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In a classroom, 40% of the boys had read a particular book. What was the probability that a student who was randomly selected from the classroom was a girl who had read the book?
(1) Three-eighths of all students in the classroom had read the book
(2) 20 girls in the classroom had not read the book
  • a)
    Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
  • b)
    Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
  • c)
    BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
  • d)
    EACH statement ALONE is sufficient to answer the question asked.
  • e)
    Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'E'. Can you explain this answer?
Verified Answer
In a classroom, 40% of the boys had read a particular book. What was t...
teps 1 & 2: Understand Question and Draw Inferences
Given:
  • We are given information about the students in the classroom based on 2 attributes:
    • Gender – Girls, Boys
    • Book – Read, Not Read
 
  • Accordingly, we can draw the following table to represent the information given in this question:
  •  Let the total number of Boys in the class be B and the total number of girls be G
    • As given: 40% of the boys read. So, their number is equal to 0.4B
    • Therefore, the number of boys who do not read = B – 0.4B = 0.6B
      • (Note: In this solution, the given information will be displayed in black font color in the table, while the inferred information will be displayed in blue font color)
 
 
To find: P(Choosing a girl has read the book)
 
  • Let the number of girls who have read the book be GR
  • So, Required Probability = 
Step 3: Analyze Statement 1 independently
Statement 1 says that ‘Three-eighths of all students in the classroom had read the book’
Therefore, 
 
  • This equation will give us an expression for GR in terms of B and G
  • So, we will get an expression for the Required Probability in terms of B and G. However, since we do not know the values of B and G (or the ratio B/G), we will not be able to find the value of the Required Probability
  • Therefore, Statement 1 alone is not sufficient.
Step 4: Analyze Statement 2 independently
Statement 2 says that ‘20 girls in the classroom had not read the book’
  • Therefore, GR = G – 20
    • (And Total Students who Read = 0.4B + G – 20)
  • So, Required Probability = 
  • However, since we do not know the values of G and B, we cannot find the value of the Required Probability
  • So, Statement 2 alone is not sufficient
 
Step 5: Analyze Both Statements Together (if needed)
Combining the 2 statements, we can write:
  • This is a linear equation with 2 unknowns. So, we cannot find unique values of B and G from this equation.
  • Therefore, we cannot find unique values of the required probability even after combining the 2 statements.
Answer: Option E
 
 
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In a classroom, 40% of the boys had read a particular book. What was the probability that a student who was randomly selected from the classroom was a girl who had read the book?(1) Three-eighths of all students in the classroom had read the book(2) 20 girls in the classroom had not read the booka)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'E'. Can you explain this answer?
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In a classroom, 40% of the boys had read a particular book. What was the probability that a student who was randomly selected from the classroom was a girl who had read the book?(1) Three-eighths of all students in the classroom had read the book(2) 20 girls in the classroom had not read the booka)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'E'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about In a classroom, 40% of the boys had read a particular book. What was the probability that a student who was randomly selected from the classroom was a girl who had read the book?(1) Three-eighths of all students in the classroom had read the book(2) 20 girls in the classroom had not read the booka)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a classroom, 40% of the boys had read a particular book. What was the probability that a student who was randomly selected from the classroom was a girl who had read the book?(1) Three-eighths of all students in the classroom had read the book(2) 20 girls in the classroom had not read the booka)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'E'. Can you explain this answer?.
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