CDS 2026 (I) Elementary Mathematics, question 40

Topic: Statistics

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Q40

The numbers 59,53,51,43,36,(8x+1),(x2+1),13,12,9,7,359,53,51,43,36,(8x+1),(x^{2}+1),13,12,9,7,3 are written in descending order and their median is 2525. What is/are the values of xx ?

  1. (a) −12-12 only
  2. (b) 44 onlyCorrect answer
  3. (c) −12,4-12,4
  4. (d) 12,−412,-4

Solution.

Answer: (b) 44 only

  1. There are 12 ordered values, so the median is the average of the sixth and seventh: [(8x+1)+(x2+1)]/2=25\left\lbrack (8x + 1) + \left( x^{2} + 1 \right) \right\rbrack/2 = 25.
  2. This gives x2+8x−48=(x+12)(x−4)=0x^{2} + 8x - 48 = (x + 12)(x - 4) = 0.
  3. At x=4x = 4, the middle entries are 33 and 17, consistent with the stated descending order.
  4. At x=−12x = - 12, they are −95- 95 and 145, which violates that order.