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Possibly a wrong solution on ManhattanPrep Quant?

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Joined: 26 Aug 2018
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Possibly a wrong solution on ManhattanPrep Quant?  [#permalink]

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24 Mar 2019, 19:13
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
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Re: Possibly a wrong solution on ManhattanPrep Quant?  [#permalink]

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24 Mar 2019, 20:05
dsmba wrote:
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

$$\frac{4}{x}<-\frac{1}{3}$$
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
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Re: Possibly a wrong solution on ManhattanPrep Quant?  [#permalink]

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27 Mar 2019, 16:50
dsmba wrote:
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

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.
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Re: Possibly a wrong solution on ManhattanPrep Quant?   [#permalink] 27 Mar 2019, 16:50
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