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necessarily true

by sanju09 » Tue May 04, 2010 4:56 am
If |a| < |b|, and a > b, which of the following is necessarily true?

A. |a + b| > |b| + |a|

B. |a + b| < a - b

C. |a| + |b| > 2|b|

D. |a - b| > a + b

E. |a| - |b| > |a - b|
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by truplayer256 » Tue May 04, 2010 6:47 am
From the statement given that |a|<|b| and a>b, we automatically know that a and b must be negative numbers.

Let's say a=-4 and b=-5

Choice A: |-9| > 4 + 5. Not right

Choice B: |-9| < 1. Not right

Choice C: 9 > 10. Nope

Choice D: 1 > -9. This works.

Choice E: -1 > 1 No.

Option D is the best choice.
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by outreach » Tue May 04, 2010 7:06 am
a=-1
b=-2

D is correct
sanju09 wrote:If |a| < |b|, and a > b, which of the following is necessarily true?

A. |a + b| > |b| + |a|

B. |a + b| < a - b

C. |a| + |b| > 2|b|

D. |a - b| > a + b

E. |a| - |b| > |a - b|
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by tryingtocrack » Tue May 04, 2010 7:07 am
IMO - D

For |a| < |b|, and a > b to be true , both should be - ve
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by vineetbatra » Tue May 04, 2010 8:03 am
truplayer256 wrote:From the statement given that |a|<|b| and a>b, we automatically know that a and b must be negative numbers.



Option D is the best choice.
You said both A and B have to negative, but A can be 3 and B can be -4; however D is still the answer, but A can be positive.

Let me know if I am missing any thing.
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by clock60 » Tue May 04, 2010 1:34 pm
vineetbatra wrote:
truplayer256 wrote:From the statement given that |a|<|b| and a>b, we automatically know that a and b must be negative numbers.



Option D is the best choice.
You said both A and B have to negative, but A can be 3 and B can be -4; however D is still the answer, but A can be positive.

Let me know if I am missing any thing.
i think you are absolutely right
only b must be -ve, but a can be -ve, or +ve
the given inequality will be valid for
(a-b)>0 and (a+b)<0
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by debmalya_dutta » Tue May 04, 2010 2:20 pm
A. |a + b| > |b| + |a| can also be equal when a, b are positive and hence not necessarily true

B. |a + b| < a - b - >not necessarily true when a & b positive

C. |a| + |b| > 2|b| not necessarily true. this basically becomes |a|>|b| which is not necessarily true

D. |a - b| > a + b not true when a & b are positive

E. |a| - |b| > |a - b|can be equal too . Hence not necessarily true

Hence , none of these are true
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by frank1 » Tue May 04, 2010 8:31 pm
well,lots of shorter ways appears if you ponder over the same question for half an hour ...

but when i looked at it and tried to solve it at first glance ,
i took -2 and -3 and tested....
and it took me almost 3 miniutes

one wrong thing was i should have started testing from C rather than testing from A,B,C....
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