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

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.

Answer: E.
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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

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

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.

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

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?

Please give your comment,
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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Yes, it does!! Many thanks, Bunuel!!

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.

Answer: E
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Bunuel chetan2u niks18 amanvermagmat




Can I not get an answer in 10 s to say that since question asks percentage and statements also
deal with percentages and not absolute values, answer shall be (E)
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Hi adkikani

I would advice not to do that generalization rather treat the question as per its wording.

Suppose Statement 2 says : There are 40% men in the Group.

So in this scenario also, you are dealing with only % but you will get a solution and the answer will be C

1. 5 % of the women have red hair. But no info on what is the % of women in the group.-----> NS
2. Info is only about men . --------------------------------------------------------------------.-----> NS
1+2. 5 % of the women have red hair. 10 % of men have red hair. But no info on what is the % of women or the men in the group in the group.-----> NS

Ans E
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niks18



Did you assume total people as 100?

St 2: 40% men in group -> 60% women in group.

St 1: Of the women in the group, 5 percent have red hair.
If total people were hundred women with red hair would be 5% of 60% of 100:
ie 3.
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Hi adkikani

Yes you can assume total to be 100 as percents are explicitly mentioned here. you can also assume total to be x, and then follow the steps, to get final answer as 3%

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

(1) Of the women in the group, 5 percent have red hair.NS //as it denotes the percentage of red hair among women but we need the percentage of women with red hair on total
(2) Of the men in the group, 10 percent have red hair.NS //as it denotes the percentage of red hair among men but we need the percentage of women with red hair on total

1+2 E because as we donot know the total (split between women and men)

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