Possibly a wrong solution on ManhattanPrep Quant?

Question

I'm working on the problem: If 4/x < -1/3, what is the possible range of values for x? and the solution says that X must be negative AND greater than -12, but shouldn't it be negative AND less than -12? If x>-12 and we plug a negative number (e.g. 4/-11) into the fraction, we'd get a value that is greater than 1/3.

This is from the 5th edition - Algebra, Chapter 11 problem #4

This is from the 5th edition - Algebra, Chapter 11 problem #4

chetan2u · Answer

\frac{4}{x}<-\frac{1}{3} If we put x as -11 or say -8, \frac{4}{-8}<-\frac{1}{3}.......... .... \frac{1}{-2}<-\frac{1}{3} Now -1/3 > -1/2.. multiply the equation by -1, the sign will change (-1)*\frac{1}{-2}>(-1)*-\frac{1}{3}. .. \frac{1}{2}>\frac{1}{3} ... That's correct so x is negative and >-12

ccooley · Answer

Try plugging in a number that's greater than -12, such as -8.

4/-8 = -1/2

-1/2 is less than -1/3, so the inequality is correct.

Now, try plugging in a number that's less than -12, such as -16.

4/-16 = -1/4

-1/4 is greater than -1/3, so the inequality is incorrect.

This shows that x must be  greater than  -12.

This is a surprisingly tricky thing to get right when you're working quickly, since both fractions and negative values make it less intuitive to tell which number is bigger (and this problem has both of them). My own trick is to actually draw a number line:

--- -1 ---- -3/4 ---- -1/2 ---- -1/4 ---- 0 ---- 1/4 ...etc

The 'smaller' number is always the one that's further to the left on the number line, which isn't necessarily the one that's closer to zero.

Possibly a wrong solution on ManhattanPrep Quant?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards