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If x, y, and z are positive numbers, Is z between x and y?

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Manager
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Joined: 02 Apr 2006
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If x, y, and z are positive numbers, Is z between x and y? [#permalink]

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New post 10 Nov 2007, 21:51
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Question Stats:

62% (01:24) correct 38% (01:21) wrong based on 229 sessions

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If x, y, and z are positive numbers, Is z between x and y?

(1) x < 2z < y
(2) 2x < z < 2y
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V
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Posts: 47015
Re: If x, y, and z are positive numbers, Is z between x and y? [#permalink]

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New post 17 Jul 2014, 01:28
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pretttyune wrote:
If x, y, and z are positive numbers, Is Z between X and Y?

(1) x < 2z < y
(2) 2x < z < 2y


If x, y and z are positive numbers, is z between x and y?

(1) x < 2z < y.

If x = 1, y = 10, and z = 1 --> answer NO.
If x = 1, y = 10, and z = 2 --> answer YES.

Not sufficient.

(2) 2x < z < 2y.

If x = 1, y = 2, and z = 3 --> answer NO.
If x = 1, y = 10, and z = 3 --> answer YES.

Not sufficient.

(1)+(2) Add the inequalities: 3x < 3z < 3y --> divide by 3: x < z < y. Sufficient.

Answer: C.
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Joined: 04 Nov 2007
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Re: If x, y, and z are positive numbers, Is z between x and y? [#permalink]

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New post Updated on: 10 Nov 2007, 22:34
1
Statement 1 & 2 will give YES & NO answers to the question when substituted with different values. So, they are not sufficient.

Take values x=1;y=6;z=2 & x=3;y=6;z=2 & you will see why statement 1 is not sufficient.

Take both the statements together.
4X<8Z<4Y
4X<Z<4Y
All values that satisfy these two statements satisfy the question with an answer YES.

Hope that helps :)

Originally posted by Vemuri on 10 Nov 2007, 22:30.
Last edited by Vemuri on 10 Nov 2007, 22:34, edited 1 time in total.
Manager
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Re: If x, y, and z are positive numbers, Is z between x and y? [#permalink]

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New post 10 Nov 2007, 22:35
Statement 1:

Assume x=1,y=2. z=2/3.
The given equation is satisfied but z is not between x & y.

Assume x=1,y=5,z=2
The given equation is satisfied and z is not between x & y.

Therefore Statement 1 is insufficient.

Statement 2:

Assume x=1,y=2,z=5.
The given equation is satisfied but z is not between x & y.

Assume x=1,y=6,z=5.
The given equation is satisfied and z is not between x & y.

Therefore Statement 2 is insufficient.

Taking both the statements together we have,

x<2z<y
x<z/4<y

You will find that for any values of x,y & z that satisfy both the equations, z will always be between x and y.

Therefore the answer is C.
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Re: If x, y, and z are positive numbers, Is z between x and y? [#permalink]

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New post 02 Mar 2018, 08:50
pretttyune wrote:
If x, y, and z are positive numbers, Is z between x and y?

(1) x < 2z < y
(2) 2x < z < 2y


it is hard
from 1
2z<y , so z< y because all are positive
but
2z>x dose not mean z>x
1 is not sufficient

similarly we know 2 is not sufficient

from both 1 and 2
we have
z<y from 1 and z>x from 2. so both is sufficient.

we do not need to pick numbers, doing so is long
Re: If x, y, and z are positive numbers, Is z between x and y?   [#permalink] 02 Mar 2018, 08:50
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