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If |a| > |b|, which of the following must be true?

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Re: If |a| > |b|, which of the following must be true? [#permalink]
hello MBAhereIcome,

Do consider posting in PS Section ( gmat-problem-solving-ps-140/ ) as this is dedicated for DS questions.

Regards
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Re: If |a| > |b|, which of the following must be true? [#permalink]
1
Kudos
A good way to think of this is that a is much further away from zero than b is. a is much "stronger" thanb is. With that you can deduce option 2 as true.

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Re: If |a| > |b|, which of the following must be true? [#permalink]
|a| > |b|

1. ab>0

need not be true . when a>0,b<0 ab<0

2. |a|+b >0

Must be true.

when a , b are of same sign , |a|+b>0

when a is +ve, b is -ve , |a|+b>0 as |a|>|b|

when a is -ve, b is +ve, |a|+b>0

when a is -ve, b is -ve , |a|+b>0 as |a|>|b|

3. a+|b|>0

Need not be true. when a<0,b>0 and |a|>|b|, a+|b|<0

4. |b|/a >0

Need not be true. when a<0,b>0 and |a|>|b|, |b|/a<0

5. |a|b>0

Need not be true. when b<0 ,|a|b<0

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Re: If |a| > |b|, which of the following must be true? [#permalink]
Hello. I dont quite get this question.

1. for |a| we have 2 options ... a or -a
2. for |b| we have 2 options ... b or -b

Option A says ab>0

so if we do a x b ... this will always be >0

a x -b <0,but that is not the same as a x b

he is asking specifically for a x b

Option B says |a| + b>0

this wd mean a + b .... which wd be >0
or
-a + b .... which wd be <0

am i reading the question wrong??
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Re: If |a| > |b|, which of the following must be true? [#permalink]
Mansoor50 wrote:
Hello. I dont quite get this question.

1. for |a| we have 2 options ... a or -a
2. for |b| we have 2 options ... b or -b

Option A says ab>0

so if we do a x b ... this will always be >0

a x -b <0,but that is not the same as a x b

he is asking specifically for a x b

Option B says |a| + b>0

this wd mean a + b .... which wd be >0
or
-a + b .... which wd be <0

am i reading the question wrong??

Hi Mansoor,

Bunuel has given you a comprehensive solution.

Another approach is to consider 2 different positive integers (absolute values). Now option B is saying add either the negative or positive value of the smaller number to the bigger and the result is positive. This is going to always be true, hence the question is answered. Take 2 and 5 for example, 5+2 and 5-2 are always going to be positive i.e greater than 0.

Best,
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Re: If |a| > |b|, which of the following must be true? [#permalink]
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$$|a| > |b|$$

A. $$ab > 0$$

Not true when one of the numbers is NEGATIVE (Take $$x = -4$$ & $$y = 3$$)

B. $$|a| + b > 0$$

TRUE for all values (Take $$x = -4$$ &$$y = 3$$ or $$x = 4$$ & $$y = -2$$ or $$x = -4$$& $$y -3$$)

C. $$a + |b| > 0$$

Not true when when a is NEGATIVE and b is positive (Take $$x = -4$$ & $$y = 3$$)

D. $$\frac{|b|}{a} > 0$$

Not true when when a is NEGATIVE (Take $$x = -4$$ & $$y = 3$$)

E. $$|a|*b > 0$$

Not true when when b is NEGATIVE (Take $$x = 4$$ & $$y = -3$$)

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Re: If |a| > |b|, which of the following must be true? [#permalink]
Thank you all for your replies. And yes, I understand what you are saying.

I realized the mistake i was making: when it wrote ab>0, i assumed that he meant the case when |a|=a ... i thought he wd write -a if |a|=-a.

Whereas in actuality, his references to a or b simply mean whatever the case maybe , ie. 'a' could be +a or -a.

Thanks Everyone!!!!!
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Re: If |a| > |b|, which of the following must be true? [#permalink]
2
Kudos
MBAhereIcome wrote:
If $$|a| > |b|$$, which of the following must be true?

A. $$ab > 0$$

B. $$|a| + b > 0$$

C. $$a + |b| > 0$$

D. $$\frac{|b|}{a} > 0$$

E. $$|a|*b > 0$$

Show SpoilerSolution
|a|>|b| so a is a bigger number than b, regardless of their signs. e.g. a=5, b=-2 OR a=-8, b=7.

a) not true if b<0 & a>0
b) TRUE. e.g.|5|-4>0 OR |-8|+7>0
c) incorrect if a<0. the sum will always be negative in this case
d) not true if a<0
e) not true if b<0

Refer to the attached file
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WhatsApp Image 2017-06-25 at 9.53.09 PM.jpeg [ 39.94 KiB | Viewed 25310 times ]

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Re: If |a| > |b|, which of the following must be true? [#permalink]
1
Kudos
Not a very foul-proof approach, but definitely time-saving.

I picked two random integers, namely a=-3 and b=2 and checked the answer choices.

Then when I noticed B to be most likely correct, I picked some other numbers and the answer still stand.
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Re: If |a| > |b|, which of the following must be true? [#permalink]
If |a|>|b|, which of the following must be true?

A. ab>0
-a and b can have different signs and this would be violated

B. |a|+b>0 CORRECT

C. a+|b|>0
-a can be negative and this would be violated

D. |b|/a>0
-a can be negative here

E. |a|∗b>0
-b can be negative
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If |a| > |b|, which of the following must be true? [#permalink]
baldururikson wrote:
Not a very foul-proof approach, but definitely time-saving.

I picked two random integers, namely a=-3 and b=2 and checked the answer choices.

Then when I noticed B to be most likely correct, I picked some other numbers and the answer still stand.

baldururikson, picking numbers might not be the best approach for a must be true question. Definitely works efficiently for a could be true question.
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Re: If |a| > |b|, which of the following must be true? [#permalink]
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Re: If |a| > |b|, which of the following must be true? [#permalink]
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