GMAT Data Sufficiency- What is the probability that a student randomly selected from a class of 60 students will be a male who has brown hair?

Question: What is the probability that a student randomly selected from a class of 60 students will be a male who has brown hair?

One-half of the students have brown hair.
One-third of the students are males.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statement TOGETHER are sufficient, but NEITHER statement ALONE are sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.

“ What is the probability that a student randomly selected from a class of 60 students will be a male who has brown hair?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation

Approach Solution 1:

Correct Answer: B

Model Answer 1

According to the information given, there are 60 students.

A student is chosen at random.
We must determine the likelihood that the student is a male with brown hair.
Half of the students in Statemet. 1 have brown hair.
Regarding the female students, we are unaware of anything. (Insufficient) -Remove A, D -

Statement. 2—Males make about one-third of the student body.
Regarding the students with brown hair, we don't know anything. A second time (insufficient) - Remove B
Combining the two, we find that 20 kids, or 1/3 of 60, are male students from St. 2 and that half of the 60 pupils, or 30, have brown hair.
Both men and women may be among the 30 students.
So it is impossible to determine how many men have dark hair.
(Insufficient)

Statements (1) and (2) TOGETHER are NOT sufficient.

Correct Answer: B

Approach Solution 2

There is another approach to answering this question which is Pretty simple

Statement 1: The number of students with brown hair is = ½ * 60 = 30
Statement 2: The number of male students is = ⅓ * 60 = 20

There's a chance that the 20 male students all have brown hair.
Because of this, P (male with brown hair) = 20/30 = ⅓
Perhaps only ten of the twenty male pupils have dark hair.
Because of this, P (male with brown hair) = 10/60 = ⅙
The two statements taken together are insufficient since the probability can take on many values.
Statements (1) and (2) TOGETHER are NOT sufficient.

Correct Answer: B

Approach Solution 3

There is another, far more simple approach of responding to this question.

Statement 1: There are 30 kids with dark hair, or ½ of all students.
Statement 2: There are 20 male students, or ⅓ of all students.

It's possible that all 20 of the male students have dark hair.
As a result, P (a man with brown hair) = 20/30 = ⅓
Of the twenty male students, perhaps ten have black hair.
P (a guy with brown hair) hence equals 10/60 or ⅙
Since the probability might have many different values, the two statements alone are insufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

Correct Answer: B

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GMAT Data Sufficiency- What is the probability that a student randomly selected from a class of 60 students will be a male who has brown hair?

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