If n 1 n 2 , . . . . . . . . . . . . . . . . . n p are p positive integers, whose sum is an even number, then the number of odd integers among them is odd.

Question

Navjyot Kalra · Answer

Consider N = n 1 + n 2 + n 3 + . . . . . . . . +n p where N is an event number. Let k numbers among these p numbers be odd, then p &ndash; k are even numbers. Now sum of (p &ndash; k) even numbers is even and for N to be an even number , sum of k odd numbers must be even which is possible only when k is even. &there4; The given statement is false.

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If n 1 n 2 , . . . . . . . . . . . . . . . . . n p are p positive integers, whose sum is an even number, then the number of odd integers among them is odd.

If n₁ n₂, . . . . . . . . . . . . . . . . . n_p are p positive integers, whose sum is an even number, then the number of odd integers among them is odd.

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If n 1 n 2 , . . . . . . . . . . . . . . . . . n p are p positive integers, whose sum is an even number, then the number of odd integers among them is odd.

If n1 n2, . . . . . . . . . . . . . . . . . np are p positive integers, whose sum is an even number, then the number of odd integers among them is odd.

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If n₁ n₂, . . . . . . . . . . . . . . . . . n_p are p positive integers, whose sum is an even number, then the number of odd integers among them is odd.