If xy

Question

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

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

M36-109

gvij2017 · Answer

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.

EgmatQuantExpert · Answer

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

https://e-gmat.com/blogs/wp-content/uploads/2018/08/Free-Session-Algebra-e1533292089856.jpg

Archit3110 · Answer

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

Bunuel · Answer

Par of  GMAT CLUB'S New Year's Quantitative Challenge Set

analytica233 · Answer

(1) |x| = 4. Clearly insufficient because we do not know anything about y.
(2) |y| = 1. Clearly insufficient because we do not know anything about x.

(1) + (2):
We have |x| > |y|, and xy have opposite signs (because xy < 0) --> |x + y| = |x| - |y| = 4 - 1 = 3. SUFFICIENT.

Answer: (C)

Bunuel · Answer

Official Solution:

If  xy < 0 , what is the value of  |x + y|  ? 
 
Notice that  xy < 0  means that  x  and  y  have different signs.
 
(1)  |x| = 4 
 
 x  is either 4 or -4. No info about  y . Not sufficient.
 
(2)  |y| = 1 
 
 y  is either 1 or -1. No info about  x . Not sufficient.
 
(1)+(2) Since  x  and  y  have different signs, then either  x=4  and  y=-1  or  x=-4  and  y=1  but in either case  |x + y|=3 . Sufficient.

Answer: C

natheodore · Answer

(1) 
|x| = 4 or - 4

However, we dont know value of y. Insufficient.

(2) 
|y| = 1 or -1

However, we dont know value of x. Insufficient.

(1) and (2),

and also xy<0 - meaning (+)(-) or (-)(+) for x and y respectively.

|-4+1| = 3
|4-1| = 3

Answer is C.

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

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