If x and y are integers, what is the value of xy ?

Question

(1) ((x - 1)(y - 1))! = 2
(2) x < 0

M36-44

Bunuel · Accepted Answer

Official Solution:

If  x  and  y  are integers, what is the value of  xy  ? 
 
(1)  ((x - 1)(y - 1))! = 2 
 
Only  2! = 2 , so we have that  (x - 1)(y - 1) = 2 .
 
Since  x  and  y  are integers, then we can have the following four cases:
 
 (x - 1)=2  and  (y - 1) = 1 . This gives  x=3  and  y=2 
 
 (x - 1)=1  and  (y - 1) = 2 . This gives  x=2  and  y=3 
 
 (x - 1)=-2  and  (y - 1) = -1 . This gives  x=-1  and  y=0 
 
 (x - 1)=-1  and  (y - 1) = -2 . This gives  x=0  and  y=-1 
 
First two cases gives  xy=6  and the last two cases give  xy=0 
 
Not sufficient.
 
(2)  x < 0 
 
Not sufficient.
 
(1)+(2) Since from (2)  x < 0 , then from (1) we have the third or fourth case, each of which gives  xy=0 . Sufficient.

Answer: C

Archit3110 · Answer

From 1; To valid : x=3 and y=2 it would be valid also xy=6 and at x= 0, y=-1, xy =-1 again it would be valid so in suffcient

From 2 , no y given in sufficient

From 1 & 2 we can say that x= -1 and y =0 , sufficient... 
xy= -1 IMO C

HAPPYatHARVARD · Answer

1: x= 2 ; y =3 or x=3; y =2
2: x<0
combining:(x=0; y = -1 )NA or (y = 0 ; x = -1)
Hence (y = 0 ; x = -1)
option C

Bunuel · Answer

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

Kinshook · Answer

Asked: If x and y are integers, what is the value of xy ?

(1) ((x - 1)(y - 1))! = 2
(x,y) = {(3,2),(2,3),(-1,0),(0,-1)}
xy ={6,0}
NOT SUFFICIENT

(2) x < 0
Since value of y is unknown
NOT SUFFCIENT

(1) + (2) 
(1) ((x - 1)(y - 1))! = 2
(2) x < 0
(x,y) = (-1,0)
xy = 0
SUFFICIENT

IMO C

Sarmadk5 · Answer

Only combining both we will get answer.

X is less than zero means its negative integer. By putting negative value to x , we will get the answer.

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If x and y are integers, what is the value of xy ?

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GMAT Data Sufficiency (DS) Questions

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