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# The sum of two positive numbers x and z is 50. If x is great

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The sum of two positive numbers x and z is 50. If x is great [#permalink]  11 Jul 2018, 09:44
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72% (01:07) correct 27% (02:02) wrong based on 11 sessions
The sum of two positive numbers x and z is 50. If x is greater than 10 more than four times z, which of the following includes the entire range of values for z?

A. $$0 < z < 4$$

B. $$0 < z < 8$$

C. $$0 < z < 10$$

D. $$8 < z < 10$$

E. $$8 < z < 50$$
[Reveal] Spoiler: OA

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Re: The sum of two positive numbers x and z is 50. If x is great [#permalink]  13 Jul 2018, 06:04
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Carcass wrote:
The sum of two positive numbers x and z is 50. If x is greater than 10 more than four times z, which of the following includes the entire range of values for z?

A. $$0 < z < 4$$

B. $$0 < z < 8$$

C. $$0 < z < 10$$

D. $$8 < z < 10$$

E. $$8 < z < 50$$

Sol. x + z = 50 => x = 50 - z.

=> x > 10 + 4z

=> sub x value in above equation.

=>50 -z > 10 + 4z
=> 40 > 5z
=> 8 > z.

since z is positive number we can consider the range 0 < z < 8.

B.
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Re: The sum of two positive numbers x and z is 50. If x is great [#permalink]  17 Jul 2018, 10:58
Carcass wrote:
The sum of two positive numbers x and z is 50. If x is greater than 10 more than four times z, which of the following includes the entire range of values for z?

A. $$0 < z < 4$$

B. $$0 < z < 8$$

C. $$0 < z < 10$$

D. $$8 < z < 10$$

E. $$8 < z < 50$$

Given

x + z = 50

x = 50 - z

and

x > 4z + 10

50 -z > 4z +10

5z < 40

z < 8.

Note : z is a positive integer.

So, we can make a range for z.

0<z<8.

Option B is the correct answer.
Re: The sum of two positive numbers x and z is 50. If x is great   [#permalink] 17 Jul 2018, 10:58
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