Data Sufficiency

If x and y are integers and x > 0, is y > 0?
(1) 7x - 2y > 0
(2) -y < x

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

IMO the answer to this is E as from both of the statements it cannot be inferred that y >0 or y <0.

please elaborate more, how you solved the stem 2.

2) -Y < X => X> -y
if X = 2 and Y =3
2>-3 therefore Y > 0

please clarify!

(1) 7x - 2y > 0

==>
x > 2/7*y (*)

these values satisfy (*):
x = 1, y = 7 ==> y > 0
x = 1, y = -1/2 ==> y < 0

INSUFF



(2) -y < x

==>
x > -y (**)

these values satisfy (**) :
x = 1, y = 7 ==> y > 0
x = 1, y = -1/2 ==> y < 0

INSUFF

Note that these values satisfy both (*) and (**), but does not tell us distinctly if y < 0.

Ans: E

(1)
y can be <0 or >0.

(2)
same case as (1). Try plugging positive and negative numbers

combined
tells us
8x>y
Insuff

Answer E

If x and y are integers and x > 0, is y > 0?
(1) 7x - 2y > 0
(2) -y < x

x>0, x & y intergers
possible values: x : + only; y: +, -, 0

1) x> 2/7 y => y has to be a multiple of 7 for x to be an int => y: 7, -7, 0; x: +
x y x>0 7x-2y>0 y>0
3 7 y y y
3 -7 y y n
1 0 y y n

Insufficient

2) x: +, y: +, -, 0 => to be scenario values same in (1) & (2), take y: 7, -7,0
x y x>0 x+y>0 y>0
1 7 y y y
8 -7 y y n
2 0 y y n

Insufficient

1& 2) x: +, y: 7, -7, 0

x y x>0 7x-2y>0 x+y>0 y>0
3 7 y y y
3 -7 y n n
1 0 y y y
Insufficient (answer E)

Hope it helps. Need one clarification: 7x-2y>0 & x+y>0 => 8x>y (is it correct???)

pnk wrote: Need one clarification: 7x-2y>0 & x+y>0 => 8x>y (is it correct???)

Yes. Inequalities with the same sign (and only the same sign) can be added (and only added).