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If 55 percent of a group of people have brown hair and 80 percent of

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Math Expert
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Joined: 02 Sep 2009
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If 55 percent of a group of people have brown hair and 80 percent of  [#permalink]

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New post 07 Feb 2019, 01:18
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

80% (02:18) correct 20% (02:34) wrong based on 44 sessions

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Re: If 55 percent of a group of people have brown hair and 80 percent of  [#permalink]

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New post 07 Feb 2019, 01:27
Bunuel wrote:
If 55 percent of a group of people have brown hair and 80 percent of the same group do not have red hair, what fraction of those who do not have brown hair have red hair?


A. 1/4

B. 4/11

C. 4/9

D. 5/9

E. 4/5


can be solved using 2x2 matrix
IMO C
4/9
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Re: If 55 percent of a group of people have brown hair and 80 percent of  [#permalink]

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New post 07 Feb 2019, 03:27
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Bunuel wrote:
If 55 percent of a group of people have brown hair and 80 percent of the same group do not have red hair, what fraction of those who do not have brown hair have red hair?


A. 1/4

B. 4/11

C. 4/9

D. 5/9

E. 4/5


55% have brown hair. So 45% do not have brown hair.
80% do not have red hair. So 20% have red hair.

"what fraction of those who do not have brown hair have red hair?"

Those who have red hair as a fraction of those who do not have brown hair = 20/45 = 4/9

Answer (C)
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Re: If 55 percent of a group of people have brown hair and 80 percent of  [#permalink]

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New post 07 Feb 2019, 14:49
Bunuel wrote:
If 55 percent of a group of people have brown hair and 80 percent of the same group do not have red hair, what fraction of those who do not have brown hair have red hair?


A. 1/4

B. 4/11

C. 4/9

D. 5/9

E. 4/5


If 55% have brown hair, that means 45% do NOT have brown hair.

We know that 80% do not have red hair, so 20% do have red hair.

They are apart of the same group so 45% * x = 20%

x = 4/9 (answer choice C)
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Re: If 55 percent of a group of people have brown hair and 80 percent of  [#permalink]

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New post 10 Feb 2019, 08:44
Bunuel wrote:
If 55 percent of a group of people have brown hair and 80 percent of the same group do not have red hair, what fraction of those who do not have brown hair have red hair?


A. 1/4

B. 4/11

C. 4/9

D. 5/9

E. 4/5


If 55% of the group have brown hair, then 100% - 55% = 45% of the group do not have brown hair (which includes people who have red hair). And since 80% of the group do not have red hair, then 20% of the group do have red hair. Thus, the ratio, or fraction, of those that do have red hair to those who do not have brown hair is:

0.20/0.45 = 20/45 = 4/9

Answer: C
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Re: If 55 percent of a group of people have brown hair and 80 percent of  [#permalink]

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New post 10 Feb 2019, 08:54
Bunuel wrote:
If 55 percent of a group of people have brown hair and 80 percent of the same group do not have red hair, what fraction of those who do not have brown hair have red hair?


A. 1/4

B. 4/11

C. 4/9

D. 5/9

E. 4/5


One of its kind :-o, Let total be 100 people

------------BH------No BH------
RH-------------------------------20
No RH---------------------------80
-----------55---------45--------100

those who do not have brown hair have red hair
20/45

4/9

C
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Re: If 55 percent of a group of people have brown hair and 80 percent of   [#permalink] 10 Feb 2019, 08:54
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