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

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

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New post Updated on: 21 Nov 2014, 09:37
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A
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C
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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


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

Originally posted by sunny3011 on 21 Nov 2014, 07:36.
Last edited by Bunuel on 21 Nov 2014, 09:37, edited 2 times in total.
Renamed the topic and edited the question.
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Re: If |x + 1|<= 5 and |y - 1| <= 5, then which of the following is the le  [#permalink]

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New post 21 Nov 2014, 09:37
1
6
sunny3011 wrote:
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


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


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

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

Answer: C.
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Re: If |x + 1|<= 5 and |y - 1| <= 5, then which of the following is the le  [#permalink]

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New post 21 Nov 2014, 09:41
Bunuel wrote:
sunny3011 wrote:
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


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


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

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

Answer: C.


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

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New post 21 Nov 2014, 10:00
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.
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Re: If |x + 1|<= 5 and |y - 1| <= 5, then which of the following is the le  [#permalink]

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New post 02 Jul 2016, 10:17
sunny3011 wrote:
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


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



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

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

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New post 24 Jul 2016, 23:35
sunny3011 wrote:
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


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


|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
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Re: If |x + 1|<= 5 and |y - 1| <= 5, then which of the following is the le  [#permalink]

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New post 06 Jan 2017, 12:40
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
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Re: If |x + 1|<= 5 and |y - 1| <= 5, then which of the following is the le  [#permalink]

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New post 28 Jan 2019, 07:48
sunny3011 wrote:
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



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
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Re: If |x + 1|<= 5 and |y - 1| <= 5, then which of the following is the le   [#permalink] 28 Jan 2019, 07:48
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