Question
Four consecutive two-digit odd numbers add up to a total
that, when divided by 10, results in a perfect square. Which of the following options could be one of these four numbers?Solution
Maximum sum of the four numbers = 384 = 99 + 97 + 95 + 93 384/10 = 38.4 So, the perfect square is a number less than 38.4 The possibilities are 36, 25, 16 and 9 For the sum to be 360, the numbers can be 87, 89, 91 and 93 The sum of four consecutive odd numbers cannot be 250 For the sum to be 160, the numbers can be 37,39,41 and 43 The sum of 4 consecutive odd numbers cannot be 90 So, from the options, the answer is 41.
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