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Re: If x, y and z are Integers and z is not 0, Find range of (x-y)/z [#permalink]
GMATinsight wrote:
If x, y and z are Integers and z is not equal to 0, Find range of \(\frac{(x-y)}{z}\)

-5 < x < 10
-11 < y < 4
-2 < z <2

(A) -4.5 < \(\frac{(x-y)}{z}\) < 10.5
(B) 6 < \(\frac{(x-y)}{z}\)< 6
(C) -9 < \(\frac{(x-y)}{z}\) < 21
(D) 9 < \(\frac{(x-y)}{z}\) < 21
(E) -21 < \(\frac{(x-y)}{z}\) < 21

Source: https://www.GMATinsight.com



Thanks GMAT insight for the question. However, can you change the title to (x-y)/z. It is still (x+y)/z.
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Re: If x, y and z are Integers and z is not 0, Find range of (x-y)/z [#permalink]
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GMATinsight wrote:
If x, y and z are Integers and z is not equal to 0, Find range of \(\frac{(x-y)}{z}\)

-5 < x < 10
-11 < y < 4
-2 < z <2

(A) -4.5 < \(\frac{(x-y)}{z}\) < 10.5
(B) 6 < \(\frac{(x-y)}{z}\)< 6
(C) -9 < \(\frac{(x-y)}{z}\) < 21
(D) 9 < \(\frac{(x-y)}{z}\) < 21
(E) -21 < \(\frac{(x-y)}{z}\) < 21

Source: https://www.GMATinsight.com


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.
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If x, y and z are Integers and z is not 0, Find range of (x-y)/z [#permalink]
GMATinsight wrote:
If x, y and z are Integers and z is not equal to 0, Find range of \(\frac{(x-y)}{z}\)

-5 < x < 10
-11 < y < 4
-2 < z <2

(A) -4.5 < \(\frac{(x-y)}{z}\) < 10.5
(B) 6 < \(\frac{(x-y)}{z}\)< 6
(C) -9 < \(\frac{(x-y)}{z}\) < 21
(D) 9 < \(\frac{(x-y)}{z}\) < 21
(E) -21 < \(\frac{(x-y)}{z}\) < 21

Source: https://www.GMATinsight.com


\(-5≤x≤10\)---------------(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
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Re: If x, y and z are Integers and z is not 0, Find range of (x-y)/z [#permalink]
rahul16singh28 wrote:
GMATinsight wrote:
If x, y and z are Integers and z is not equal to 0, Find range of \(\frac{(x-y)}{z}\)

-5 < x < 10
-11 < y < 4
-2 < z <2

(A) -4.5 < \(\frac{(x-y)}{z}\) < 10.5
(B) 6 < \(\frac{(x-y)}{z}\)< 6
(C) -9 < \(\frac{(x-y)}{z}\) < 21
(D) 9 < \(\frac{(x-y)}{z}\) < 21
(E) -21 < \(\frac{(x-y)}{z}\) < 21

Source: https://www.GMATinsight.com


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.


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
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Re: If x, y and z are Integers and z is not 0, Find range of (x-y)/z [#permalink]
niks18 wrote:
rahul16singh28 wrote:
GMATinsight wrote:
If x, y and z are Integers and z is not equal to 0, Find range of \(\frac{(x-y)}{z}\)

-5 < x < 10
-11 < y < 4
-2 < z <2

(A) -4.5 < \(\frac{(x-y)}{z}\) < 10.5
(B) 6 < \(\frac{(x-y)}{z}\)< 6
(C) -9 < \(\frac{(x-y)}{z}\) < 21
(D) 9 < \(\frac{(x-y)}{z}\) < 21
(E) -21 < \(\frac{(x-y)}{z}\) < 21

Source: https://www.GMATinsight.com


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.


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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Re: If x, y and z are Integers and z is not 0, Find range of (x-y)/z [#permalink]
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Re: If x, y and z are Integers and z is not 0, Find range of (x-y)/z [#permalink]
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