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Given below are two statements.
Statement 1: A set of numbers arranged in ascending order is: 12, 15, 16, 16, m, n, 25, 28. The arithmetic mean of the set is 19.5. If the median of the set is 18, then m × n = 500.
Statement 2: Let m and n be any two positive integers. If 2m + n + 3mn = 1382, then n – m = 3.
Which of the following options 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...
Explanation:

  • Statement 1: The set of numbers is arranged in ascending order as 12, 15, 16, 16, m, n, 25 and 28. The arithmetic mean of the set is 19.5.

  • Let us say the value of m and n are p and q respectively. Then, the sum of the set of numbers is 12 + 15 + 16 + 16 + p + q + 25 + 28 = 118 + p + q.

  • Also, the mean of the set is given by (118 + p + q)/8 = 19.5.

  • From the above two equations, we can get p + q = 47.

  • The median of the set is given by the middle value of the set. Here, the middle value is the average of the two middle numbers. So, the median is (16 + m)/2 = 18, which gives m = 20.

  • Therefore, n = 47 - p = 47 - 20 = 27.

  • So, m × n = 20 × 27 = 540, which is not equal to 500.

  • Hence, statement 1 is false.



  • Statement 2: Let m and n be any two positive integers. Then, 2m + n + 3mn = 1382.

  • We need to find the value of n - m.

  • Let us rewrite the given equation as 3mn + n + 2m = 1382.

  • Now, we can factorise the left-hand side of the equation as n(3m + 1) + 2m = 1382.

  • Since m and n are positive integers, n(3m + 1) + 2m > 1382.

  • So, the given equation does not have any solution in positive integers m and n.

  • Hence, statement 2 is also false.



  • Therefore, option B is the correct answer.

Free Test
Community Answer
Given below are two statements.Statement 1: A set of numbers arranged...
The mean of the set is 19.5.
Mean of the given data =
m + n + 112 = 156
m + n = 44
Given series: 12, 15, 16, 16, m, n, 25, 28
Total number of terms = 8, which is even
To find the median, we have to find the average of the terms.
Therefore, median of the given data = average of the 4th and 5th terms =
16 + m = 36
m = 20
Therefore,
m + n = 44
20 + n = 44
n = 24
m × n = 20 × 24 = 480
Hence, statement 1 is false.
Statement 2:
The information given in the condition is not proper because there are two variables and the equation is only one.
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: 12, 15, 16, 16, m, n, 25, 28. The arithmetic mean of the set is 19.5. If the median of the set is 18, then m × n = 500.Statement 2: Let m and n be any two positive integers. If 2m + n + 3mn = 1382, then n – m = 3.Which of the following options 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: 12, 15, 16, 16, m, n, 25, 28. The arithmetic mean of the set is 19.5. If the median of the set is 18, then m × n = 500.Statement 2: Let m and n be any two positive integers. If 2m + n + 3mn = 1382, then n – m = 3.Which of the following options 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: 12, 15, 16, 16, m, n, 25, 28. The arithmetic mean of the set is 19.5. If the median of the set is 18, then m × n = 500.Statement 2: Let m and n be any two positive integers. If 2m + n + 3mn = 1382, then n – m = 3.Which of the following options 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: 12, 15, 16, 16, m, n, 25, 28. The arithmetic mean of the set is 19.5. If the median of the set is 18, then m × n = 500.Statement 2: Let m and n be any two positive integers. If 2m + n + 3mn = 1382, then n – m = 3.Which of the following options 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: 12, 15, 16, 16, m, n, 25, 28. The arithmetic mean of the set is 19.5. If the median of the set is 18, then m × n = 500.Statement 2: Let m and n be any two positive integers. If 2m + n + 3mn = 1382, then n – m = 3.Which of the following options 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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