Vincen wrote:An odd number added to itself an odd number of times yields
(A) an odd number
(B) an even number
(C) a prime number
(D) a positive number
(E) a perfect square
The OA is A.
I did it for a particular number, but is there any way to prove it in general?
Say an odd number is 3, and it is added 5 times (odd number of times) to itself (3).
Thus, the result = 3 + 3 + 3 + 3 + 3 = 15, and odd number.
An algebraic approach:
Say an odd number is n and it is added m times, where m is also an odd number.
Thus, the result = n + n + n + ... m times = m*n = Odd * Odd = Odd.
The question is not drafted well. The correct should be: An odd number added to itself an odd number of times
must yield
Otherwise, except option B, all the options can also be correct, though not always. For example, if 1 is added 3 times, the result is a prime and a positive number. Similarly, if 3 is added 3 times, the result is a perfect square number.
Thus, except B, all option could be correct; however, only A must be correct.
Hope this helps!
-Jay
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