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Herd of Goats

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Herd of Goats

by kartikshah » Sun Jul 22, 2012 5:20 am
A herd of goats consists of A males and B females. In that herd, half of the goats that have horns are females. If C goats of the herd do not have horns, then the total number of male goats in the herd that do NOT have horns, in terms of A, B and C is -
A. (A-B+C)/2
B. (A-B-C)/2
C. (A+B+C)/2
D. (A+B-C)/2
E. (2A-B+C)/2

Source: Master GMAT

I quite enjoyed solving this question correctly. I hope others get it right too! OA will be shared after a few answers begin to come in.
(BTW, Master GMAT's free content has some nice questions on sets)
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by theCEO » Sun Jul 22, 2012 5:34 am
imo D
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by eagleeye » Sun Jul 22, 2012 5:41 am
kartikshah wrote:A herd of goats consists of A males and B females. In that herd, half of the goats that have horns are females. If C goats of the herd do not have horns, then the total number of male goats in the herd that do NOT have horns, in terms of A, B and C is -
A. (A-B+C)/2
B. (A-B-C)/2
C. (A+B+C)/2
D. (A+B-C)/2
E. (2A-B+C)/2

Source: Master GMAT

I quite enjoyed solving this question correctly. I hope others get it right too! OA will be shared after a few answers begin to come in.
(BTW, Master GMAT's free content has some nice questions on sets)
Total Goats = T = A+B
Goats without horns =C
Goats with horns = A+B-C
half of these are males
So male goats with horns = (A+B-C)/2
So male goats without horns = total males - horned males = A - (A+B-C)/2 = (A-B+C)/2.

A is correct.

Alternatively, Let A=2, B=2 and C=4.
Then Goats with horns = 4-4 = 0. So both male goats do not have horns. Let's check the option that gives us 2.
Now test the options:

(2-2+4)/2 = 2 (works)
(2-2-4)/2 = -ve (NO)
(2+2+4)/2 = 4 (NO)
(2+2-4)/2 = 0 (NO)
(4-2+4)/2 = 3 (NO)

A is correct. :)
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by theCEO » Sun Jul 22, 2012 5:47 am
eagleeye wrote:
kartikshah wrote:A herd of goats consists of A males and B females. In that herd, half of the goats that have horns are females. If C goats of the herd do not have horns, then the total number of male goats in the herd that do NOT have horns, in terms of A, B and C is -
A. (A-B+C)/2
B. (A-B-C)/2
C. (A+B+C)/2
D. (A+B-C)/2
E. (2A-B+C)/2

Source: Master GMAT

I quite enjoyed solving this question correctly. I hope others get it right too! OA will be shared after a few answers begin to come in.
(BTW, Master GMAT's free content has some nice questions on sets)
Total Goats = T = A+B
Goats without horns =C
Goats with horns = A+B-C
half of these are males
So male goats with horns = (A+B-C)/2
So male goats without horns = total males - horned males = A - (A+B-C)/2 = (A-B+C)/2.

A is correct.

Alternatively, Let A=2, B=2 and C=4.
Then Goats with horns = 4-4 = 0. So both male goats do not have horns. Let's check the option that gives us 2.
Now test the options:

(2-2+4)/2 = 2 (works)
(2-2-4)/2 = -ve (NO)
(2+2+4)/2 = 4 (NO)
(2+2-4)/2 = 0 (NO)
(4-2+4)/2 = 3 (NO)

A is correct. :)
Its funny how the word NOT is capitalized and I did not see it. Hope I get back my eyesight before the day of the exam :)
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by tisrar02 » Mon Jul 23, 2012 6:23 pm
A=10
B=10
Assume C=4

Half of the goats with horns are females= 2 Females have horns
That means 2 Males have horns.

What is the total number of Males without horns?

10-2=8---> NUMBER WE WANT!!!!!

(A-B+C)/2= (10-10+16)/2= 8

Answer- A

I would recommend going through all the answer choices to see if any other answers yield the number we want.
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