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How many of the numbers x, y, and z are positive if each of

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carcass
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How many of the numbers x, y, and z are positive if each of [#permalink] New post   Updated on: 12 Jun 2013, 03:50
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How many of the numbers x, y, and z are positive if each of these numbers is less than 10?

(1) x + y + z = 20
(2) x + y = 14
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A

Originally posted by carcass on 14 May 2012, 10:39.
Last edited by Bunuel on 12 Jun 2013, 03:50, edited 1 time in total.
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carcass
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Re: How many of the numbers x, y, and z are positive ??? [#permalink] New post   14 May 2012, 11:49
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for me is C.

I wait confirm from experts :)
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Bunuel
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Re: How many of the numbers x, y, and z are positive if each of [#permalink] New post   14 May 2012, 13:56
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How many of the numbers x, y, and z are positive if each of these numbers is less than 10?

(1) x + y + z = 20. If even one of the number is not positive then the sum of the other two must be more than or equal to 20 in order the sum of all three to be 20, but since we are told that each number is less than 10 then it's not possible. Therefore all 3 numbers must be positive. Sufficient.

(2) x + y = 14. Clearly insufficient as no info about z.

Answer: A.
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carcass
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Re: How many of the numbers x, y, and z are positive if each of [#permalink] New post   14 May 2012, 14:23
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:( why sometimes I do not active my brain ..........

Thank you Bunuel
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Re: How many of the numbers x, y, and z are positive if each of [#permalink] New post   07 Jul 2016, 02:19
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For (1) x+y+z=20
if x=y=10 and c=0 ? then c is not positive hence we are not sure if all three are positive. Isn't (1) insufficient then?
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Re: How many of the numbers x, y, and z are positive if each of [#permalink] New post   07 Jul 2016, 04:07
take any 2 numbers x,y, or z

given y,x, and z<10

i am taking x and Y

max value of x and y can be 9.99 or 9.999999

given , x+y+z=20

x and y won't alone give 20 so z has to be +ve

So all 3 number are positive.

2) no info about z

So answer is A
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Re: How many of the numbers x, y, and z are positive if each of [#permalink] New post   20 May 2021, 10:54
carcass wrote:
How many of the numbers x, y, and z are positive if each of these numbers is less than 10?

(1) x + y + z = 20
(2) x + y = 14



Key is to remember that x,y,z each is <10.

(1) \(x + y + z = 20\)

If any of the number is -ve, then there's no way the sum can be=20. so, they all must be +Ve

(2) \(x + y = 14\)

this is also possible when x and y are both +Ve. so, we know at least 2 are positive. but what about z?

Not sufficient.
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Re: How many of the numbers x, y, and z are positive if each of [#permalink] New post   20 May 2021, 12:38
Statement A: x+y+z=20
The maximum value of these numbers can be 9. Assume x=y=9. Hence, z will have to be 2. There is no way we can exceed sum of two vaiables by 20 and then have a third number negative to bring the sum to 20. Hence all three have to be positive. Sufficient

Statement B: x+y=14
Case 1: x=8, y=6 Possible
Case 2: x=9 y=5 Possible
Hence x and y have to be positive. But what about z. Nothing mentioned about z. So insufficient

Hence option A
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Re: How many of the numbers x, y, and z are positive if each of [#permalink] New post   20 May 2021, 23:25
The answer is A.

Though I selected D.

Stmt 1: x + y + z = 20

9.9 + 9.9 + 0.2 = 20. All three positive.

Stmt 2. x + y = 14. There is no information about z. But i kept assuming x + y + z = 20 and thought z would be 6.

I wish i stop making this silly mistakes
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Re: How many of the numbers x, y, and z are positive if each of [#permalink] New post   10 Aug 2023, 08:44
Hello from the GMAT Club BumpBot!

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Re: How many of the numbers x, y, and z are positive if each of [#permalink]
10 Aug 2023, 08:44
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