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# if |a|>|b|, which of the following must be true? a) ab

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if |a|>|b|, which of the following must be true? a) ab [#permalink]  30 Aug 2011, 02:32
00:00

Difficulty:

25% (medium)

Question Stats:

58% (01:47) correct 42% (00:33) wrong based on 60 sessions
if |a|>|b|, which of the following must be true?

a) ab > 0
b) |a|+b > 0
c) a+|b| > 0
d) |b|/a > 0
e) |a|*b > 0

[Reveal] 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
[Reveal] Spoiler: OA

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Re: absolute - must be true [#permalink]  30 Aug 2011, 03:07
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

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Re: absolute - must be true [#permalink]  30 Aug 2011, 03:12
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: absolute - must be true [#permalink]  30 Aug 2011, 10:52
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: absolute - must be true [#permalink]  30 Aug 2011, 16:38
|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

Re: absolute - must be true   [#permalink] 30 Aug 2011, 16:38
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