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|
necessarily true
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- sanju09
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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.
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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a=-1
b=-2
D is correct
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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- vineetbatra
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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.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.
Let me know if I am missing any thing.
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i think you are absolutely rightvineetbatra wrote: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.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.
Let me know if I am missing any thing.
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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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
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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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....
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....