function

[okigbo]

If # is defined by a # b = a + b - ab, then which is true?
a # b = b # a
a # 0 = a
(a # b) # c = a # (b # c)
a. I
b. II
c. I & II
d. I & III
e. I, II & III

[gmatv09]

IMO e...

[palvarez]

Same answer choices, but different question stems. Try these questions


1. a#b = |a-b|
2. a#b = 1 + ab
3. a#b = |a|b
4. a#b = a^2 + b^2

[heshamelaziry]

What is the operation in the stem? I tried +,-,*,/ a =3 and b = 2 but the two sides did not match ?

[mp2437]

I get C. Not sure how choice III could always be true...

[heshamelaziry]

I get C. Not sure how choice III could always be true...

What is the operation in the original equation ? could you give example ?

[mp2437]

Apologies! Answer should be E - I was too quick with my decision.

We know this:

a # b = a + b - ab

Now, we need to find if these are true.

I. a # b = b # a

a # b = a + b - ab
b # a = b + a - ba

This is true since additive and distributive rules tell you that a + b is always b + a and a * b is the same as b * a.

II. a # 0 = a

a # 0 = a + 0 - a*0 = a, so this is true

III. (a # b) # c = a # (b # c)

Parenthesis first!

a # b = a + b - ab

so (a # b) # c = (a + b - ab) # c =
(a + b - ab) + c - (a + b - ab) * c This becomes:
a + b + c - ab - ac - bc - abc

Is this the same as a # (b # c) ?? Let's see:

b # c (remember, parenthesis first!) = b + c - bc

a # (b # c) = a # (b + c - bc) = a + (b + c - bc) - (b + c - bc) * a. This becomes:
a + b + c - bc - ab - ac - bca

You can see when you expand both terms fully, they are the same. So all choices are correct.

[heshamelaziry]

WHAT IS THE OPERATION IN THE ORIGINAL STEM ?????????

I AM NOT INTELLIGENT TO ANSWER THIS QUESTION WITHOUT KNOWING THE OPERATION. DOES # MEAN -,+,*,/ OR A COMBINATION ?

[mp2437]

# is used to describe the function, its just a symbol. It says when you see a # b, that means you take the number on the left and the number on the right (a,b) and plug it into this formula: a + b - a*b

It doesn't have to be #, it could be any symbol, like a question mark.

If I tell you that a ? b = a + b - a*b, then in the answer choices when you see the question mark you know what formula you have to use.

[heshamelaziry]

Thank you for the try. I still do not get it. in all other symbol questions, the question required us to identify the operation. I don't see how to identify the answer choice without knowing what # is .

[gmatv09]

the only possibility for # is either '+' or '*'
if you look at all the options ... we can conclude that the operation # is "+"

[Stuart@KaplanGMAT]

Thank you for the try. I still do not get it. in all other symbol questions, the question required us to identify the operation. I don't see how to identify the answer choice without knowing what # is .

Most of these weird symbol questions make up a definition and then force you to apply that definition in some way to answer the question.

The "#" operation is made up specifically for this question. It doesn't just represent one mathematical operation, it represents everything on the right side of the equation.

We're told that:

a # b = a + b - ab

This means that anytime we see two numbers (or variables) separated by the # sign, we simply substitute them into the right side of the equation.

For example:

7#4 = 7 + 4 - 7*4
(-3)#12 = -3 + 12 - (-3)*12
6#d = 6 + d - 6d

If you're used to solving functions, you can think of all of these weird operations in those terms as well. In this case, the original operation could have been defined as:

f(a,b) = a + b - ab