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

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New post 11 Dec 2018, 02:08
1
4
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

69% (01:00) correct 31% (01:00) wrong based on 144 sessions

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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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New post 11 Dec 2018, 02:47
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

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

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New post 11 Dec 2018, 04:31

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.

Answer: 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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New post 11 Dec 2018, 05:29
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
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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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New post 24 Dec 2018, 01:17
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Re: If xy < 0, what is the value of |x + y| ? (1) |x| = 4 (2) |y| = 1   [#permalink] 24 Dec 2018, 01:17
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