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# Is ab = 1? (1) aba = a (2) bab = b

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Director
Joined: 03 Jul 2003
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Is ab = 1? (1) aba = a (2) bab = b [#permalink]

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13 Dec 2003, 21:47
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Is ab = 1?

(1) aba = a
(2) bab = b

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Director
Joined: 14 Oct 2003
Posts: 583

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Location: On Vacation at My Crawford, Texas Ranch

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13 Dec 2003, 22:51
Trick question

ab=a does not necessarily mean ab=1 if ab=0 then aba=a also holds true

bab=b same priniciple holds true

both tell us nothing

E

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Director
Joined: 13 Nov 2003
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Location: Florida

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13 Dec 2003, 23:36
Titleist wrote:
Trick question

ab=a does not necessarily mean ab=1 if ab=0 then aba=a also holds true

bab=b same priniciple holds true

both tell us nothing

E

ab=0 means b=0 (aba/a=1, a can't be zero).
when b=0, aba can't be equal to a.
same holds true for B.

I think, it should be D. or, m I thinking too much

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Director
Joined: 14 Oct 2003
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Location: On Vacation at My Crawford, Texas Ranch

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13 Dec 2003, 23:42
a and b can both equal zero? a=0 b=0 ab=0 or aba=a

the question stem never mentions that a is not equal to b.

maybe i'm thinking too much at 1:45 in the morning too!

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Manager
Joined: 12 Oct 2003
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14 Dec 2003, 07:04
E

1.
a = 0; b = 0 ==> aba = a
a = 1; b = 1 ==> aba = a

2.
a = 0; b = 0 ==> bab = b
a = 1; b = 1 ==> bab = b

both combined ; still it holds true that a = b = 0 or a = b = 1

nothing sufficient to claim that ab = 1

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CEO
Joined: 15 Aug 2003
Posts: 3454

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14 Dec 2003, 07:28
ok..i think i should explain.

from (1)

aba - a = 0

(ab -1 ) a = 0

ab = 1 OR a =0

Not sufficient..cant say for sure...as a = 0 gives the same solution.

from (2)

bab - b =0

b ( ab-1) = 0

b = 0 or ab = 1

not sufficient , cant say...as b =0 gives the same solution

Combine A and B , sufficient.

we can say yes, ab = 1.

anything wrong?

thanks
praetorian

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Director
Joined: 03 Jul 2003
Posts: 651

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16 Dec 2003, 13:25
praetorian123 wrote:
ok..i think i should explain.

from (1)

aba - a = 0

(ab -1 ) a = 0

ab = 1 OR a =0

Not sufficient..cant say for sure...as a = 0 gives the same solution.

from (2)

bab - b =0

b ( ab-1) = 0

b = 0 or ab = 1

not sufficient , cant say...as b =0 gives the same solution

Combine A and B , sufficient.

we can say yes, ab = 1.

anything wrong?

thanks
praetorian

praetorian123

I've also solved this problem the similar way as you've.
But the official answer is E.

Any experts want to help us with why this method is not working
for this problem?

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Director
Joined: 28 Oct 2003
Posts: 501

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Location: 55405

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16 Dec 2003, 13:33
from 1)
ab = 1 OR a =0

from 2)
ab = 1 OR b =0

You can't combine these statements to come up with ab=1, because nothing in either statement disproves the zero hypotheses.

so ab is either 1 or zero.

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Director
Joined: 14 Oct 2003
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Location: On Vacation at My Crawford, Texas Ranch

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16 Dec 2003, 14:45
kpadma, I think pitts2004 and stoolfi have the best explanation!

Last edited by Titleist on 17 Dec 2003, 11:19, edited 1 time in total.

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Manager
Joined: 26 Aug 2003
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17 Dec 2003, 06:45
stoolfi wrote:
from 1)
ab = 1 OR a =0

from 2)
ab = 1 OR b =0

You can't combine these statements to come up with ab=1, because nothing in either statement disproves the zero hypotheses.

so ab is either 1 or zero.

Good explanation... Right on target!

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CEO
Joined: 15 Aug 2003
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17 Dec 2003, 07:04
stoolfi wrote:
from 1)
ab = 1 OR a =0

from 2)
ab = 1 OR b =0

You can't combine these statements to come up with ab=1, because nothing in either statement disproves the zero hypotheses.

so ab is either 1 or zero.

i see.

so if it was
1. ab = 1 or a=0
2. ab =1 or a =1

then C would be the right answer?

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Director
Joined: 28 Oct 2003
Posts: 501

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Location: 55405

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17 Dec 2003, 07:23
Quote:
so if it was
1. ab = 1 or a=0
2. ab =1 or a =1

then C would be the right answer?

I think so, Praetorian...

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17 Dec 2003, 07:23
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