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Given below are two statements.
Statement 1: A set of numbers arranged in ascending order is: 30, 30, 31, 32, 32, a, b, 38, 38, 40. The arithmetic mean and the median of the set are 34 and 33, respectively. Then a × b = 1156.
Statement 2: Let a and b be any 2 positive integers. If a + 3b = 24, then a – b = 4.
Which of the above is correct?
  • a)
    Both Statements 1 and 2 are true.
  • b)
    Both Statements 1 and 2 are false.
  • c)
    Statement 1 is true but statement 2 is false.
  • d)
    Statement 1 is false but statement 2 is true.
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Given below are two statements.Statement 1: A set of numbers arranged...

Statement Analysis:

Statement 1:
The given set of numbers in ascending order is: 30, 30, 31, 32, 32, a, b, 38, 38, 40
Arithmetic mean = (30 + 30 + 31 + 32 + 32 + a + b + 38 + 38 + 40)/10 = 34
Median = Middle value = (32 + a)/2 = 33
From the above, we get a = 34, b = 36
a × b = 34 × 36 = 1224

Statement 2:
Given a + 3b = 24
Substitute b = (24 - a)/3 in a - b = 4
We get a - (24 - a)/3 = 4
Solving, we get a = 12, b = 4
But, these values do not satisfy the given equation a + 3b = 24
Hence, statement 2 is false.

Therefore, the correct answer is option B: Both Statements 1 and 2 are false.
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Community Answer
Given below are two statements.Statement 1: A set of numbers arranged...
The mean of the set is 34.
a + b + 271 = 340
a + b = 69
Given series
30, 30, 31, 32, 32, a, b, 38, 38, 40
n = 10, which is even
To find the median, we have to find average of n/2 th term and ( n/2 + 1)th term
n/2th term = 5th term = 32
(n/2 + 1)th term = 6th term = a
Therefore, median of the given data is:
Average of 5th term and 6th term = = 33
32 + a = 66
a = 34
∴ a + b = 69
34 + b = 69
b = 35
a × b = 1190
Statement 2
The information given in the condition is not proper because there are two variables and the equation is only 1.
So, statement 2 is false.
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Given below are two statements.Statement 1: A set of numbers arranged in ascending order is: 30, 30, 31, 32, 32, a, b, 38, 38, 40. The arithmetic mean and the median of the set are 34 and 33, respectively. Then a × b = 1156.Statement 2: Let a and b be any 2 positive integers. If a + 3b = 24, then a – b = 4.Which of the above is correct?a)Both Statements 1 and 2 are true.b)Both Statements 1 and 2 are false.c)Statement 1 is true but statement 2 is false.d)Statement 1 is false but statement 2 is true.Correct answer is option 'B'. Can you explain this answer?
Question Description
Given below are two statements.Statement 1: A set of numbers arranged in ascending order is: 30, 30, 31, 32, 32, a, b, 38, 38, 40. The arithmetic mean and the median of the set are 34 and 33, respectively. Then a × b = 1156.Statement 2: Let a and b be any 2 positive integers. If a + 3b = 24, then a – b = 4.Which of the above is correct?a)Both Statements 1 and 2 are true.b)Both Statements 1 and 2 are false.c)Statement 1 is true but statement 2 is false.d)Statement 1 is false but statement 2 is true.Correct answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Given below are two statements.Statement 1: A set of numbers arranged in ascending order is: 30, 30, 31, 32, 32, a, b, 38, 38, 40. The arithmetic mean and the median of the set are 34 and 33, respectively. Then a × b = 1156.Statement 2: Let a and b be any 2 positive integers. If a + 3b = 24, then a – b = 4.Which of the above is correct?a)Both Statements 1 and 2 are true.b)Both Statements 1 and 2 are false.c)Statement 1 is true but statement 2 is false.d)Statement 1 is false but statement 2 is true.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given below are two statements.Statement 1: A set of numbers arranged in ascending order is: 30, 30, 31, 32, 32, a, b, 38, 38, 40. The arithmetic mean and the median of the set are 34 and 33, respectively. Then a × b = 1156.Statement 2: Let a and b be any 2 positive integers. If a + 3b = 24, then a – b = 4.Which of the above is correct?a)Both Statements 1 and 2 are true.b)Both Statements 1 and 2 are false.c)Statement 1 is true but statement 2 is false.d)Statement 1 is false but statement 2 is true.Correct answer is option 'B'. Can you explain this answer?.
Solutions for Given below are two statements.Statement 1: A set of numbers arranged in ascending order is: 30, 30, 31, 32, 32, a, b, 38, 38, 40. The arithmetic mean and the median of the set are 34 and 33, respectively. Then a × b = 1156.Statement 2: Let a and b be any 2 positive integers. If a + 3b = 24, then a – b = 4.Which of the above is correct?a)Both Statements 1 and 2 are true.b)Both Statements 1 and 2 are false.c)Statement 1 is true but statement 2 is false.d)Statement 1 is false but statement 2 is true.Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT. Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
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