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# The sum of two positive numbers x and z is 50. If x is greater than 10

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Math Expert
Joined: 02 Sep 2009
Posts: 50627
The sum of two positive numbers x and z is 50. If x is greater than 10  [#permalink]

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12 Jul 2018, 00:13
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Difficulty:

35% (medium)

Question Stats:

70% (01:16) correct 30% (02:00) wrong based on 46 sessions

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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. $$8 < z < 50$$

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The sum of two positive numbers x and z is 50. If x is greater than 10  [#permalink]

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12 Jul 2018, 00:21
Bunuel 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. $$8 < z < 50$$

As we're explciitly given ranges to test, we'll just test them.
This is an Alternative approach.

Looking at our answers, the left side of the range is either 0 or 8. If z = 0 then x = 50 - 0 = 50, which is greater than 4z +10 = 0 + 10 = 10.
So a positive number just over zero could work, meaning that (D) and (E) are eliminated (as they do not include these numbers)
This gives options of 4,8 or 10 for the right side of the range. If z = 10 then x = 50 - 10 = 40 which is not larger than 4z +10 = 40 + 10 = 50.
(C) is eliminated.
If z = 8 then x = 50 - 8 = 42 which is exactly equal to 4z +10 = 32 + 10 = 42. Since we have an equality at the edge of our range, then any number just inside the range, that is a lttle smaller than 8 will make x a little larger than 42 as required.

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The sum of two positive numbers x and z is 50. If x is greater than 10  [#permalink]

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12 Jul 2018, 06:08
Bunuel 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.......................1

and

x > 4z + 10......................2

Combining both statements :

50 - z > 4z + 10

40 > 5z

z < 8.

Option B meets the condition . Note: As the value pf z is given as a range , value of x will also be affected. It is told in the question that z is a positive integer.

So,

0< z < 8

The sum of two positive numbers x and z is 50. If x is greater than 10 &nbs [#permalink] 12 Jul 2018, 06:08
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