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If B + A < B - A < A - B, which of the following is correct?

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If B + A < B - A < A - B, which of the following is correct? [#permalink]

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New post 07 Jul 2016, 06:02
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Re: If B + A < B - A < A - B, which of the following is correct? [#permalink]

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New post 07 Jul 2016, 08:01
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Bunuel wrote:
If B + A < B - A < A - B, which of the following is correct?

A. A<B<0.
B. B<A<0.
C. B<0<A.
D. 0<B<A.
E. B>A>0.

Check first inequality
B + A < B - A
A<-A
A is -ve
Check another equality
B - A < A - B
-2A<-2B
A>B
Combining both 0>A>B
Option B fits only

Ans B

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Re: If B + A < B - A < A - B, which of the following is correct? [#permalink]

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New post 08 Jul 2016, 10:28
Bunuel wrote:
If B + A < B - A < A - B, which of the following is correct?

A. A<B<0.
B. B<A<0.
C. B<0<A.
D. 0<B<A.
E. B>A>0.


B + A < B - A < A - B

Subtract B from all sides of equations

A<-A<A-2B

A<-A can only be possible when A is -ve

So A<0. Only options A and B are contenders now.

-A<A-2B
-2A<-2B
A>B

Hence B<A<0
B is the correct option
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Re: If B + A < B - A < A - B, which of the following is correct? [#permalink]

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New post 12 Aug 2017, 06:46
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Re: If B + A < B - A < A - B, which of the following is correct? [#permalink]

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New post 12 Aug 2017, 08:13
Bunuel wrote:
If B + A < B - A < A - B, which of the following is correct?

A. A<B<0.
B. B<A<0.
C. B<0<A.
D. 0<B<A.
E. B>A>0.



Since A-B is greatest and A+B is smallest. it clearly shows that B is -ve
Two possibilities A >0 or A<0
Case 1 : A>0
B-A<A+B<A-B
(-3)-5<5+(-3) <5-(-3)

Case 2: A<0 : Two cases A<B, B<A
Case 2a: B<A
A+B<B-A<A-B
(-3)+(-5) <(-5)-(-3)<(-3)-(-5)


Case 2b : A<B
A+B<A-B<B-A
(-5)+(-3)<(-5)-(-3)<(-3)-(-5)

So, B<A<0


Answer B
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Re: If B + A < B - A < A - B, which of the following is correct? [#permalink]

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New post 12 Aug 2017, 09:35
B + A < B - A < A - B

Split to 2 equations :
(i) B+A<B-A = 2A < 0 ; A < 0
(ii) B-A<A-B = 2B < 2A ; B < A

Hence, B < A < 0
Please let me know if this method works too!

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Re: If B + A < B - A < A - B, which of the following is correct?   [#permalink] 12 Aug 2017, 09:35
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