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Inequality

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by adi_800 » Sat Sep 04, 2010 9:23 am
If ax+b=0, is x>0?
1) a+b>0
2) a-b>0


ax = -b

1. a + b > 0
= a -ax > 0
= a(1-x) > 0
= a > 0 AND (1-x) > 0 OR a < 0 AND (1-x) < 0
= a > 0 AND 1 > x OR a < 0 AND 1 < x => x can be less than 1 or x is greater than 1....So can not answered..

2. a - b > 0
= a + ax > 0
= a(1+x) > 0
= a > 0 AND (1+x) > 0 OR a < 0 AND (1+x) < 0
= a > 0 AND x > -1 OR a < 0 AND x < -1 => x can be greater than -1 or x is less than -1...so can not be answered...

Is my work till this point fine?

N how to club the these two statements...
OA E
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Source: — Data Sufficiency |
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by Gurpinder » Sat Sep 04, 2010 9:30 am
your doing too much adi....

If ax+b=0, is x>0?

rephrase the question first
ax=-b
x=-b/a

1) a+b>0

a>-b
insuficient.

2) a-b>0
a>b
insufficient.

together:
insufficient.

hence (E)
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- Alfred A. Montapert, Philosopher.
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by selango » Sat Sep 04, 2010 9:41 am
adi_800 wrote:If ax+b=0, is x>0?
1) a+b>0
2) a-b>0


ax = -b

1. a + b > 0
= a -ax > 0
= a(1-x) > 0
= a > 0 AND (1-x) > 0 OR a < 0 AND (1-x) < 0
= a > 0 AND 1 > x OR a < 0 AND 1 < x => x can be less than 1 or x is greater than 1....So can not answered..

2. a - b > 0
= a + ax > 0
= a(1+x) > 0
= a > 0 AND (1+x) > 0 OR a < 0 AND (1+x) < 0
= a > 0 AND x > -1 OR a < 0 AND x < -1 => x can be greater than -1 or x is less than -1...so can not be answered...

Is my work till this point fine?

N how to club the these two statements...
OA E
adi ur steps are fine.

a-ax>0-->Eqn1

a+ax>0-->Eqn2

Eqn1+Eqn2 gives a>0

Eqn1-->1-x>0 or x<1

Eqn2-->1+x>0 or x>-1

-1>x<1

X can be -0.5 or 0.5

We don't know value of x.Insufficient
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by arora007 » Sat Sep 04, 2010 11:44 am
adi_800 wrote:If ax+b=0, is x>0?
1) a+b>0
2) a-b>0


ax = -b

1. a + b > 0
= a -ax > 0
= a(1-x) > 0
= a > 0 AND (1-x) > 0 OR a < 0 AND (1-x) < 0
= a > 0 AND 1 > x OR a < 0 AND 1 < x => x can be less than 1 or x is greater than 1....So can not answered..

2. a - b > 0
= a + ax > 0
= a(1+x) > 0
= a > 0 AND (1+x) > 0 OR a < 0 AND (1+x) < 0
= a > 0 AND x > -1 OR a < 0 AND x < -1 => x can be greater than -1 or x is less than -1...so can not be answered...

Is my work till this point fine?

N how to club the these two statements...
OA E
your steps are fine... Plugging in values, and u will see that the values can neither be A nor be B, it a C or E question.
now when you want to combine in equalities, add them up...

a+b>0 ADDED TO a-b>0
gives 2a >0 which means a>0

now assume values a=1 , case 1) then b could be 1, 10 , 0.1, -0.1
for which x would be -1, -10, -0.1 or 0.1
thus does not suffice!
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