If |x + 1|

Question

If |x + 1|<= 5 and |y - 1| <= 5, then which of the following is the least value of xy?

A. 36
B. -24
C. -36
D. -16
E. -10

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Got values of X<=4 & X>=6 & Y<=6 & Y>=4 ?
Need help ? Also I doubt on official answer also ?

Bunuel · Accepted Answer

|x + 1| \leq 5  -->  -5 \leq x + 1 \leq 5  -->  -6 \leq x \leq 4 ;
 |y - 1| \leq 5  -->  -5 \leq y - 1 \leq 5  -->  -4 \leq y \leq 6 .

Te least value is obtained when x = -6 and y = 6 --> xy = -36.

Answer: C.

Bunuel · Answer

Similar questions to practice: if-4-x-7-and-6-y-3-which-of-the-following-specifies-all-the-107764.html 12-easy-pieces-or-not-126366.html#p1033925 12-easy-pieces-or-not-126366-20.html#p1033949

Krage17 · Answer

You forgot to switch the signs when you simplified the inequalities. It should the following:

\(-5<=x+1<=5\) => \(-6<=x<=4\)
\(-5<=y-1<=5\) => \(-4<=y<=6\)

Although, I am getting C, not B, since x could be -6 and y could be 6, thus, 6*(-6)=-36.

Correct me if I am wrong.

PS Just saw Bunuel's answer above.

AkshdeepS · Answer

My solution:

|x+1|\geq{5}  and  |y-1|\leq{5}

{-5}\leq x+1\leq{5} ---->  {-5-1}\leq x \leq{5-1}  ---->  {-6}\leq x \leq{4}

{-5}\leq y-1\leq{5} ---->  {-5+1}\leq y \leq {5+1} ----->  {-4}\leq x \leq {6}

Thus, least value of xy is when x= -6 and y= 6----> -6*6= -36

LogicGuru1 · Answer

|x + 1|<= 5 ; x<=4 or x>= -6 |y - 1| <= 5 ; y<=6 or y>= -4 Take x=6 and y=-6 xy = -36 This is the smallest xy value given to us in the options ANSWER IS D

kanusha · Answer

Least xy = ?
Case 1:
x + 1  \leq{5} 
x  \leq{4} 
Case 2:
 -x-1 \leq{5} 
 -x \leq {6} 
 x\geq{-6}

Case 1:
 y-1 \leq{5} 
 y \leq 6 
Case 2:
 -y+1 \leq{5} 
 -y \leq{4} 
 y \geq{-4}

xy values are : 24,-16,-36,24
Least xy = -36
C

KanishkM · Answer

If |x + 1|<= 5 and |y - 1| <= 5

|x + 1|< 5 or |x + 1|= 5 (b)  and |y - 1| < 5 or |y - 1| = 5 (d)

Now from the answer options, least value of xy can be -36,

If i can get that i am good

when x = -6 in (b) and y = 6 in (d), i should be good

Or condition any one of the condition can be satisfied to use the equality

D

armaankumar · Answer

|x + 1|<= 5 ; |y - 1| <= 5 i) x + 1<= 5 ; y - 1 <= 5 x<= 4 ; y<= 6 ii) -x - 1<= 5 ; -y + 1 <= 5 x>= -6 ; y>= -4 -6<=x<=4 ; -4<=y<=6 Least possible value of x*y = -6*6= -36

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If |x + 1|<= 5 and |y - 1| <= 5, then which of the following is the le

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