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12 Nov 2015, 21:43
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Is xy < 0?
(1) -x + y > 5
(2) 3y - x < -9
for xy to be < 0 both x and y should be of opposite sign
Stmt 1:
-x + y > 5
When x=-1 & y=5 -x+y=6 > 5
And x=1 & y=8 -x+y=7 > 5
So x and y can either be of same sign or different. -> Not sufficient.
Stmt 2:
3y - x < -9
When x=15 & y=1 3y - x=-12 < -9
And x=7 & y=-1 3y - x=-10 < -9
So x and y can either be of same sign or different. -> Not sufficient.
Stmt 1 + Stmt 2:
We can re-write the two inequality statements as
-x+y-5>0
x-3y-9>0
---------
-2y-14>0 -> Adding the two statements
-y-14>0
y<-14
Now add this to first statement
-x+y-5>0
-y-14>0
----------
-x-19>0
x<-19
So, x<-19 and y<-14, which implies that both x and y has the same sign. Hence xy is always >0. -> Sufficient.
Ans: C
(1) -x + y > 5
(2) 3y - x < -9
for xy to be < 0 both x and y should be of opposite sign
Stmt 1:
-x + y > 5
When x=-1 & y=5 -x+y=6 > 5
And x=1 & y=8 -x+y=7 > 5
So x and y can either be of same sign or different. -> Not sufficient.
Stmt 2:
3y - x < -9
When x=15 & y=1 3y - x=-12 < -9
And x=7 & y=-1 3y - x=-10 < -9
So x and y can either be of same sign or different. -> Not sufficient.
Stmt 1 + Stmt 2:
We can re-write the two inequality statements as
-x+y-5>0
x-3y-9>0
---------
-2y-14>0 -> Adding the two statements
-y-14>0
y<-14
Now add this to first statement
-x+y-5>0
-y-14>0
----------
-x-19>0
x<-19
So, x<-19 and y<-14, which implies that both x and y has the same sign. Hence xy is always >0. -> Sufficient.
Ans: C
13 Nov 2015, 00:02
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A question asking for sufficient information.
xy<o only when 1 factor has negative and 1 has positive sign.
1) The first condition is y>5+x. x and y can be both negative(or positive) or have opposite signs. A is not sufficient. Eliminate A and D.
2) The second condition can be written as y<1/3x-3. Uncertain about signs as well. Eliminate B.
We have CE.
Put 2 conditions together we have 1/3x-3>y>5+x. Meaning
1/3x-3>5+x => -8>2/3x
=> x<0
=> 1/3x-3<0 => y<0
=> we can know the sign of xy (in this case xy>0)
Therefore, combination of 1) and 2) give sufficient information.
Answer is C.
xy<o only when 1 factor has negative and 1 has positive sign.
1) The first condition is y>5+x. x and y can be both negative(or positive) or have opposite signs. A is not sufficient. Eliminate A and D.
2) The second condition can be written as y<1/3x-3. Uncertain about signs as well. Eliminate B.
We have CE.
Put 2 conditions together we have 1/3x-3>y>5+x. Meaning
1/3x-3>5+x => -8>2/3x
=> x<0
=> 1/3x-3<0 => y<0
=> we can know the sign of xy (in this case xy>0)
Therefore, combination of 1) and 2) give sufficient information.
Answer is C.
13 Nov 2015, 04:43
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Question asks if x and y are of different signs. Basically it is a "Yes" or "No" Data Sufficiency Question. Our aim is to get a yes and no for a choice. If we can get that, we can say that choice is insufficient.
(1) -x + y > 5
x = -5 , y=2 -(-5) +2 = 7 which is greater than 5.
x y = -5 *2 < 0 -- Yes
x =3 , y=10
-3 +10 =7 which is greater than 5.
xy= 3*10 =30 >0 No
So statement A is insufficient.
2)3y-x<-9
y = -1 x =13
3*(-1) -13 =-16 <-9
xy =-1 *13 < 0 Yes
y=1 x =13
3(1) -13 =-10 < -9
xy =1 *13 >0 No
So statement B is also insufficient.
Now combining 2 statements A and B
-x + y > 5 --- 1
3y - x < -9
Multiplying choice 2 by -1 to reverse the sign of inequality--> x -3y>9 ----------2
Solving inequalities 1 & 2 we get
-2y>14
-y>7
y<-7
-x + y >5
-x > 5 -y
x <y -5 Since y is -ve x is also negative.
Since both x and y are negative, xy is not less than 0.
Both statements combined are sufficient to answer the question. So choice C.
(1) -x + y > 5
x = -5 , y=2 -(-5) +2 = 7 which is greater than 5.
x y = -5 *2 < 0 -- Yes
x =3 , y=10
-3 +10 =7 which is greater than 5.
xy= 3*10 =30 >0 No
So statement A is insufficient.
2)3y-x<-9
y = -1 x =13
3*(-1) -13 =-16 <-9
xy =-1 *13 < 0 Yes
y=1 x =13
3(1) -13 =-10 < -9
xy =1 *13 >0 No
So statement B is also insufficient.
Now combining 2 statements A and B
-x + y > 5 --- 1
3y - x < -9
Multiplying choice 2 by -1 to reverse the sign of inequality--> x -3y>9 ----------2
Solving inequalities 1 & 2 we get
-2y>14
-y>7
y<-7
-x + y >5
-x > 5 -y
x <y -5 Since y is -ve x is also negative.
Since both x and y are negative, xy is not less than 0.
Both statements combined are sufficient to answer the question. So choice C.
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