IF A = B + 4 C , THEN SHOW THAT

     
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If (abc > 0), then which of the following must be true?a. (fracab b. (a > 0)c. (fracabc > 0)d. (bc e. A(> bc)


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abc > 0.Means either all 3 are positive or 2 positive & 1 negative.Only option C satisfies this condition.For any value of a, b and c.Option C is always true.C is the answer
AkshdeepS Can you please explain the solution with case by case example for all 5 answer choices? I didn"t understand how the answer was arrived.Navin B
abc > 0.Means either all 3 are positive or 2 positive và 1 negative.Only option C satisfies this condition.For any value of a, b & c.Option C is always true.C is the answer
If abc>0 then it can be all three positive or two negative and one positive. But ur answer says the other way outPosted from my mobile device
If (abc > 0), then which of the following must be true?a. (fracab b. (a > 0)c. (fracabc > 0)d. (bc e. (a > bc)


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Let us first analysis all the possible cases of "(abc > 0)".1) (a > 0 , b > 0 , c > 0), then (abc > 0) (always) (+ + +)2) (a 0), then also (abc > 0) (- - +)Case 2 has two more variations as any 2 of the 3 variables can be positive và one negative2.1) (a 0 , c (- + -)2.2) (a > 0 , b (+ - -)All the above cases are those which are true as per given condition in the question.Now we can kiểm tra options which are 100% true according to above given information.Remember we are not looking for could be true options. Let us try lớn prove the options false & eliminate one by onea. (fracab Not true for case (2)As per case (2) a & b both are negative, and if we divide -a by -b, we well get positive result. Eliminateb. (a > 0)As per case (2) and (2.2) this information is not true. Eliminatec. (fracabc > 0)1) ((+)*(+)/(+) > 0)2)((-) * (-)/ (+) > 0)2.1 ((-)* (+) / (-) > 0)2.2) ((+) *(-)/ (-) > 0)This information is true for every case. Correct.d. (bc As per case (1) & (2.2) this information is not true. Eliminatee. (a > bc)This information may or may not be true as no real values are known.If a = 10 , b = 2, c = 1 (True)If a = -5 , b = 2, c = -1 (abc > 0), but a is not greater than bc. (False)Hope this helps.As there are lot of signs there may be some typos
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