If x is not equal to zero is xy 0 ?

Question

If x is not equal to zero is xy > 0 ?

(1) x >0

(2) 1/x < y

Bunuel · Accepted Answer

If x is not equal to zero is xy > 0 ?

xy will be positive if x and y have the same sign, when both are negative or both are positive.

(1) x > 0. No info about \(y\). Not sufficient.

(2) 1/x < y. If \(x=-1\) and \(y=1\) then the answer is NO but if \(x=2\) and \(y=1\) then the answer is YES. Not sufficient.

(1)+(2) Since from (1) \(x>0\), then \(\frac{1}{x}>0\), hence from (2) we have that \(0<\frac{1}{x}<y\) --> \(y>0\). Thus both \(x\) and \(y\) are positive. Sufficient.

Answer: C.

IanStewart · Answer

xy will be positive if x and y have the same sign. Statement 1 gives no information about y, and from Statement 2, it is possible that x and y are both positive or both negative, or that x is negative and y is positive.

Using both statements, we know x is positive, so 1/x is positive. From Statement 2, if y > 1/x, then y is greater than something positive, so y is also positive, and xy is positive, so the answer is C.

Marcyfal · Answer

Sorry but I don't understand why the answer can not be B. 
 
B) 1/x < y This can be transformed in xy > 1. So if xy>1 it should be also true xy > 0.

Please could you tell me where I am wrong?

Thank you

Bunuel · Answer

Never multiply an inequality by variable (or expression with variable) unless you know the sign of variable (or expression with variable). Because if x>0 you should write xy>1 BUT if x<0 , you should write xy<1 (flip the sign when multiplying by negative expression). Hope it helps.

Marcyfal · Answer

All right, Thank you very much. By the way I follow all your answers. You are great!

GMATinsight · Answer

Question : Is xy > 0? Statement 1 : x>0 i.e. x is positive but we have no information about y being positive or Negtive, Hence NOT SUFFICIENT Statement 2 : 1/x0 NOT SUFFICIENT Combining the two statements x is positive and y>1/x i.e. y too is positive hence, xy>0 SUFFICIENT Answer: Option C

rocky1988 · Answer

hi bunuel,

Cant we write the option B as y>1/x= (x-y)/x>0 and if you put both the statements together and try few values as mentioned below it is satisfying for neg/pos value of Y.

X=10 Y=8 and X=10 and Y=-8 in both cases above equation holds.

Kindly explain!! Thanks

GMATinsight · Answer

y is NOT greater than 1/x as per highlighted set of values so they can't be taken as they violate the information os Second statement.

I hope this helps

ENGRTOMBA2018 · Answer

You can not perform the calculations you have mentioned above. y>1/x eq (x-y)/x>0 You can although, rewrite statement 2 as y-1/x > 0 --->(xy-1)/x>0 and as x>0 ---> for this fraction to be >0 --> xy-1>0 ---> xy>1 . Again, 2 cases possible, x>0 and y>0 and x<0 and y<0. Thus this statement is NOT sufficient.

rocky620 · Answer

chetan2u From 2 : \frac{1}{x} < y => \frac{1}{x} -y < 0 => \frac{1-xy}{x} < 0 => 1-xy < 0 => 1 < xy Since xy is greater than 1, it is greater than 0. Hence sufficient, So why the OA is E. Kindly Help.

chetan2u · Answer

\frac{1-xy}{x}<0 This means x and 1-xy have opposite sign If x>0, then 1-xy<0 or xy>1 If x<0, then 1-xy>0 or xy<1 So, you cannot say whether xy>1, unless you know x>0. This is exactly what statement I tells you. Hence, both with statements combined, we can tell that xy>1>0. Ans is C

If x is not equal to zero is xy > 0 ?

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If x is not equal to zero is xy > 0 ?

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