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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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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 am; Thanked: 1 times; Followed by:5 members

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

by M7MBA » Sun Feb 11, 2018 3:38 am

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

The OA is the option B.

Experts, how can I get an answer here? Should I try option by option? Could you give me some help, please? Thanks in advanced.

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Source: Beat The GMAT — Problem Solving | Sun Feb 11, 2018 3:38 am

regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

by regor60 » Mon Feb 12, 2018 9:12 am

M7MBA 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

The OA is the option B.

Experts, how can I get an answer here? Should I try option by option? Could you give me some help, please? Thanks in advanced.

a#b= 0 means that a +b -ab = 0 also.

Which means that a+b=ab

Test the answers. Can b=2 ? Substitute 2 for b

a+2=2a works if a=2 so yes it's possible

Can b=1 ?

a+1=a > only possible if 1=0, which isn't true, therefore 1, B

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Tue Feb 13, 2018 5:34 pm

M7MBA 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

We are given that a#b=a + b - ab and that a#b=0. Thus we have

a + b - ab = 0

a + b = ab

Now let's look at the choices:

A. If b = 2, then

a + 2 = a(2)

2 = a

So b can be 2.

B. If b = 1, then

a + 1 = a(1)

We see that a + 1 (1 more than a) can't be equal to a itself. So b CANNOT be 1, and that is the number we are looking for.

Alternate Solution:

We are given that a#b=a + b - ab and that a#b=0. Thus we have

a + b - ab = 0

a + b = ab

b = ab - a

b = a(b - 1)

We observe here that for any value of b other than 1, we can divide each side of the equality by b - 1 and express a as b/(b - 1). Thus, the only value that b cannot assume is 1.

Answer: B

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