function
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heshamelaziry
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What is the operation in the stem? I tried +,-,*,/ a =3 and b = 2 but the two sides did not match ?
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heshamelaziry
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mp2437 wrote:I get C. Not sure how choice III could always be true...
What is the operation in the original equation ? could you give example ?
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.
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.
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heshamelaziry
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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 ?
I AM NOT INTELLIGENT TO ANSWER THIS QUESTION WITHOUT KNOWING THE OPERATION. DOES # MEAN -,+,*,/ OR A COMBINATION ?
# 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.
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.
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heshamelaziry
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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 .
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Stuart@KaplanGMAT
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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.heshamelaziry wrote: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 .
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
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
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