80%.
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Re: According to a certain estimation, the total number of black cats is 2  [#permalink]

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New post 20 May 2015, 22:49
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The question can be solved by representing the information visually in the form of a tree structure. Refer the diagram below

Image

It's given to us that total number of black cats is 25% greater than the number of black male cats. If we assume the number of black male cats as \(x\) we have the number of black cats as \(1.25x\). That would give us the number of black female cats as \(0.25x\).

It's also given that total number of female cats = 5 times the female black cats = \(5 * 0.25x = 1.25x\).

Since total number of female cats = female black cats + female non-black cats

\(1.25x = 0.25x +\) female non-black cats i.e. female non-black cats = \(x\)

Since we are not told anything about the number of non-black male cats let's assume the number of non-black male cats as y. That would give us the total number of non-black cats as \((x + y)\). Hence total number of cats = \(2.25x + y\)

We are also told that male cats are 50% of total cats i.e. \(x + y = \frac{(2.25x + y)}{2}\) which would give us \(y = 0.25x.\)

We are asked to find the ratio of male black cats to the total male cats i.e. \(\frac{x}{(x + y)}\).

Substituting \(y = 0.25x\) would give us the value of \(\frac{x}{(x + y)} = \frac{1}{1.25} = 80\)%.

Hope it's clear :)

Regards
Harsh
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Re: According to a certain estimation, the total number of black cats is 2  [#permalink]

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New post 25 Jun 2016, 05:13
i am going to use short abbreviations for cats(BC-black cats,BMC-black male cats,BFC-black female cats,AC-all cats,AFC-all female cats and AMC-all male cats)

let s take a number and start this problem.

Suppose BMC=100, then BC=125 as per the question now BFC=125-100=25

Now, AFC=5*25=125
further the questions says that AMC =50% of AC..that means 50% is AFC,

Since, AC=AFC+AMC so, AMC=125 also

now to calculate %age,what % of AMC is BMC.

so (100/125) *100 is ur answer that is 80%
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According to a certain estimation, the total number of black cats is 2  [#permalink]

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New post 10 Jul 2016, 04:22
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Given that male = 50% hence female=50% ; 5y=50 so y =10
X+10=1.25x
X=40
1.25x=50
We were asked to find what percent of male cats are black?
S0 40/50 =80%
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According to a certain estimation, the total number of black cats is 2  [#permalink]

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New post 02 Oct 2017, 11:41
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Please see the attachment.
Attachment:
Capture.PNG
Capture.PNG [ 4.77 KiB | Viewed 903 times ]


\(1.25x+50-x+40=100\)
\(=>0.25x=10\)
\(=>x=40\)

\(∴ \frac{40}{50}=80\)%
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Re: According to a certain estimation, the total number of black cats is 2  [#permalink]

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New post 05 Oct 2017, 10:18
reto wrote:
According to a certain estimation, the total number of black cats is 25% greater than the number of black male cats, and the number of all female cats is 5 times the number of black female cats. If the male cats are 50% of all cats, then what percent of male cats are black?

A. 10
B. 20
C. 40
D. 50
E. 80


We can let the total number of cats = 1,000. (This is a convenient number to use, but we could use 10,000, or 100,000, or any other number.)

Thus, there are 500 male cats.

Since the number of all female cats is 5 times the number of black female cats (f):

500 = 5f

100 = f

Since the total number of black cats (b) is 25% greater than the number of black male cats (m):

b = 1.25m

Since f + m = b:

100 + m = 1.25m

100 = 0.25m

400 = m

Thus, the number of black male cats is 400. Since there are 500 male cats, the percentage of male cats that are black is:

400/500 = 80/100 = 80%

Answer: E
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Re: According to a certain estimation, the total number of black cats is 2 &nbs [#permalink] 05 Oct 2017, 10:18
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