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

Question

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

Bunuel · Accepted Answer

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.

Carcass · Answer

for me is C. I wait confirm from experts

Carcass · Answer

why sometimes I do not active my brain .......... Thank you Bunuel

gaurav0480 · Answer

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?

hsbinfy · Answer

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

ueh55406 · Answer

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.

omkarkhanvilkar · Answer

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

LaveenaPanchal · Answer

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

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