Is z + z 4z (2) z^3

Question

Is z + z < z ?

(1) -4z > 4z
(2) z^3 < z^2

Bunuel · Answer

9. Inequalities 
     Theory   
 Inequalities Made Easy! 
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 Solving Quadratic Inequalities: Graphic Approach 
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Gladiator59 · Answer

IMO A.

The question is asking if 
2z < z

If we can certainly tell if z if either positive or negative we can answer the question.

St 1 : -4z > 4z
This is only true for z < 0.
Hence suff.

St 2 : z^3 < z^2

Two possibilities :

1) z could be negative 
Hence z^3 ( neg no.) < z^2 ( positive no.)

2) z could be positive and less than 1.

Z^3 < z^2 still holds.

Not sufficient .

Hence A.

Posted from my mobile device

AkshdeepS · Answer

Question: Is z + z < z ? or Is 2z - z < 0 ? or Is z < 0 ? St 1: - 4z > 4z or 8z < 0 or z < 0 Sufficient St 2 : z^3 < z^2 or z^3 - z^2 < 0 or z^2 ( z - 1) < 0 z^2 > 0 for z < 0 or z > 0 z - 1 < 0 z < 1 Therefore combined range is z < 0 or 0 < z < 1. Not sufficient (A)

u1983 · Answer

1. -4z>4z => z is +ve hence 2z>z ---->S 2. z^3 z is -ve or 0 2zS but if z is -ve or 02z>z ---->NS Thus 2. is NS Hence I would go for option A.

MathRevolution · Answer

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. The question is modified as follows. 2z < z ? ⇔ z < 0 ? Condition 1) -4z > 4z ⇔ 0 > 8z ⇔ 0 > z It is same as the question. Condition 1) is sufficient. Condition 2) z^3 < z^2 ⇔ z^3 - z^2 < 0 ⇔ z^2(z-1) < 0 ⇔ z - 1 < 0 since z^2 > 0 ⇔ z < 1 Since the range of the question does not include that of the condition 2), the condition 2) is not sufficient. Therefore, the answer is A.

Mo2men · Answer

Rephrase the question:

Is z <0??

(1) -4z > 4z

8z < 0....Z must be negative...........Answer is always Yes.

Sufficient

(2) z^3 < z^2

Let x = 1/2 ............1/8 < 1/4 ..........Answer is NO
Let x =-1/2 .......... -1/8 < 1/4 ..........Answer is Yes

Insufficient

Answer: A

RastogiSarthak99 · Answer

My 2 cents on this:

Question stem can be broken down as follows:

is z+z< z? ---> is 2z<z? ---> is 2z-z<0? --->is z<0?

St1: -4z<4z --> -4z-4z<0 --> -8z<0 --> z<0. Sufficient.

St2: z^3 < z2 --> z^3-z^2<0 --> z^2(z-1) < 0 --> We know that z^2 can never be less than 0 and so we are only getting z<1 which is insufficient to answer whether z<0 or not. It could be. It could not be as well. Insufficient.

A

bumpbot · Answer

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Is z + z < z ? (1) -4z > 4z (2) z^3 < z^2

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