Multiple choice

The mean and median of $10,22,26,29,34,x,42,67,70$,y (in increasing order) are $ 42$ and $35$ respectively then the value $\dfrac{y}{x}$is

  1. $\dfrac{9}{2}$
  2. $\dfrac{5}{3}$
  3. $\dfrac{7}{3}$
  4. $\dfrac{7}{2}$
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C Correct answer
Explanation

Median of 10 terms is the average of 5th and 6th terms: (34 + x) / 2 = 35, so 34 + x = 70, x = 36. Mean = (10+22+26+29+34+36+42+67+70+y) / 10 = 42. Sum = 336 + y = 420, y = 84. y/x = 84/36 = 7/3.

AI explanation

Since there are 10 observations, the median is the average of the 5th and 6th terms, giving the equation (34 plus x) divided by 2 equals 35. Solving this equation yields x equals 36. The mean is the sum of all observations divided by 10, so (10 plus 22 plus 26 plus 29 plus 34 plus 36 plus 42 plus 67 plus 70 plus y) divided by 10 equals 42. This simplifies to 336 plus y equals 420, meaning y equals 84. Therefore, the value of y divided by x is 84 divided by 36, which simplifies to 7 divided by 3.

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