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Carcass
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ab<0 [#permalink] New post   16 Feb 2021, 04:59
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\(ab<0\)

Quantity A
Quantity B
\(|a+b|\)
\(|a|+|b|\)



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

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Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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B
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ab<0 [#permalink] New post   16 Feb 2021, 08:01
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Carcass wrote:
\(ab<0\)

Quantity A
Quantity B
\(|a+b|\)
\(|a|+|b|\)




In general, we can say:

If \(ab<0\), then \(|a+b| < |a|+|b|\)
If \(ab>0\), then \(|a+b| = |a|+|b|\)

Answer: B
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Re: ab<0 [#permalink] New post   16 Feb 2021, 07:30
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Hi,

ab<0
Thus, either a or b could be negative and the other has to be positive both of them cannot be positive or negative or zero.

Quantity A: |a+b|--> If a=1 & b=-2=|1+(-2)|=1
Quantity B: |a|+|b|-->If a=1 & b=-2=|1|+|-2|=3

You can try other numbers A<B

IMO B
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Re: ab<0 [#permalink] New post   16 Feb 2021, 07:44
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ab < 0 means, a and b have different sign. if a is positive, then b is negative or a is negative while b is positive.

For Qnt A = | a + b|, there will be a difference just because of different signs.
And, Qnt B = | a | + | b |, the will be no difference, both numbers will add up.

So, the Answer is B.
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Re: ab<0 [#permalink]
16 Feb 2021, 07:44
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