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Question Stats:
87% (01:18) correct
12% (00:28) wrong based on 1 sessions
If Z is an integer, what is the value of Z ? 1. Z^2 \le 02. Z^3 \le 0Source: GMAT Club Tests - hardest GMAT questions Does anyone has an explanation for A)
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SVP
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GMAT scope includes only real numbers. Hence, from stmt1: Z will be real on if Z = 0. Hence, sufficient.
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rishi4you wrote: If Z is an integer, what is the value of z
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.
Hence the answer is A.
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it's A.
given that Z is an integer , so Z Sq cannot be negative. It has to be 0.Sufficient
When Z power 3 is -ve , it could be any -ve integer. not Sufficient.
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Manager
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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
Therefore A is the answer.
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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.
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Intern
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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?
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Intern
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Its A.
1. Squares are non-negative. So Z is 0
2. Z can be 0 or negative number
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Intern
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Z must be an integer rules out imaginary numbers.
Zsquared must be positive but cannot due to z <= 0 limit so Z must be zero. Suff
Zcubed allows for negative numbers. Insuff.
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Z must be zero, given statement 1. Statement 2 is insuffiicent since Z can be 0 or any negative integer.
Answer must be A
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indeed, zero never occurred to me, doh! 
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Manager
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gtr022001 wrote: indeed, zero never occurred to me, doh! Of course, the "hard" problems never seem hard after you have a little more time to think about them 
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Manager
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same here.. i just lazily chose E... instead of thinking deeper and considering "0".
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A : if and only if Z=0 : OK
B : any integer that satisfies Z<=0 : so NG
IMO - A
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Intern
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GMAT TIGER wrote: rishi4you wrote: If Z is an integer, what is the value of z
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.
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Manager
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After asking google whether zero was an integer, I brilliantly chose A.
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Manager
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GaryDunn wrote: GMAT TIGER wrote: rishi4you wrote: If Z is an integer, what is the value of z
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 positi ve (+ve) and negati ve (-ve).
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Director
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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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easy one. Statement 1 is sufficient to answer the question. keep in mind that GMAT never ask for Imaginary numbers. it works on Real No only.
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