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If a , b, and c are integers and ab2 / c is a positive even integer, which of the following must be true?
I. ab is even
II. ab > 0
III. c is even?
- a)I only
- b)II only
- c)I and III only
- d)I, II, and III
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If a , b, and c are integers and ab2 / c is a positive even integer, w...
I. ab is even: This statement is true because if ab^2 / c is a positive even integer, then ab^2 must be divisible by 2. Since 2 is a prime number, either a or b must be divisible by 2 in order for ab^2 to be divisible by 2. Therefore, ab is even.
II. ab^2 is even: This statement is not necessarily true. Although ab^2 / c is a positive even integer, it does not guarantee that ab^2 itself is even. It is possible for ab^2 to be divisible by an odd number other than 2, making it an odd number.
Thus, only statement I is necessarily true.
II. ab^2 is even: This statement is not necessarily true. Although ab^2 / c is a positive even integer, it does not guarantee that ab^2 itself is even. It is possible for ab^2 to be divisible by an odd number other than 2, making it an odd number.
Thus, only statement I is necessarily true.
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If a , b, and c are integers and ab2 / c is a positive even integer, w...
Given: 
= even > 0 ab2 = c* even = even--> either a is even or b or both.
I. ab is even --> according to the above this must be true;
II. ab > 0 --> not necessarily true, bb could be positive as well as negative (for example a=1, c = 1 and b =−2);
III. c is even --> not necessarily true, see above example.
= even > 0 ab2 = c* even = even--> either a is even or b or both.I. ab is even --> according to the above this must be true;
II. ab > 0 --> not necessarily true, bb could be positive as well as negative (for example a=1, c = 1 and b =−2);
III. c is even --> not necessarily true, see above example.
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If a , b, and c are integers and ab2 / c is a positive even integer, which of the following must be true?I. ab is even II. ab > 0 III. c is even?a)I onlyb)II onlyc)I and III onlyd)I, II, and IIICorrect answer is option 'A'. Can you explain this answer?
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