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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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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Sun Jun 09, 2019 4:39 am

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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

OA B

Source: GMAT Prep

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Source: Beat The GMAT — Problem Solving | Sun Jun 09, 2019 4:39 am

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Sun Jun 09, 2019 10:59 pm

BTGmoderatorDC 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

OA B

Source: GMAT Prep

We have a#b = a + b - ab = 0

From a + b - ab = 0, we have a = 1/(b - 1)

Since if b = 1, the value of a would be indeterminable, we have b â‰ 1.

The correct answer: B

Hope this helps!

-Jay
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8151; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Tue Jun 11, 2019 7:16 pm

BTGmoderatorDC 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

OA B

Source: GMAT Prep

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 b = 1 results in the inconsistent result of 1 = 0. Thus, the only value that b cannot assume is 1.

Answer: B

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