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1) Z^2<=0 (read as z raised to the power 2 is less than equal to 0) 2) z^3<=0 (read as z raised to the power 3 is less than equal to 0)

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

Does anyone has an explanation for A)

A. z = 0. 1: z cannot be -ve. so it has to be 0. suff. 2: z can be -ve or 0. so nsf..
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I guess you already have your answer but I'll just type it out thoroughly.

(a) notes that square of a number is less than or equal to zero. You know that square of any positive or negative integer is positive, so the value cannot be less than 0. So only answer is "zero". Sufficient.

(b) notes that raised to 3 power is less than or equal to 0. 0x0x0 = true, -1x-1x-1 is less than 0 = true. You have multiple values, so this one is insufficient.

As per the equation one we have Z^2 <=0 that means either Z is 0 or not real. In case of GMAT we only need to consider real numbers . So A is sufficient.

As per B we have Z^3 <= 0 , so Z can be either 0 or negative , therefore we dont have unique answer .So B is not sufficient

For any integer Z, Z^2 is always positive, ie Z^2 >= 0 (1) states that Z^2 <= 0

Thus we can figure that Z^2 = 0, ie Z=0

Z^3 can have positive and negative values (2) states that Z^3 <= 0 For z=0, Z^3 = 0 For z=-1, Z^3 = -1, both are <=0, therefore we cannot reach a conclusion.

Is it me, or have the past few quant questions of the day (including this one) been far too easy?

I don't mean to sound high and mighty. I mean I know that I am at a 600-700 level for quant, so these should be pretty challenging for me, but the last few have not been. Thoughts?

1) Z^2<=0 (read as z raised to the power 2 is less than equal to 0) 2) z^3<=0 (read as z raised to the power 3 is less than equal to 0)

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

Does anyone has an explanation for A)

A. z = 0. 1: z cannot be -ve. so it has to be 0. suff. 2: z can be -ve or 0. so nsf..

Can someone explain the ve/-ve notation please.

I think it is shorthand (laziness?) for positive (+ve) and negative (-ve).

I don't think i have a better explanation than what have been given above. Generally, if x^2<0, then x must be an invalid number on the number line. x must be 0, A is sufficient.
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