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Is x*y^2 < 0? (1) |x| = -x (2) y^3 = 8 27 Apr 2020, 06:24
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

55% (hard)

Question Stats:

42% (00:56) correct 58% (00:51) wrong based on 134 sessions

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Is \(x*y^2<0?\)

(1) \(|x| = -x\)
(2) \(y^3= 8\)


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E
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Is x*y^2 < 0? (1) |x| = -x (2) y^3 = 8 27 Apr 2020, 06:42
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Required conditions for \(xy^2<0\)
i. \(y\) is non zero
ii. \(x\) is negative

1. \(|x|=-x\)

This is true for \(x≤0\) and we don't know if \(y\) is non zero

1 is not sufficient

2. \(y^3=8\)

So \(y=2\). But we have no info about \(x\)

2 is not sufficient

(1)+(2)

Combining, we get that \(x≤0\) and \(y=2\),

If \(x<0\), \(xy^2<0\)
If \(x=0\), \(xy^2=0\)

Not sufficient

Answer is (E)

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Is x*y^2 < 0? (1) |x| = -x (2) y^3 = 8 27 Apr 2020, 06:52
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Is \(x*y^2<0?\)
1) \(|x| = -x\)
2) \(y^3= 8\)


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\(x*y^{2} < 0\)
—> x < 0 ?

(Statement1): \(|x| = —x \)
—> If x< 0, then Yes.
If x= 0, then No.
Insufficient

(Statement2): \(y^{3} =8 \)
Nothing tells us about what x is
Insufficient

Taken together 1&2,
y =2, —> x < 0 ?
Again x could be less than zero (Yes) or could be equal to zero (No)
Insufficient

Answer (E)

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Is x*y^2 < 0? (1) |x| = -x (2) y^3 = 8 15 Jun 2020, 22:35
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Is \(x*y^6<0?\)
1) |x| = -x
2) \(y^3= 8\)
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Question: Is \(x*y^6<0?\)

y^6 is always non Negative hence the question is primarily about x

Statement 1: |x| = -x

i.e. x ≤ 0

If x < 0 and y ≠ 0 then \(x*y^6<0\) i.e. YES

If x = 0 and y ≠ 0 then \(x*y^6=0\) i,e. NOT less than zero i.e. NO

NOT SUFFICIENT

Statement 2:\(y^3= 8\)
i.e. y is non zero and y = 2
i.e. \(y^6\) is always positive
but if x < 0 then \(x*y^6<0\) i.e. YES
If x = 0 then \(x*y^6=0\) i.e. NOT less than zero i.e. NO

NOT SUFFICIENT

COmbining the two statements

If x < 0 and y = 2 then \(x*y^6<0\) i.e. YES

If x = 0 and y = 2 then \(x*y^6=0\) i,e. NOT less than zero i.e. NO

NOT SUFFICIENT

Answer: Option E
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Is x*y^2 < 0? (1) |x| = -x (2) y^3 = 8 17 Jul 2023, 07:21
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Is \(x*y^6<0?\)
1) |x| = -x
2) \(y^3= 8\)

Question: Is \(x*y^6<0?\)

y^6 is always non Negative hence the question is primarily about x

Statement 1: |x| = -x

i.e. x ≤ 0

If x < 0 and y ≠ 0 then \(x*y^6<0\) i.e. YES

If x = 0 and y ≠ 0 then \(x*y^6=0\) i,e. NOT less than zero i.e. NO

NOT SUFFICIENT

Statement 2:\(y^3= 8\)
i.e. y is non zero and y = 2
i.e. \(y^6\) is always positive
but if x < 0 then \(x*y^6<0\) i.e. YES
If x = 0 then \(x*y^6=0\) i.e. NOT less than zero i.e. NO

NOT SUFFICIENT

COmbining the two statements

If x < 0 and y = 2 then \(x*y^6<0\) i.e. YES

If x = 0 and y = 2 then \(x*y^6=0\) i,e. NOT less than zero i.e. NO

NOT SUFFICIENT

Answer: Option E
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I suppose from Statement 1: we infer x<0 not that i.e. x ≤ 0 ???

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Is x*y^2 < 0? (1) |x| = -x (2) y^3 = 8 17 Jul 2023, 07:27
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Nabneet
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Is \(x*y^6<0?\)
1) |x| = -x
2) \(y^3= 8\)

Question: Is \(x*y^6<0?\)

y^6 is always non Negative hence the question is primarily about x

Statement 1: |x| = -x

i.e. x ≤ 0

If x < 0 and y ≠ 0 then \(x*y^6<0\) i.e. YES

If x = 0 and y ≠ 0 then \(x*y^6=0\) i,e. NOT less than zero i.e. NO

NOT SUFFICIENT

Statement 2:\(y^3= 8\)
i.e. y is non zero and y = 2
i.e. \(y^6\) is always positive
but if x < 0 then \(x*y^6<0\) i.e. YES
If x = 0 then \(x*y^6=0\) i.e. NOT less than zero i.e. NO

NOT SUFFICIENT

COmbining the two statements

If x < 0 and y = 2 then \(x*y^6<0\) i.e. YES

If x = 0 and y = 2 then \(x*y^6=0\) i,e. NOT less than zero i.e. NO

NOT SUFFICIENT

Answer: Option E

I suppose from Statement 1: we infer x<0 not that i.e. x ≤ 0 ???

Bunuel
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No, |x| = -x means that x can be 0 or negative. Note, that |0| = -0 is correct equation because -0 = 0.
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Is x*y^2 < 0? (1) |x| = -x (2) y^3 = 8 19 Jul 2023, 02:54
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|x| is always positive right? So shouldn't the only way that |x| = -x be true is when x = 0?
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Is x*y^2 < 0? (1) |x| = -x (2) y^3 = 8 19 Jul 2023, 03:24
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arnkaprx
|x| is always positive right? So shouldn't the only way that |x| = -x be true is when x = 0?
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|x| is always non-negative, so |x| can only be 0 or positive.

|x| = -x means that x ≤ 0. You can easily check this by plugging numbers.
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