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# For any numbers a and b, a * b=a+b-ab If a*b=0, which of

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Manager
Joined: 02 Oct 2007
Posts: 112
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For any numbers a and b, a * b=a+b-ab If a*b=0, which of [#permalink]  15 Oct 2007, 18:24
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For any numbers a and b, a * b=a+b-ab
If a*b=0, which of the following cannot be a value of b?

A 2
B 1
C 0
D -1
E -3/2

Also, how would this be simplified

((sqt(3/2)) * ((sqt(2))/2)/2

sqt=square root
Director
Joined: 03 May 2007
Posts: 894
Schools: University of Chicago, Wharton School
Followers: 6

Kudos [?]: 63 [0], given: 7

Re: PS [#permalink]  15 Oct 2007, 18:51
JDMBA wrote:
For any numbers a and b, a * b=a+b-ab
If a*b=0, which of the following cannot be a value of b?

A 2
B 1
C 0
D -1
E -3/2

C. should be 0. if either x or y is 0, a*b cannot be 0.
Director
Joined: 03 May 2007
Posts: 894
Schools: University of Chicago, Wharton School
Followers: 6

Kudos [?]: 63 [0], given: 7

Re: PS [#permalink]  15 Oct 2007, 18:56
JDMBA wrote:
Also, how would this be simplified

((sqt(3/2)) * ((sqt(2))/2)/2

sqt=square root

this how i understand the expression:

= [{sqt (3/2)} * {sqt(2)}/2] / 2
= sqt (3) / 4
VP
Joined: 09 Jul 2007
Posts: 1108
Location: London
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Kudos [?]: 74 [0], given: 0

Re: PS [#permalink]  15 Oct 2007, 19:24
For any numbers a and b, a * b=a+b-ab
If a*b=0, which of the following cannot be a value of b?

A 2
B 1
C 0
D -1
E -3/2

a+b-ab=0
a(1-b)=-b
a=-b/(1-b)
so b should not be equal to 1

B

Also, how would this be simplified

((sqt(3/2)) * ((sqt(2))/2)/2

(sqrt3)/4
Manager
Joined: 02 Oct 2007
Posts: 112
Followers: 1

Kudos [?]: 1 [0], given: 0

The answer is B - 1

How did you come about to sqt(3)/4?
SVP
Joined: 01 May 2006
Posts: 1805
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Kudos [?]: 98 [0], given: 0

((sqt(3/2)) * ((sqt(2))/2)/2
= sqrt(3)/sqrt(2) * sqrt(2)/2 * 1/2
= sqrt(3)/4

SVP
Joined: 01 May 2006
Posts: 1805
Followers: 8

Kudos [?]: 98 [0], given: 0

(B) for me too

a * b=a+b-ab = 0 (1)

A) b=2
(1) <=> a + 2 - 2a = 0
<=> a = 2..... It works

B) b=1
(1) <=> a + 1 - a = 0
<=> 1 = 0..... Bingo... It doesn't work !

We could stop here.... But we could continue to verify...

C) b=0
(1) <=> a + 0 - a*0 = 0
<=> a = 0..... It works

D) b=-1
(1) <=> a - 1 + a = 0
<=> a = 1/2..... It works

E) b=-3/2
(1) <=> a - 3/2 + 3*a/2 = 0
<=> a = 3/5..... It works
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