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  • Question
  • The sum of five consecutive odd numbers is equal to 175. What is the sum of the second largest number and the square of the smallest number among them together?


  • Options
  • A. 989
  • B. 997
  • C. 979
  • D. 995

  • Correct Answer
  •  

    Explanation

    Method 1 to solve this question.
    Let p be the first odd number.
    Then next odd number is p + 2.
    According to question,
    Sum of five consecutive odd numbers 175
    ? p + p + 2 + p + 4 + p + 6 + p + 8 = 175
    ? 5p + 20 = 175
    ? p = (175 - 20)/5 = 31
    According to question,
    Sum of the second largest and square of smallest one = (31 + 6) + (31)2
    Sum of the second largest and square of smallest one = 37 + 961 = 998

    Method 2 to solve this question.
    Let p be the even number.
    Then next odd number is p + 1. so on p + 3 , p + 5................ P + 9
    According to question,
    Sum of five consecutive odd numbers 175
    ? p + 1 + p + 3 + p + 5 + p + 7 + p + 9 = 175
    ? 5p + 25 = 175
    ? p = (175 - 25)/5
    ? p = (150)/5
    ? p = 30
    First odd number = p + 1 = 30 + 1 = 31
    According to question,
    Sum of the second largest and square of smallest one = (30 + 7) + (30 + 1)2
    Sum of the second largest and square of smallest one = 37 + 961 = 998


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