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A herd of goats consists of A males and B females. In that herd, half

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A herd of goats consists of A males and B females. In that herd, half  [#permalink]

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25 Sep 2016, 09:40
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Difficulty:

65% (hard)

Question Stats:

61% (02:42) correct 39% (02:31) wrong based on 129 sessions

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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

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Re: A herd of goats consists of A males and B females. In that herd, half  [#permalink]

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25 Sep 2016, 10:05
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Bunuel 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

Male Goats = A

Female Goats = B

1/2 of Horn Goats = Females = x (say)
Therefore, other half will be Male = x

Now, Male Goats without horn = A -x -- (1)

Also, Total Goats without horn = C = (A -x) + (B-x)

or x = (A+B - C)/2

Substituting the value of x in equation (1)

We will have A - x =(A−B+C)/2.
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Re: A herd of goats consists of A males and B females. In that herd, half  [#permalink]

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14 Sep 2018, 17:42
Bunuel 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

The number of goats that have horns is A + B - C. Since half of the goats that have horns are females, the other half are males. Thus, the number of male goats that have horns is (A + B - C)/2 and, hence, the number of male goats that do not have horns is:

A - (A + B - C)/2 = 2A/2 - (A + B - C)/2 = (A - B + C)/2

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Re: A herd of goats consists of A males and B females. In that herd, half   [#permalink] 14 Sep 2018, 17:42
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