# Another SAT Question

• August 13th 2011, 03:17 PM
RK29
Another SAT Question
for all numbers x and y, let the operation # be defined as x#y=x-xy. If a and b are positive integers, whuich can be equal to zero?

1) a#b
2) (a+b)#b
3) A # (a+b)

1 only
2 only
3 only
1 and 3
1 and 2
• August 13th 2011, 03:51 PM
SammyS
Re: SAT question
Quote:

Originally Posted by RK29
for all numbers x and y, let the operation # be defined as x#y=x-xy. If a and b are positive integers, which can be equal to zero?

1) a#b
2) (a+b)#b
3) A # (a+b)

1 only
2 only
3 only
1 and 3
1 and 2

What have you tried?

Where are you stuck?
• August 13th 2011, 03:53 PM
RK29
Re: SAT question
well, i tried each option but non of them give me zero. I used number 4 for a and 2 for b
• August 13th 2011, 04:04 PM
SammyS
Re: SAT question
Just picking any two numbers to plug in, virtually never gets the job done --- especially for this problem.

For a#b:
Use the definition of a#b, set it to zero & solve for a and/or b.

a-ab = 0

a(1-b) = 0

What are the solutions?
• August 13th 2011, 05:48 PM
RK29
Re: SAT question
Quote:

Originally Posted by SammyS
Just picking any two numbers to plug in, virtually never gets the job done --- especially for this problem.

For a#b:
Use the definition of a#b, set it to zero & solve for a and/or b.

a-ab = 0

a(1-b) = 0

What are the solutions?

i have a=0
and b=1

how does that help me to get my solution. I am not getting a clear picture
• August 13th 2011, 06:08 PM
Plato
Re: Another SAT Question
Quote:

Originally Posted by RK29
for all numbers x and y, let the operation # be defined as x#y=x-xy. If a and b are positive integers, whuich can be equal to zero?
1) a#b
2) (a+b)#b
3) A # (a+b)

Here is a huge hint: $\left( {\forall x} \right)\left[ {x\text{*} 1 = 0} \right]$. (*=#)

BTW: $0$ is not a positive integer.
• August 13th 2011, 06:32 PM
SammyS
Re: SAT question
Quote:

Originally Posted by RK29
i have a=0
and b=1

how does that help me to get my solution. I am not getting a clear picture

Those are two independent solutions. In other words: Either a=0, OR b = 1, will ensure that a#b = 0. As Plato points out, 0 is not positive, so that leaves you with b=1. Of course (check for yourself) if b = 1, then a can be any (positive for this problem) number.

So you know that 1) can be equal to zero.

Now try 2) and 3) .
• August 14th 2011, 06:37 AM
HallsofIvy
Re: SAT question
x#y= x- xy= x(1- y). In order to be 0, either x= 0 or y= 1.

1) a#b. x= a, b= y. a cannot be 0 but b can be 1.

2)(a+ b)#b. x= a+ b, y= b.

3)a#(a+ b). x= a, y= a+ b. Remember that a and b must be positive integers.

This looks to me exactly like your previous "SAT question".