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

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Manager
Status: mba here i come!
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If |a| > |b|, which of the following must be true?  [#permalink]

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Updated on: 24 Jun 2017, 14:35
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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. $$|a|*b > 0$$

Spoiler: :: Solution
|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

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Originally posted by MBAhereIcome on 30 Aug 2011, 03:32.
Last edited by Bunuel on 24 Jun 2017, 14:35, edited 3 times in total.
Renamed the topic and edited the question.
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Re: If |a| > |b|, which of the following must be true?  [#permalink]

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30 Aug 2011, 04:07
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2
Hello,

lets take each one given |a| > |b|

a) ab > 0

Not allways . If a,b are both negative then true, either positive then fails.

b) |a|+b > 0

Since we know that absolute value of a is greater than absolute value of b , we can for sure say that |a| > b

The above would fail only if |a| = |b| or |b| > |a| so B is the answer because -- given |a| > |b|

c) a+|b| > 0

Not always consider a = -7 and b = -5 (given |a| > |b|)

-7 + 5 = -2 <0 hence not possible ;

d) |b|/a > 0

not always if a is positive then true, if a is negative then false because for all values of {b} except zero |B| is always positive

e) |a|*b > 0

not always if b is positive then true, if b is negative then false because for all values of {a} except zero |a| is always positive

Hope my explanation was helpful. OA is B

Regards
Raghav.V

Consider Kudos if you think my explanation was helpful
##### General Discussion
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Re: If |a| > |b|, which of the following must be true?  [#permalink]

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30 Aug 2011, 04:12
hello MBAhereIcome,

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

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

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30 Aug 2011, 11:52
1
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]

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30 Aug 2011, 17:38
|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]

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24 Jun 2017, 14:12
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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If |a| > |b|, which of the following must be true?  [#permalink]

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24 Jun 2017, 14:29
1
2
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??

$$|a| = a$$, when $$a \geq 0$$ and $$|a| = -a$$, when $$a\leq 0$$. You cannot simply plug a or -a if you don't know which case you have.

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

$$|a| > |b|$$ means that a is further from 0 than b is. So, we can have one of the following 4 cases:

1. ----a----b----0---------------
2. ----a---------0----b----------
3. ---------b----0---------a-----
4. --------------0----b----a-----

A. $$ab > 0$$ --> Not true for cases in which a and b have different signs (cases 2 and 3). Discard.

B. $$|a| + b > 0$$ --> true for all cases.

C. $$a + |b| > 0$$ --> not true for cases in which a is negative (cases 1 and 2). Discard.

D. $$\frac{|b|}{a} > 0$$ --> not true for cases in which a is negative (cases 1 and 2). Discard.

E. $$|a|*b > 0$$ --> not true for cases in which b is negative (cases 1 and 3). Discard.

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

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24 Jun 2017, 14:49
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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24 Jun 2017, 14:52
$$|a| > |b|$$

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]

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25 Jun 2017, 01:16
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]

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25 Jun 2017, 10:55
1
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. $$|a|*b > 0$$

Spoiler: :: Solution
|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 5858 times ]

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

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23 Mar 2019, 00:15
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] 23 Mar 2019, 00:15
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