If x, y and z are Integers and z is not 0, Find range of (x-y)/z

Dear GMATinsight,

With all due respect, my friend, there appears to be some problems with this question.
1) In the prompt, the relationship of the three inequalities below the text is not clear. On a GMAT Quant question, something would be explicitly said. For example, the three inequalities might be stated above the words, and then the words could say, "If x, y and z are Integers in the ranges give above and ..." In one way or another, the words have to make clear reference to the role of those three inequality statements.

2) I believe there's a missing negative sign in choice (C), because otherwise, the expression could only equal 6.

3) Most importantly, given that those three equalities at the beginning specify ranges for the variables, then I don't find the answer listed.
If we want the numerator, the value (x + y), to have the biggest absolute value, x and y need to have the same sign.
x + y = 10 + 4 = 14 if we add the highest positive values
x + y = (-11) + (-5) = -16 if we add the lowest negative values: this is better.
To make this positive, we need to divide by the smallest allowable negative number, which is -1.
Max value = ((-11) + (-5))/(-1) = +16
To make this a large negative value, we would divide by the smallest allowable positive number, which is +1.
Max value = ((-11) + (-5))/(+1) = -16
The range is from -16 to +16, an option not given.

Does all this make sense?
Mike
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Thank you mikemcgarry

I made and posted two questions one with (x+y)/z and other with (x-y)/z but in this question i missed changing sign between x and y in the uestion

Really sorry for causing this waste of your time... Have made correction in question.

Thanks GMAT insight for the question. However, can you change the title to (x-y)/z. It is still (x+y)/z.

Hi Bunuel, GMATinsight

Can you please help me to understand this.

As per the given range of x & y.. the minimum value of x - y has to be -9 assuming z = 1. I am unable to find any combination of x & y for which x - y = -21.

\(-5≤x≤10\)---------------(1)

\(-11≤y≤4\). Multiply the inequality by \(-1 => -4≤-y≤11\)---------------(2) Add inequality (1) & (2)

\(-9≤x-y≤21\)------------(3)

Max value of \(\frac{(x-y)}{z}\) will be when division by \(z\) has no impact on Max value of \((x-y)\) i.e when \(z=1\) and \(x-y=21\)

so Max \(\frac{(x-y)}{z}=\frac{21}{1} => \frac{(x-y)}{z}≤21\)

Min value of \(\frac{(x-y)}{z}\) will be when division by \(z\) changes the Max value of \((x-y)\) into negative i.e when \(z=-1\) and \(x-y=21\)

so Min \(\frac{(x-y)}{z}=\frac{21}{-1} => -21≤\frac{(x-y)}{z}\)

Hence Range will be -\(21≤\frac{(x-y)}{z}≤21\)

Option E

Hi rahul16singh28

Min value of (x-y) will be direct opposite of Max value i.e. you convert the Max value simply by changing the sign and this can be done when z=-1.

to calculate the range you only need min and max values here. -9 is the min value of (x-y) only and not of (x-y)/z

Thanks @niks18

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