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

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Is z + z < z ? (1) -4z > 4z (2) z^3 < z^2  [#permalink]

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New post 13 Mar 2018, 06:56
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A
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C
D
E

Difficulty:

  55% (hard)

Question Stats:

51% (01:28) correct 49% (01:31) wrong based on 53 sessions

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Re: Is z + z < z ? (1) -4z > 4z (2) z^3 < z^2  [#permalink]

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New post 13 Mar 2018, 06:57
Bunuel wrote:
Is z + z < z ?

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


9. Inequalities



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Re: Is z + z < z ? (1) -4z > 4z (2) z^3 < z^2  [#permalink]

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New post 13 Mar 2018, 07:09
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.

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Is z + z < z ? (1) -4z > 4z (2) z^3 < z^2  [#permalink]

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New post 13 Mar 2018, 10:10
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Bunuel wrote:
Is z + z < z ?

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


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)
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Re: Is z + z < z ? (1) -4z > 4z (2) z^3 < z^2  [#permalink]

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New post 13 Mar 2018, 10:29
1. -4z>4z => z is +ve hence 2z>z ---->S
2. z^3 <z^2 => z is -ve or 0<z<1
if z is -ve => 2z<z ---->S
but if z is -ve or 0<z<1 =>2z>z ---->NS Thus 2. is NS

Hence I would go for option A.
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Re: Is z + z < z ? (1) -4z > 4z (2) z^3 < z^2  [#permalink]

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New post 15 Mar 2018, 13:03
Bunuel wrote:
Is z + z < z ?

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


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.
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Re: Is z + z < z ? (1) -4z > 4z (2) z^3 < z^2  [#permalink]

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New post 15 Mar 2018, 13:10
Bunuel wrote:
Is z + z < z ?

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



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
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Re: Is z + z < z ? (1) -4z > 4z (2) z^3 < z^2   [#permalink] 15 Mar 2018, 13:10
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