a&b

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shibal: Master | Next Rank: 500 Posts; Posts: 345; Joined: Wed Mar 18, 2009 6:53 pm; Location: Sao Paulo-Brazil; Thanked: 12 times; GMAT Score:660

by shibal » Fri May 01, 2009 11:13 am

for any number 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

OA: B

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Source: Beat The GMAT — Problem Solving | Fri May 01, 2009 11:13 am

dmateer25: Community Manager; Posts: 1049; Joined: Sun Apr 06, 2008 5:15 pmFollowed by: 27 members; Location: Pittsburgh, PA; Thanked: 113 times; GMAT Score:710

by dmateer25 » Fri May 01, 2009 11:25 am

0 = a + b – ab

ab = a + b

Now just plug in.

a) 2
2a = a + 2
a= 2

This works

b)1

a = a + 1
0 = 1

Doesn’t work
This has to be the answer.

c) 0

0 = a + 0
a = 0

This Works

d) -1

-a = a – 1
-2a = -1
a = 1/2

This Works

e) -3/2

-3a/2 = a – 3/2
-3a = 2a – 3
-5a = -3
a = 3/5

This works

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maihuna: Legendary Member; Posts: 1578; Joined: Sun Dec 28, 2008 1:49 amFollowed by: 9 members; Thanked: 82 times; GMAT Score:720

by maihuna » Fri May 01, 2009 11:30 am

there is an easy way out: as a&b = 0
a + b -ab = 0
=>a(b-1) = b
=> a = b/(b-1)

If b = 1 a will be INFINITY so b cant be 1

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