If x, y and z are Integers and z is not equal to 0, Find range of
$$\frac{\left(x+y\right)}{z}$$
$$-2<z<2$$
$$-5<x<10$$
$$-11<y<4$$
$$\left(A\right)-8<\frac{\left(x+y\right)}{z}<7$$
$$\left(B\right)8<\frac{\left(x+y\right)}{z}<-7$$
$$\left(C\right)-16<\frac{\left(x+y\right)}{z}<14$$
$$\left(D\right)-14<\frac{\left(x+y\right)}{z}<14$$
$$\left(E\right)-16<\frac{\left(x+y\right)}{z}<16$$
The OA is E.
I need help with this PS question. Can any expert explain it please? Thanks.
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Hi LUANDATO,
When a Quant question asks you to define the 'range' of a particular calculation, you should take a good look at the 'extreme' values for each variable and think about how those values (as well as any other strategic values) would impact the calculation. The answer choices actually provide a nice 'shortcut' so that you can avoid some of the 'math work' in this question.
We're told that all 3 variables are INTEGERS and we're given the following ranges to work with:
-5 < X < 10
-11 < Y < 4
-2 < Z < 2
We're asked to determine the range of values of:
(X+Y)/Z
Since we're dealing with a fraction, to get the MAXIMUM value, we have to consider both +/+ and -/-.
IF....
X = really close to -5
Y = really close to -11
Z = -1
We end up with (almost -16)/(-1) = almost 16. There's only one answer that includes that maximum value, so we can stop working.
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
When a Quant question asks you to define the 'range' of a particular calculation, you should take a good look at the 'extreme' values for each variable and think about how those values (as well as any other strategic values) would impact the calculation. The answer choices actually provide a nice 'shortcut' so that you can avoid some of the 'math work' in this question.
We're told that all 3 variables are INTEGERS and we're given the following ranges to work with:
-5 < X < 10
-11 < Y < 4
-2 < Z < 2
We're asked to determine the range of values of:
(X+Y)/Z
Since we're dealing with a fraction, to get the MAXIMUM value, we have to consider both +/+ and -/-.
IF....
X = really close to -5
Y = really close to -11
Z = -1
We end up with (almost -16)/(-1) = almost 16. There's only one answer that includes that maximum value, so we can stop working.
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
