SOLUTION: If a non-zero integer n is chosen such that (2-16/n) is an integer less than 6 Which of the following must be true of n ? A -8 b -6 c -4 d -3 e -1

Question 277460: If a non-zero integer n is chosen such that (2-16/n) is an integer less than 6
Which of the following must be true of n ?
A -8 b -6 c -4 d -3 e -1

Found 3 solutions by stanbon, Edwin McCravy, vleith:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
If a non-zero integer n is chosen such that (2-16/n) is an integer less than 6
Which of the following must be true of n ?
------
Solve (2-(16/n)) < 6
Factor out a "2" and divide both sides by it:
(1-(8/n) < 3
8/n > -2
------------
Check: n = -8
8/-8 > -2
-1 > -2
true
---
Check: n = -6
8/-6 > -2
-4/3 > -2
true
---
Check: n = -4
8/-2> -2
-4> -2
false
======
Answer: n could be -8 or n could be -6
============================================
Cheers,
Stan H.

A -8 b -6 c -4 d -3 e -1

Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
If a non-zero integer n is chosen such that is an integer less than 6
Which of the following must be true of n ?
A -8 b -6 c -4 d -3 e -1

The other tutor's answer is incorrect. He did not observe the fact that must be an integer! --------------------------------------------- Plug those 5 values into Plugging in , That's possible. Let's see if any of the others are: Plugging in , . No, that's not an integer! Plugging in , . No, 6 is not less than 6. Plugging in , . No, that's not an integer! Plugging in , No, that's not less than 6. So a) -8 is the only one of those that works. Comment: The question is worded very badly, because there are other values n could be which are not listed besides just -8. For instance n could be any of these: -16, -8, 1, 2, 4, 8, 16 and would be an integer less than 6. It's just that -8 was the only one listed as a choice. So the question should have read: "Which of the following could n be?" not "must be true of n"!!! Edwin

Answer by vleith(2983)   (Show Source): You can put this solution on YOUR website!
Given
n is a non-zero integer and

find n
collect like terms

Now here is the tricky part. In order to isolate n, we need to multiply through by n. If n is positive, then the inequality sign stays 'less than'. However, if n is negative, then the inequalty changes to 'greater than'.
when n > 0
when n < 0
Every one of the possible answers A through E are negative. So we need to use the second equation.

Which possible answers are less than -4? Only -8 and -6 (A and B)
BUT, your problem stated the result had to be < 6 and an integer. You can see that 16/-6 is not an integer, so -6 won't work. 16/-8 is an integer.
Answer is -8 (A)
Check that answer by plugging -8 in

which is true. So -8 works

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