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# If xy < 0, what is the value of |x + y| ? (1) |x| = 4 (2) |y| = 1

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Math Expert
Joined: 02 Sep 2009
Posts: 64222
If xy < 0, what is the value of |x + y| ? (1) |x| = 4 (2) |y| = 1  [#permalink]

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11 Dec 2018, 01:08
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5
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Difficulty:

25% (medium)

Question Stats:

68% (01:00) correct 32% (00:58) wrong based on 175 sessions

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If xy < 0, what is the value of |x + y| ?

(1) |x| = 4
(2) |y| = 1

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Joined: 08 Aug 2017
Posts: 727
Re: If xy < 0, what is the value of |x + y| ? (1) |x| = 4 (2) |y| = 1  [#permalink]

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11 Dec 2018, 01:47
Statement 1
|x|= 4 => x= 4, -4
Not sufficient

Statement 2
|y|= 1 => y= 1, -1
Not sufficient

St. 1+2
as we know xy<0
means x and y are of opposite sign. (4, -1) or (-4, 1)
In both cases |x+y|= 3

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Joined: 04 Jan 2015
Posts: 3367
If xy < 0, what is the value of |x + y| ? (1) |x| = 4 (2) |y| = 1  [#permalink]

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11 Dec 2018, 03:31

Solution

Given:
• xy < 0
o Implies, either x < 0 or y < 0

To find:
• The value of |x + y|

Analysing Statement 1
|x| = 4
• Implies, x = 4 or -4
• However, we do not have any information about y

Therefore, statement 1 is not sufficient

Analysing Statement 2
|y| = 1
• Implies, y = 1 or -1
• However, we do not have any information about x

Therefore, statement 2 is not sufficient

Combining Both Statements
Combining both statements, we get,
• x = ±4 and y = ±1
• Thus,
o If x = 4, then y = -1
 Implies, |x + y| = |4 – 1| = 3

o If x = -4, then y = 1
 Implies, |x + y| = |-4 + 1| = |-3| = 3

Therefore, both statements together are sufficient

Hence, the correct answer is Option C.

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Re: If xy < 0, what is the value of |x + y| ? (1) |x| = 4 (2) |y| = 1  [#permalink]

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11 Dec 2018, 04:29
Bunuel wrote:
If xy < 0, what is the value of |x + y| ?

(1) |x| = 4
(2) |y| = 1

for xy < 0 to be valid
either x or y has to be -ve

from 1 : lxl can be +4 or -4 , y not given not sufficient

from 2 : lyl can be +/-1 , x not given not sufficient

from 1 or 2 substitutting either values of x or y as + or -ve we would get

l-4+1l = l4-1l

which would be 3

IMO C sufficient
Math Expert
Joined: 02 Sep 2009
Posts: 64222
Re: If xy < 0, what is the value of |x + y| ? (1) |x| = 4 (2) |y| = 1  [#permalink]

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24 Dec 2018, 00:17
Bunuel wrote:
If xy < 0, what is the value of |x + y| ?

(1) |x| = 4
(2) |y| = 1

_________________
Re: If xy < 0, what is the value of |x + y| ? (1) |x| = 4 (2) |y| = 1   [#permalink] 24 Dec 2018, 00:17