Two more form internet #17, 18, section 14

[isisalaska]

17- If x<0, is y>0?
10 x/y <0
2) 7-x>0
Why is A? I am thinking what if x=-3 and y=-4, still x/y ,0 BUT y <0
but if x=-3 and y=4 , y>0, I am confused...

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18- If x,y,z are positive integers, is x-y odd?
1) x=Z^2
2) y=(z-1)^2

Answer is C

[jayhawk2001]

17- If x<0, is y>0?
10 x/y <0
2) 7-x>0
Why is A? I am thinking what if x=-3 and y=-4, still x/y ,0 BUT y <0
but if x=-3 and y=4 , y>0, I am confused...

If x=-3 and y=-4, x/y is positive. Basically for x/y to be < 0, either
x < 0 or y < 0 but not both. So, if we know that x < 0, then y has
to be positive.

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18- If x,y,z are positive integers, is x-y odd?
1) x=Z^2
2) y=(z-1)^2

Answer is C

1 - insufficient. Don't know y
2- insufficient. Don't know x

Combining 1 and 2, z or z-1 has to be even.
If z is even, x is even and y is odd and x-y is always odd
If z is odd, x is odd and y is even and so x-y is again odd

So C

[Cybermusings]

17- If x<0, is y>0?
10 x/y <0
2) 7-x>0

Substitute values to find the answer. x<0. thus x is negative

Thus for x/y to be less 0 y would have to be positive else the x/y won't be less than 0. hence A itself is sufficient

Take the second statement

7-x > 0

This doesnt tell us anything about the variable y. Hence 2 alone is insufficient.

Thus it is choice A for question 17

[Cybermusings]

If x,y,z are positive integers, is x-y odd?
1) x=Z^2
2) y=(z-1)^2

Statement 1 just tells us that x is the square of z. It doesn't mention anything about y. Moreover x can be odd ( example 3^2 = 9 ) or even (4 ^ 2 = 8). Thus Statement 1 alone is insufficient

Statement 2 says that y is the square of a number 1 less than z. Again z can be even or odd and thus the square of z - 1 can be odd or even respectively. Moreover it doesn't say anything about x which can be even or odd. Hence 2 alone is insufficient

Now combine the 2

Let's take z = 6 (an even number)

x = 6^2 = 36

y = (6-1)^2 = 25

36 - 25 = 11 (odd)

Lets take a case where z is odd (11)

x = 11^2 = 121

y = 10^2 = 100

121 - 100 = 21 (odd)

Hence both statements together are sufficient but neither statement alone will suffice. it's C