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# If xy≠0, is |x|>|y|？ 1) x=-2y 2) x=y^4

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If xy≠0, is |x|>|y|？ 1) x=-2y 2) x=y^4 [#permalink]

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17 Aug 2017, 00:52
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If xy≠0, is |x|>|y|？

1) x=-2y
2) x=y^4
[Reveal] Spoiler: OA

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Re: If xy≠0, is |x|>|y|？ 1) x=-2y 2) x=y^4 [#permalink]

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17 Aug 2017, 01:03
(1) from x=-2y it follows that in all cases |x|>|y|
(2) x=y^4
case 1: 16=2^4 => |16|>|2| then YES
case 2: 1/16=(1/2)^4 => |1/16|<|1/2| then NO

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Re: If xy≠0, is |x|>|y|？ 1) x=-2y 2) x=y^4 [#permalink]

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17 Aug 2017, 01:14
If xy≠0, is |x|>|y|？

1) x=-2y
2) x=y^4

Statement 1: How is the first statement sufficient?

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Re: If xy≠0, is |x|>|y|？ 1) x=-2y 2) x=y^4 [#permalink]

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17 Aug 2017, 04:58
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Bounce1987 wrote:
If xy≠0, is |x|>|y|？

1) x=-2y
2) x=y^4

Statement 1: How is the first statement sufficient?

Here is my point:

Statement 1 : x=-2y ,or $$\frac{x}{y}$$=-2 ;here x is divided by y and the remainder =0,so y must be a factor of x and whether x or y is positive or negative, |x|>|y| ;Sufficient

Thanks.
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Re: If xy≠0, is |x|>|y|？ 1) x=-2y 2) x=y^4 [#permalink]

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17 Aug 2017, 05:15
MathRevolution wrote:
If xy≠0, is |x|>|y|？

1) x=-2y
2) x=y^4

1) x = -2y
=> x = 2, y = -1
=> x = -1, y = $$\frac{1}{2}$$
In both cases |x| > |y|
Hence, Sufficient.

2) x = $$y^4$$
x = 16, y = 2 => |x| > |y| -> YES
x = 1, y = 1 => |x| = |y| -> NO
Insufficient.

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Re: If xy≠0, is |x|>|y|？ 1) x=-2y 2) x=y^4 [#permalink]

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17 Aug 2017, 07:40
Statement 1: x= -2y
Therefore |-2y| will always be greater than y
Sufficient

Statement 2: x=y^4
2 cases: y>1, y<1
when y>1 |x|>|y|
when y<1 |x|<|y|
Not sufficient

Hence A
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Re: If xy≠0, is |x|>|y|？ 1) x=-2y 2) x=y^4 [#permalink]

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17 Aug 2017, 11:15
xy≠0 ---- (given)
we have to find whether |x|>|y|
Now consider |x|>|y|
|x|>|y| can also be written as |x|/|y| > 1
i.e. x/y > +1 or x/y < -1

Now, 1) x= -2y
X/y = -2. here x/y is less than -1; this information is sufficient to answer the question.
Hence 1) is sufficient.

2) x=y^4
therefore x/y = y^3.
as we don't know anything about y, we can not predict value of x/y.
Hence 2) is insufficient.

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Re: If xy≠0, is |x|>|y|？ 1) x=-2y 2) x=y^4 [#permalink]

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20 Aug 2017, 19:07
=>Condition 1)

|x| = |-2y| = 2|y| > |y|.
Thus this is sufficient.

Condition 2)

If y = 2, then x = 16 and so |x| > |y|.
If y = ½, then x = 1/16 and so |x| < |y|.
This is not sufficient.

Ans: A
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Re: If xy≠0, is |x|>|y|？ 1) x=-2y 2) x=y^4   [#permalink] 20 Aug 2017, 19:07
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