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# What percent of a group of people are women with red hair?

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Math Expert
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What percent of a group of people are women with red hair? [#permalink]

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23 Jul 2012, 04:45
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Difficulty:

5% (low)

Question Stats:

80% (00:43) correct 20% (00:39) wrong based on 1003 sessions

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What percent of a group of people are women with red hair?

(1) Of the women in the group, 5 percent have red hair.
(2) Of the men in the group, 10 percent have red hair.

Practice Questions
Question: 2
Page: 275
Difficulty: 550
[Reveal] Spoiler: OA

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Math Expert
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Re: What percent of a group of people are women with red hair? [#permalink]

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23 Jul 2012, 04:45
SOLUTION

What percent of a group of people are women with red hair?

(1) Of the women in the group, 5 percent have red hair.
(2) Of the men in the group, 10 percent have red hair.

Even taken together the statements are not sufficient to answer the question, since we don't know what percent of the group are women.

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Re: What percent of a group of people are women with red hair? [#permalink]

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25 Jul 2012, 02:34
1
KUDOS
Let women be x and men be y;

Then based on the first condition; 0.05x of the women are red-haired, thus % of red haired women as a group = .05x/x+y => Not Sufficient

Second Condition: 0.1y = number of red-haired men; thus, not sufficient

Combining, not extra information.. still we cannot derive the percentage of red-haired women as the group.

Thus, E

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Re: What percent of a group of people are women with red hair? [#permalink]

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27 Jul 2012, 07:45
SOLUTION

What percent of a group of people are women with red hair?

(1) Of the women in the group, 5 percent have red hair.
(2) Of the men in the group, 10 percent have red hair.

Even taken together the statements are not sufficient to answer the question, since we don't know what percent of the group are women.

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Re: What percent of a group of people are women with red hair? [#permalink]

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29 Apr 2013, 14:02
I thought are was enough becuase it said what percentage of a group of people are women with red hair.

the statment one says 5% of the women in the group have red hair

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Re: What percent of a group of people are women with red hair? [#permalink]

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29 Oct 2013, 23:07
2
KUDOS
What percent of a group of people are women with red hair? Based on question stem there is not much work that can be performed prior to evaluating the 2 statements. However, it may be helpful to understand that to determine the percent of a group you must have a value for the part and for the whole or the % of the part of the whole.

(1) Of the women in the group, 5 percent have red hair. - I/S - We don't know what % (part) of women represent of the whole even though we know what percent of the women have red hair. In addition we don't know have many classifications are in the group - is it men & women, men, women and children. Lots of unknowns.

(2) Of the men in the group, 10 percent have red hair. I/S - from the stmt. we know that there are men in the group but we still don't what % (part) of group (whole) men represents. We could back solve to determine the % of women. Therefore another insufficient stmt.

Taking both stmts together, its still I/S. We don't know the size of the group, % or value that are women or men. If we had that information we could solve because we known what percent of women have red hair based on stmt 1. So Answer is E.

Difficulty level seems appropriate - 550.

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Re: What percent of a group of people are women with red hair? [#permalink]

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18 May 2014, 10:55
1
KUDOS
IMO E

What we need to know --> (Red haired women)/Total x 100

1) 0.05 w = red hair women ...but doesn't tell us anything about the total

insufficient

2) only tells us about red haired men

c) combining doesn't help because we don't know the total numbers of women, men or the total population

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What percent of a group of people are women with red hair? [#permalink]

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18 Jun 2014, 20:39
Bunuel wrote:
What percent of a group of people are women with red hair?

(1) Of the women in the group, 5 percent have red hair.
(2) Of the men in the group, 10 percent have red hair.

Practice Questions
Question: 2
Page: 275
Difficulty: 550

Hi Bunuel,

I want to confirm 1) the meaning of the question and 2) the OA explanation here.

1. Percent of a group of people are women with red hair = women with red hair/total number of people in group OR Percent of a group of people are women with red hair = women with red hair/total number of women in group ? Which one is correct? I think both is correct because OA explanation quoted as following clearly mentions that.

2. OA explanation (OG12-p290) for the (1) of the question says that: "This indicates that 5 percent of the women have red hair, but neither the total number of women nor the total number of people in the group is known. Therefore, further information is needed; NOT sufficient". If OA includes "the total number of women" as the denominator, then (1) should be correct because clearly (1) is stated that: Of the women in the group, 5 percent have red hair. I understand this statement like this: women with red hair/women in group = 5%. Does that mean we already know the number of women and the % of women with red hair. It should be sufficient. Right?

Thank you so much!
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Re: What percent of a group of people are women with red hair? [#permalink]

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21 Jun 2014, 07:23
LucyDang wrote:
Bunuel wrote:
What percent of a group of people are women with red hair?

(1) Of the women in the group, 5 percent have red hair.
(2) Of the men in the group, 10 percent have red hair.

Practice Questions
Question: 2
Page: 275
Difficulty: 550

Hi Bunuel,

I want to confirm 1) the meaning of the question and 2) the OA explanation here.

1. Percent of a group of people are women with red hair = women with red hair/total number of people in group OR Percent of a group of people are women with red hair = women with red hair/total number of women in group ? Which one is correct? I think both is correct because OA explanation quoted as following clearly mentions that.

2. OA explanation (OG12-p290) for the (1) of the question says that: "This indicates that 5 percent of the women have red hair, but neither the total number of women nor the total number of people in the group is known. Therefore, further information is needed; NOT sufficient". If OA includes "the total number of women" as the denominator, then (1) should be correct because clearly (1) is stated that: Of the women in the group, 5 percent have red hair. I understand this statement like this: women with red hair/women in group = 5%. Does that mean we already know the number of women and the % of women with red hair. It should be sufficient. Right?

Thank you so much!

What percent of a group of people are women with red hair?
The question asks to find (women with red hair)/(total number of people).

(1) Of the women in the group, 5 percent have red hair
(women with red hair) = 0.05*(total # of women) --> so we need to find 0.05*(total # of women)/(total number of people).

Here the OG says: neither the total number of women nor the total number of people in the group is known. Thus we cannot find the required ratio.

Does this make sense?
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Re: What percent of a group of people are women with red hair? [#permalink]

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25 Jun 2014, 23:07
Bunuel wrote:
LucyDang wrote:
Bunuel wrote:
What percent of a group of people are women with red hair?

(1) Of the women in the group, 5 percent have red hair.
(2) Of the men in the group, 10 percent have red hair.

Practice Questions
Question: 2
Page: 275
Difficulty: 550

Hi Bunuel,

I want to confirm 1) the meaning of the question and 2) the OA explanation here.

1. Percent of a group of people are women with red hair = women with red hair/total number of people in group OR Percent of a group of people are women with red hair = women with red hair/total number of women in group ? Which one is correct? I think both is correct because OA explanation quoted as following clearly mentions that.

2. OA explanation (OG12-p290) for the (1) of the question says that: "This indicates that 5 percent of the women have red hair, but neither the total number of women nor the total number of people in the group is known. Therefore, further information is needed; NOT sufficient". If OA includes "the total number of women" as the denominator, then (1) should be correct because clearly (1) is stated that: Of the women in the group, 5 percent have red hair. I understand this statement like this: women with red hair/women in group = 5%. Does that mean we already know the number of women and the % of women with red hair. It should be sufficient. Right?

Thank you so much!

What percent of a group of people are women with red hair?
The question asks to find (women with red hair)/(total number of people).

(1) Of the women in the group, 5 percent have red hair
(women with red hair) = 0.05*(total # of women) --> so we need to find 0.05*(total # of women)/(total number of people).

Here the OG says: neither the total number of women nor the total number of people in the group is known. Thus we cannot find the required ratio.

Does this make sense?

Yes, it does!! Many thanks, Bunuel!!
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Re: What percent of a group of people are women with red hair? [#permalink]

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25 Oct 2015, 17:33
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Re: What percent of a group of people are women with red hair? [#permalink]

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21 Jul 2016, 10:55
Bunuel wrote:
What percent of a group of people are women with red hair?

(1) Of the women in the group, 5 percent have red hair.
(2) Of the men in the group, 10 percent have red hair.

An easy way to solve the problem is to set up a double set matrix. In our matrix we’ll have two main categories: gender and red hair. More specifically, our table will be labeled with:

1) Number of people who have red hair (RH)

2) Number of people who do not have red hair (No RH)

3) Number of Women

4) Number of Men

(To save room on our table headings we will use the abbreviations for the categories.)

Since we are asked “what percent” of the people are women with red hair, we can use the convenient number 100 as the total number of people in the group.

Thus, we know:

Total people = 100

Let’s fill all the information into a table.

Now we can consider the statements.

Statement One Alone:

Of the women in the group, 5 percent have red hair.

Since we do not know the number of women in the group, we can let the number of women in the group = w. Thus, 0.05w = the number of women in the group with red hair.

Let’s fill the information into the table.

The information provided is not enough to determine the percentage of people who are women with red hair. Statement one alone is not sufficient. Eliminate answer choices A and D.

Statement Two Alone:

Of the men in the group, 10 percent have red hair.

Since we do not know the number of men in the group, we can let the number of men in the group = m. Thus, 0.1m = the number of men in the group with red hair.

Let’s fill the information into the table.

The information provided is not enough to determine the percentage of people who are women with red hair. Eliminate answer choice B.

Statements One and Two Together:

We know the following:

We see that with the information in the table we still cannot determine the values of w and m, and thus we cannot determine what percent of the group of people are women with red hair.

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Re: What percent of a group of people are women with red hair?   [#permalink] 21 Jul 2016, 10:55
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