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What is the value of y ? (1) |x| ≤ y ≤ −|x| (2) |y| ≥ x ≥ −|y|

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Bunuel
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What is the value of y ? (1) |x| ≤ y ≤ −|x| (2) |y| ≥ x ≥ −|y| [#permalink] New post   24 Jun 2020, 02:27
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What is the value of y ?


(1) |x| ≤ y ≤ −|x|

(2) |y| ≥ x ≥ −|y|


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Re: What is the value of y ? (1) |x| ≤ y ≤ −|x| (2) |y| ≥ x ≥ −|y| [#permalink] New post   24 Jun 2020, 02:46
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What is the value of y ?

(1) |x| ≤ y ≤ −|x|
'+' ≤ y ≤ '−'
This is only possible when both |x| and -|x| equal 'zero'.
0 ≤ y ≤ −0 i.e. 0 ≤ y ≤ 0
Hence y = 0

SUFFICIENT.

(2) |y| ≥ x ≥ −|y|
|2| ≥ x ≥ −|2| i.e. 2 ≥ x ≥ −2
OR
|3| ≥ x ≥ −|3| i.e. 3 ≥ x ≥ −3
Not a unique value of y is available.

INSUFFICIENT.

Answer A.
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Re: What is the value of y ? (1) |x| ≤ y ≤ −|x| (2) |y| ≥ x ≥ −|y| [#permalink] New post   24 Jun 2020, 03:24
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IMO A

(1) |x| ≤ y ≤ −|x|

For any Value of x other than zero, the above inequality will not make sense.
eg. x = 3
From Inequality, y>3 & y< -5 , So no such values possible for y

So, x= 0. y=0
Sufficient

(2) |y| ≥ x ≥ −|y|

Here y can have any value, correspondingly x can take multiple values.
Not Sufficient.
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Re: What is the value of y ? (1) |x| ≤ y ≤ −|x| (2) |y| ≥ x ≥ −|y| [#permalink] New post   24 Jun 2020, 04:42
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What is the value of y ?


(1) |x| ≤ y ≤ −|x|:

-> |x| ≤ y ≤ -|x|
-> y cannot be less than a negative but greater than a positive number, y must = x = 0
-> Sufficient

(2) |y| ≥ x ≥ −|y|:
-> -|y| ≤ x ≤ |y|
-> y can be any number in between or equal to x
-> Insufficient

IMO answer choice A
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Re: What is the value of y ? (1) |x| ≤ y ≤ −|x| (2) |y| ≥ x ≥ −|y| [#permalink] New post   24 Jun 2020, 05:28
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What is the value of y ?


(1) |x| ≤ y ≤ −|x|
The minimum value of |x| is 0, so y is at least 0.
The maximum value of -|x| is 0, so y cannot be greater than 0.
only possible value of y is 0.

(2) |y| ≥ x ≥ −|y|
y can be anything.

A
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Re: What is the value of y ? (1) |x| ≤ y ≤ −|x| (2) |y| ≥ x ≥ −|y| [#permalink] New post   24 Jun 2020, 12:39
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Quote:
What is the value of y ?


(1) |x| ≤ y ≤ −|x|

(2) |y| ≥ x ≥ −|y|


S1: The only way this can be true is if x=0, in which case y=0. SUFFICIENT

S2: y could be any number. NOT SUFFICIENT.

ANSWER: A
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Re: What is the value of y ? (1) |x| ≤ y ≤ −|x| (2) |y| ≥ x ≥ −|y| [#permalink] New post   24 Jun 2020, 18:25
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Quote:
What is the value of y ?
(1) |x| ≤ y ≤ −|x|
(2) |y| ≥ x ≥ −|y|


(1) sufic
y≥positive or zero
y≤negative or zero
y must be = 0

(2) insufic
x≥negative or zero
x≤positive or zero
y=anything

Ans (A)
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Re: What is the value of y ? (1) |x| ≤ y ≤ −|x| (2) |y| ≥ x ≥ −|y| [#permalink] New post   26 Jun 2020, 23:10
Kindly see the attachment.
IMO A
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Re: What is the value of y ? (1) |x| ≤ y ≤ −|x| (2) |y| ≥ x ≥ −|y| [#permalink]
26 Jun 2020, 23:10
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