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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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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, 00:32
n(Lice) = n(Only lice) + n(Both lice and fleas)
n(Both lice and fleas) = 84
n(Lice) = 94
n(Only lice) = 94-84 = 10
Since, it is also said that exactly half the sheep have lice, it can be inferred that half the number of sheep is 94.


Therefore, the total number of sheep having only fleas is 10(Option A)
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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, 14:53
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, 08:20
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, 08:47
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, 21:49
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, 21:54
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Half of the sheep have lice and this half is=94 hence total sheep=188
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Kudos [?]: 14 [1], given: 111

Re: In Gabriel's sheep herd, every sheep has either fleas or lice or both.   [#permalink] 19 Nov 2017, 21:54
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