If x is a positive integer, then x(x − 1) is

Question

A. divisible by 5 whenever x is even.
B. divisible by 9 whenever x is odd.
C. odd only when x is odd.
D. always odd.
E. always even.

pushpitkc · Answer

x - 1 and x are consecutive integers. We are told that the integers are both positive.
Two positive integers which are consecutive will have one odd and one even integer.

Therefore, the product of these integers is always even (Option E)

Archit3110 · Answer

x is odd or even integer x(x − 1)
will always be even
IMO E

Abhishek009 · Answer

1. If x is even ( x - 1 ) is Odd , now Odd * Even = Even
2. If x is Odd ( x - 1 ) is Even, now Odd * Even = Even

Thus, Answer must always be Even , Answer must be (E)

ScottTargetTestPrep · Answer

Since (x - 1) will be even when x is odd and vice versa, x(x - 1) is always even.

Alternate Solution:

We see that x and (x - 1) are consecutive integers, which means that one of them is even and the other one is odd. We also know that even x odd = even. Therefore, the product x(x - 1) must be even.

Answer: E

suyashahuja · Answer

x and x-1 are consecutive, so one of them must be even. Thus, x * (x-1) would always be even.

Answer is E.

If x is a positive integer, then x(x − 1) is

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If x is a positive integer, then x(x − 1) is

Prep Toolkit

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