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# Does x = 15? (1) The average of x, y, and z is 5. (2) y = -z

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Math Expert
Joined: 02 Sep 2009
Posts: 56257
Does x = 15? (1) The average of x, y, and z is 5. (2) y = -z  [#permalink]

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21 Feb 2018, 23:04
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92% (00:42) correct 8% (00:24) wrong based on 48 sessions

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Does x = 15?

(1) The average of x, y, and z is 5.

(2) y = -z

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Joined: 07 Jan 2016
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Re: Does x = 15? (1) The average of x, y, and z is 5. (2) y = -z  [#permalink]

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21 Feb 2018, 23:40
Bunuel wrote:
Does x = 15?

(1) The average of x, y, and z is 5.

(2) y = -z

(1) x+y+z = 15

x can be 15 but we don't know that yet

(2) insufficient, provides no data about X

combining we know that y+z = 0

x= 15

(C) imo
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Does x = 15? (1) The average of x, y, and z is 5. (2) y = -z  [#permalink]

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21 Feb 2018, 23:42
Statement 1: $$\frac{x+y+z}{3}$$= 5

x+y+z= 15 . No inf about x, y and z [Insuff]

Statement 2: y=-z

So y+z=0

Put (2) in (1)

x+y=z= 15
x+0= 15
x= 15 [Suff]

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Re: Does x = 15? (1) The average of x, y, and z is 5. (2) y = -z  [#permalink]

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21 Feb 2018, 23:43
Bunuel wrote:
Does x = 15?

(1) The average of x, y, and z is 5.

(2) y = -z

Let's try using numbers, an Alternative approach.

(1) If x = 15 and y=z=0 then statement (1) holds and x=15. However, If x=y=z=5 statement (1) holds and x=5.
Insufficient.

(2) Ok... but what is the value of x?
Insufficient.

Combined:
Let's say x=15. Then y=z=0 and both statements (1) and (2) hold.
Let's try making x different from 15. Say x = 10. Then y+z=15-10=5. But y = -z so y+z = 0! This is impossible.
Trying another number, say x = 5, we will get y+z=15-5=10, which is also impossible.
In fact, because y+z=0 than only x=15 can work.
Sufficient.

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Re: Does x = 15? (1) The average of x, y, and z is 5. (2) y = -z  [#permalink]

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23 Feb 2018, 00:16
Bunuel wrote:
Does x = 15?

(1) The average of x, y, and z is 5.

(2) y = -z

IMO C
as we can say from first statement x+y+z= 15 it means x=15 y=0,z=0 or X=5,y=5,z=5 so we can't say anything insufficient.
second statement y=-z doesn't tell anything about x and combining both we get to know that y and z will be cancelled only x=15.
Re: Does x = 15? (1) The average of x, y, and z is 5. (2) y = -z   [#permalink] 23 Feb 2018, 00:16
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