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Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If |x + 1|<= 5 and |y - 1| <= 5, then which of the following is the le

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Intern  Joined: 06 Dec 2012
Posts: 23
Concentration: Finance, International Business
GMAT 1: 510 Q46 V21 GPA: 3.5
If |x + 1|<= 5 and |y - 1| <= 5, then which of the following is the le  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 70% (01:37) correct 30% (01:43) wrong based on 998 sessions

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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.
Math Expert V
Joined: 02 Sep 2009
Posts: 58434
Re: If |x + 1|<= 5 and |y - 1| <= 5, then which of the following is the le  [#permalink]

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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.

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Math Expert V
Joined: 02 Sep 2009
Posts: 58434
Re: If |x + 1|<= 5 and |y - 1| <= 5, then which of the following is the le  [#permalink]

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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.

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Manager  Joined: 11 May 2013
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Concentration: Finance, Strategy
GMAT 1: 710 Q48 V39 GPA: 3.94
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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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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.
SVP  V
Status: It's near - I can see.
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Posts: 1687
Location: India
Concentration: International Business, Operations
Schools: INSEAD Jan '19
GPA: 3.01
WE: Engineering (Real Estate)
Re: If |x + 1|<= 5 and |y - 1| <= 5, then which of the following is the le  [#permalink]

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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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Director  B
Joined: 04 Jun 2016
Posts: 556
GMAT 1: 750 Q49 V43 If |x + 1|<= 5 and |y - 1| <= 5, then which of the following is the le  [#permalink]

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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

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Manager  S
Joined: 25 Mar 2013
Posts: 226
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5
Re: If |x + 1|<= 5 and |y - 1| <= 5, then which of the following is the le  [#permalink]

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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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Joined: 09 Mar 2018
Posts: 994
Location: India
Re: If |x + 1|<= 5 and |y - 1| <= 5, then which of the following is the le  [#permalink]

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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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Many of life's failures happen with people who do not realize how close they were to success when they gave up. 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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