If a and b are nonzero integers such that 2a/5 = b, then each of the following must be true EXCEPT Choose the correct choice from the following answers: A) 0 < b/a < 1 B) ab is positive. C) On the number line, b lies between 0 and a. D) The ratio of a to b is equivalent to 10/4. E) a – b is positive.
This question can be solved by TESTing VALUES. Based on its wording, you would likely need to do 2 TESTs to get to the correct answer though.   We're told that A and B are NONZERO INTEGERS and that 2a/5 = b or 2a = 5b. We're told that each of the answer is always true EXCEPT for one of them...   Before we get to the actual work, it's important to note a few details:   1) We are NOT told that A and B are positive - we're just told that they're NONZERO - that's interesting - it means that we have to consider the possibility that they're both NEGATIVE...   2) 4 of the answers will always be true, while one of them will EITHER be sometimes true OR never true. We'll have to keep working until we find 1 answer that is not true (for whatever reason) - that will be the solution to this question.   Since 2A = 5B, I'm going to run 2 pairs of TESTs at the same time...   A = 5   B = 2   AND   A = -5   B = -2   Answer A: 0 &lt; B/A &lt; 1   2/5 and -2/-5 both = 2/5. Answer A appears true.   Answer B: AB is positive   (2)(5) and (-2)(-5) both = +10. Answer B appears true.   Answer C: B is between 0 and A on the number line   0....2....5   -5....-2....0   Answer C appears true.   Answer D: A/B = 10/4   5/2 = -5/-2   10/4 = 5/2   Answer D appears true.   Answer E: A - B is positive     5 - 2= 
<gadget id="calculator">  5 - 2</gadget>
<output>3</output>
3   -5 - (-2)= -3 *****This is NOT always true.   Final Answer:   a – b is positive.
<result>E</result>
If a and b are nonzero integers such that 2a/5 = b, then each of the following must be true EXCEPT