What is the probability that a student randomly selected from a class GMAT data sufficiency

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

(1). One-half of the students have brown hair.
(2). One-third of the students are males.

A. Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are not sufficient.

Answer: E

Solution and Explanation:

Approach Solution 1:
There are four student groups here:
M(b) stands for men with brown hair,
M(n) for men with hair that is not brown.
Brown-haired women are classified as F(b);
F(n) - Ladies having hair that isn't brown;
M(b) / (M(b) + M(n) + F(b) + F(n)) = M(b)/60 = ?
1. (M(b) + F(b))/ (M(b) + M(n) + F(b) + F(n)) = ½ → M(b) + F(b) = M(n) + F(n).
= M(b) / (M(b) + M(b) + F(b) + F(b)) = M(b) / (2M(b) + 2F(b)) = M(b) / 60 (It is not sufficient)
2. (M(b) + M(b))/ (M(b) + M(n) + F(b) + F(n)) = 1/3 → 2M(b) + 2F(n) = F(b) + F(n).
= M(b) / (M(b) + M(n) + 2M(b) + 2M(n)) = M(b) / (3M(b) + 3M(n)) = M(b) / 60 (It is not sufficient)
(1)+(2) In essence, we have two equations, each containing three variables. We are unable to articulate variables in order to obtain the requested fraction's numerical value. It's not enough.
Correct option: E

Approach Solution 2:
What is the likelihood that a male with brown hair will be randomly chosen from a class of 60 students?
(1) Brown hair is seen on half of the students.
(2) Males make up one-third of the student body.
In its original form, the question, which is a "2 by 2" inquiry, is regularly asked on the GMAT Math test.
 

The above equation (a+b+c+d=60) has 4 variables (a, b, c, and d) and should match the equations for numbers. Then you need three more equations. For 1) 1 equation and for 2) 1 equation, E is probably the correct response.
With 1) & 2), a+b=30 and b+d=20 are insufficient since you cannot determine the value of b in a specific way.
Correct option: E

Approach Solution 3:
Here is a method using the double matrix that is step-by-step.
In this community of students, there are two criteria to consider: whether the person is male or female, and whether or not they have brown hair.
There are a total of 60 students, thus we can arrange our diagram as follows:

What is the likelihood that a student chosen at random from a class of 60 pupils will be a guy with brown hair?
Thus, we must ascertain how many of the 60 students are brown-haired men. Let's add a STAR to the box that has the following information:

The majority of the students, or 50%, have dark hair.
In light of the fact that 30 of the pupils have brown hair, the other 30 do not.
The result of adding this information to our diagram is:

Do we now possess sufficient knowledge to identify the number in the starred box? No.
As a result, assertion 1 is insufficient.
Assertion 2: Males make up one-third of the student body
20 of the students are therefore masculine, indicating that the other 40 students are NOT male.
The result of adding this information to our diagram is:

Do we now possess sufficient knowledge to identify the number in the starred box? No.
As a result, assertion 2 is insufficient.
Statements 1 and 2 taken together
Integrating the data, we discover:

Do we now possess sufficient knowledge to identify the number in the starred box? No. Consider these two opposing situations:
Case a:

P(selected student is male with brown hair) = 0/60 because there are no male students with brown hair out of the 60 total pupils.
Case b:

In this case, 5 of the 60 students are guys with brown hair, hence the probability that the chosen student has brown hair is 5/60.
The combined statements are insufficient because we lack clarity in our ability to respond to the target inquiry.
Correct option: E

“What is the probability that a student randomly selected from a class GMAT data sufficiency" - is a topic of the GMAT data sufficiency section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT data sufficiency questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and two statements. By using mathematics to answer the question, the candidate must select the appropriate response among five choices which states which statement is sufficient to answer the problem. The data sufficiency section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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