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6≤|x|≤8 1≤|y|≤2 3≤|z|≤4 If x, y, and z satisfy the ine

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alamin
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6≤|x|≤8 1≤|y|≤2 3≤|z|≤4 If x, y, and z satisfy the ine [#permalink] New post   27 Mar 2019, 08:57
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6 ≤ |x| ≤ 8

1 ≤ |y| ≤ 2

3 ≤ |z| ≤ 4

If x, y, and z satisfy the inequalities shown, what is the least possible value of |x+y+z |?

A. 0
B. 1
C. 2
D. 3
E. 4
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GreenlightTestPrep
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Re: 6≤|x|≤8 1≤|y|≤2 3≤|z|≤4 If x, y, and z satisfy the ine [#permalink] New post   27 Mar 2019, 12:30
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alamin wrote:
6 ≤ |x| ≤ 8

1 ≤ |y| ≤ 2

3 ≤ |z| ≤ 4

If x, y, and z satisfy the inequalities shown, what is the least possible value of |x+y+z |?
A. 0
B. 1
C. 2
D. 3
E. 4


If 6 ≤ |x| ≤ 8 , then EITHER 6 ≤ x ≤ 8 OR -8 ≤ x ≤ -6
If 1 ≤ |y| ≤ 2 , then EITHER 1 ≤ y ≤ 2 OR -2 ≤ y ≤ -1
If 3 ≤ |x| ≤ 4 , then EITHER 3 ≤ z ≤ 4 OR -4 ≤ z ≤ -3

What is the least possible value of |x + y + z|?
If x = -6, y = 2 and z = 4, then |x + y + z| = |(-6) + 2 + 4| = 0

Since 0 is the smallest answer choice, the correct answer must be A

Cheers,
Brent
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Title information 6≤|x|≤8 1≤|y|≤2 3≤|z|≤4 [#permalink] New post   08 Feb 2020, 08:53
\(6≤|x|≤8\)

\(1≤|y|≤2\)

\(3≤|z|≤4\)

If x, y, and z satisfy the inequalities shown, what is the least possible value of \(|x+y+z|\) ?

A. 0

B. 1

C. 2

D. 3

E. 4
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Re: 6≤|x|≤8 1≤|y|≤2 3≤|z|≤4 If x, y, and z satisfy the ine [#permalink] New post   08 Feb 2020, 10:25
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Re: 6≤|x|≤8 1≤|y|≤2 3≤|z|≤4 If x, y, and z satisfy the ine [#permalink] New post   21 May 2021, 19:18
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GreenlightTestPrep wrote:
alamin wrote:
6 ≤ |x| ≤ 8

1 ≤ |y| ≤ 2

3 ≤ |z| ≤ 4

If x, y, and z satisfy the inequalities shown, what is the least possible value of |x+y+z |?
A. 0
B. 1
C. 2
D. 3
E. 4


If 6 ≤ |x| ≤ 8 , then EITHER 6 ≤ x ≤ 8 OR -8 ≤ x ≤ -6
If 1 ≤ |y| ≤ 2 , then EITHER 1 ≤ y ≤ 2 OR -2 ≤ y ≤ -1
If 3 ≤ |x| ≤ 4 , then EITHER 3 ≤ z ≤ 4 OR -4 ≤ z ≤ -3

What is the least possible value of |x + y + z|?
If x = -6, y = 2 and z = 4, then |x + y + z| = |(-6) + 2 + 4| = 0

Since 0 is the smallest answer choice, the correct answer must be A

Cheers,
Brent


I didnot understand why you flip the sign in ''EITHER 6 ≤ x ≤ 8 OR -8 ≤ x ≤ -6'' part.
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Re: 6≤|x|≤8 1≤|y|≤2 3≤|z|≤4 If x, y, and z satisfy the ine [#permalink] New post   22 May 2021, 00:18
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Hey,

We need to find the least value. And it is |x+y+z| so will always be > \(0\) so \(0\) ideally would be the Least value.

\(6 ≤ |x| ≤ 8\) - This means that \(x\), when +ve, can be between \(6\) and \(8\) & when -ve , can be between \(-8\) and \(-6\)

Please ask if the doubt remains.

kumarneupane4344 wrote:
GreenlightTestPrep wrote:
alamin wrote:
6 ≤ |x| ≤ 8

1 ≤ |y| ≤ 2

3 ≤ |z| ≤ 4

If x, y, and z satisfy the inequalities shown, what is the least possible value of |x+y+z |?
A. 0
B. 1
C. 2
D. 3
E. 4


If 6 ≤ |x| ≤ 8 , then EITHER 6 ≤ x ≤ 8 OR -8 ≤ x ≤ -6
If 1 ≤ |y| ≤ 2 , then EITHER 1 ≤ y ≤ 2 OR -2 ≤ y ≤ -1
If 3 ≤ |x| ≤ 4 , then EITHER 3 ≤ z ≤ 4 OR -4 ≤ z ≤ -3

What is the least possible value of |x + y + z|?
If x = -6, y = 2 and z = 4, then |x + y + z| = |(-6) + 2 + 4| = 0

Since 0 is the smallest answer choice, the correct answer must be A

Cheers,
Brent


I didnot understand why you flip the sign in ''EITHER 6 ≤ x ≤ 8 OR -8 ≤ x ≤ -6'' part.
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Re: 6≤|x|≤8 1≤|y|≤2 3≤|z|≤4 If x, y, and z satisfy the ine [#permalink] New post   22 May 2021, 00:27
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rx10 Gotcha :heart . :blushing: :blushing: You have great style of teaching. Very much appreciated.
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Re: 6|x|8 1|y|2 3|z|4 If x, y, and z satisfy the ine [#permalink] New post   04 Aug 2022, 08:27
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: 6|x|8 1|y|2 3|z|4 If x, y, and z satisfy the ine [#permalink]
04 Aug 2022, 08:27
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