Multiple choice general knowledge math & puzzles

The sum of the even numbers between 1 and n is 79*80, where n is an odd number, then n=?

  1. 157

  2. 159

  3. 79

  4. 81
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Even numbers between 1 and n are 2, 4, 6, ..., (n-1). Sum = 2+4+6+...+(n-1) = 2(1+2+3+...+(n-1)/2). Number of terms = (n-1)/2. Sum = 2 × [(n-1)/2 × ((n-1)/2 + 1)] / 2 = (n-1)/2 × (n+1)/2 = (n²-1)/4. Given (n²-1)/4 = 79×80, so n²-1 = 31680, n² = 31681, n = 177. But wait - let's recalculate: sum of first k even numbers = k(k+1). Here k = (n-1)/2, so sum = (n-1)/2 × (n+1)/2 = 79×80. Solving: (n²-1)/4 = 6320, n²-1 = 25280, n² = 25281, n = 159.

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