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|a| is the distance point a is from the origin on the numbe

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Carcass
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|a| is the distance point a is from the origin on the numbe [#permalink] New post   12 Mar 2019, 10:38
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\(|a|\) is the distance point a is from the origin on the number line. \(x ≠ 0\).

Quantity A
Quantity B
\(|x| + |-2|\)
\(| x - 2 |\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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D
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GreenlightTestPrep
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|a| is the distance point a is from the origin on the numbe [#permalink] New post   12 Mar 2019, 13:51
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Carcass wrote:
\(|a|\) is the distance point a is from the origin on the number line. \(x ≠ 0\).

Quantity A
Quantity B
\(|x| + |-2|\)
\(| x - 2 |\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


Let's test some possible cases

case i: x = 1
We get:
QUANTITY A: |x| + |-2| = |1| + |-2| = 1 + 2 = 3
QUANTITY B: |x - 2| = |1 - 2| = |-1| = 1
In this case, Quantity A is greater


case ii: x = -1
We get:
QUANTITY A: |x| + |-2| = |-1| + |-2| = 1 + 2 = 3
QUANTITY B: |x - 2| = |-1 - 2| = |-3| = 3
In this case, the two quantities are equal

Answer: D

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saptadas1809
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Re: |a| is the distance point a is from the origin on the numbe [#permalink] New post   16 Dec 2021, 12:08
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Carcass wrote:
\(|a|\) is the distance point a is from the origin on the number line. \(x ≠ 0\).

Quantity A
Quantity B
\(|x| + |-2|\)
\(| x - 2 |\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


This is similar to the case of: |x| + |y| >= |x + y|
here assume y as -2, so quantity A can either be greater than or equal to B. So answer is option D
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AjinkyaGupta88
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Re: |a| is the distance point a is from the origin on the numbe [#permalink] New post   16 May 2022, 00:38
GreenlightTestPrep wrote:
Carcass wrote:
\(|a|\) is the distance point a is from the origin on the number line. \(x ≠ 0\).

Quantity A
Quantity B
\(|x| + |-2|\)
\(| x - 2 |\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


Let's test some possible cases

case i: x = 1
We get:
QUANTITY A: |x| + |-2| = |1| + |-2| = 1 + 2 = 3
QUANTITY B: |x - 2| = |1 - 2| = |-1| = 1
In this case, Quantity A is greater


case ii: x = -1
We get:
QUANTITY A: |x| + |-2| = |-1| + |-2| = 1 + 2 = 3
QUANTITY B: |x - 2| = |-1 - 2| = |-3| = 3
In this case, the two quantities are equal

Answer: D

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Re: |a| is the distance point a is from the origin on the numbe [#permalink]
16 May 2022, 00:38
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