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In Gabriel's sheep herd, every sheep has either fleas or lice or both.

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In Gabriel's sheep herd, every sheep has either fleas or lice or both. [#permalink]

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In Gabriel's sheep herd, every sheep has either fleas or lice or both. Half of the sheep have lice, and 84 sheep have both pests. If 94 sheep have lice, how many sheep have only fleas?

A. 10
B. 20
C. 84
D. 94
E. 178
[Reveal] Spoiler: OA

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In Gabriel's sheep herd, every sheep has either fleas or lice or both. [#permalink]

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New post 18 Oct 2016, 23:32
The total number of sheep is twice the number of sheep having lice(2*94 = 188)

P(Total) = 188
P(Both) = 84
P(Lice) = 94
Therefore, P(Only Lice) = 94 - 84 = 10

P(Total) = P(Only Lice) + P(Only Fleas) + P(Both)
\(188 = 10 + x + 84\)
\(x = 188 - 94 = 94\)

Therefore, the total number of sheep having only fleas is 94(Option D)
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Re: In Gabriel's sheep herd, every sheep has either fleas or lice or both. [#permalink]

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New post 19 Oct 2016, 13:53
Bunuel wrote:
In Gabriel's sheep herd, every sheep has either fleas or lice or both. Half of the sheep have lice, and 84 sheep have both pests. If 94 sheep have lice, how many sheep have only fleas?

A. 10
B. 20
C. 84
D. 94
E. 178


Total = Lice + Fleas - Both
2(94) = 94 + F - 84
188 = 10 + F
F = 178
Since out of that 178, 84 have fleas, that leaves 94 with fleas only.

A Venn diagram might be helpful here.
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Re: In Gabriel's sheep herd, every sheep has either fleas or lice or both. [#permalink]

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New post 27 Oct 2017, 07:20
Chakolate wrote:
Since out of that 178, 84 have fleas, that leaves 94 with fleas only.


Since out of that 178, 84 have both fleas and lice, that leaves 94 with fleas only.
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Re: In Gabriel's sheep herd, every sheep has either fleas or lice or both. [#permalink]

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New post 27 Oct 2017, 07:47
let x be total of sheep
=> 0.5 x = 94 => x = 188
now T = f + l - both
=> 188 = f + 94 - 84
=> f = 178
now sheep having "only" fleece = 178 - both = 178 - 84 = 94
ans: D
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Re: In Gabriel's sheep herd, every sheep has either fleas or lice or both. [#permalink]

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New post 19 Nov 2017, 20:49
Bunuel wrote:
In Gabriel's sheep herd, every sheep has either fleas or lice or both. Half of the sheep have lice, and 84 sheep have both pests. If 94 sheep have lice, how many sheep have only fleas?

A. 10
B. 20
C. 84
D. 94
E. 178

Hi
Is the answer 94?
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Re: In Gabriel's sheep herd, every sheep has either fleas or lice or both. [#permalink]

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New post 19 Nov 2017, 20:54
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Half of the sheep have lice and this half is=94 hence total sheep=188
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Re: In Gabriel's sheep herd, every sheep has either fleas or lice or both.   [#permalink] 19 Nov 2017, 20:54
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