A computer program first generates 50 odd numbers randomly, and adds them. Call the sum X. Then, it generates 50 even numbers randomly, and adds them. Call the sum Y. Finally, it adds X and Y. Call the result Z. Will Z be odd or even?
Answers
Z will be even.
Step-by-step explanation:
We are given that a computer program first generates 50 odd numbers randomly, and adds them. Call the sum X.
Then, it generates 50 even numbers randomly, and adds them. Call the sum Y.
Firstly, as we know that sum of two odd numbers is always even, that is sum of 3 + 5 = 8. But the sum of three odd numbers will be odd, that is 3 + 5 + 7 = 15.
So, this means that sum of randomly 50 odd numbers will definitely be even as 50 is even number. SO, X is a even number which is a sum of all 50 odd numbers.
Similarly, as we know that sum of two even numbers is always even, that is sum of 4 + 8 = 12. And the sum of three even numbers will also be even, that is 4 + 8 + 12 = 24.
So, this means that sum of randomly 50 even numbers will definitely be even number. SO, Y is also a even number which is a sum of all 50 even numbers.
This means that sum of X + Y = Z will also be an even number as sum of two even numbers is always an even number.
Answer:
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Step-by-step explanation: