Is y^2y*|y|?

Question

Is  y^2>y*|y| ?
(1) y is an integer.
(2) y is not a positive integer.

self made.....

Mortysmith · Answer

I believe the answer is E

Fact 1: Y is an integer. 
Consider two cases.
- Case 1: Y = to any positive integer then, in this case, the two sides of the equation are equal. 
- Case 2: Y = to any negative integer then, in this case, the left side is greater than the right. 
Not Sufficient

Fact 2: y is not a positive integer
Consider two cases.
- Case 1: Y = to any negative integer then, in this case, the left side is greater than the right. 
- Case 2: Y = 0 then, in this case, the left side is equal to the right. 
Not Sufficient

No need to even test the combined because Fact 2 captures Fact 1.

Therefore, the answer is E Not Sufficient

unverifiedvoracity · Answer

y^2 > y * |y| will only be true when y <0. So, the question really asks whether y < 0 (or whether y is negative)

1) y is an integer, but y can be positive, negative or zero. Not Sufficient

2) y is not a positive integer, so y is either 0 or negative. Not Sufficient.

Two statements combined are also not sufficient. IMO answer is E.

Divyadisha · Answer

y^2>y*|y| can be possible if y is -ve (1) y is an integer. It doesn't tell us if y is +ve, -ve or 0 Insufficient (2) y is not a positive integer. It doesn't tell us if y is -ve or 0 Insufficient Both statements together are insufficient. Hence E should be the answer

MathRevolution · Answer

We can modify the original condition and the question. If y>0, the sign of inequality does not change even if we divide each side by y. Then, we got y>|y|?. However, this is not possible in any cases.
If y<0, and if we divide each side by y, the sign of inequality change. Then we get y<|y|?. The answer is yes.
The questions states y^2>y|y|? and this is same as y<0?.
However, using the condition 1) and the condition 2), we do not have y<0. The condition, hence, is not sufficient and the correct answer is E. In other words, when y=0, the answer is no and when y=-1, the answer becomes yes. The conditions are not sufficient and the correct answer is E.

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Is y^2>y*|y|?

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