function

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okigbo: Master | Next Rank: 500 Posts; Posts: 177; Joined: Sun Aug 02, 2009 9:39 pm; Thanked: 6 times

by okigbo » Thu Nov 12, 2009 4:02 pm

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

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Source: Beat The GMAT — Problem Solving | Thu Nov 12, 2009 4:02 pm

gmatv09: Master | Next Rank: 500 Posts; Posts: 256; Joined: Mon Aug 10, 2009 6:31 pm; Thanked: 3 times

by gmatv09 » Thu Nov 12, 2009 8:20 pm

IMO e...

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palvarez: Master | Next Rank: 500 Posts; Posts: 199; Joined: Sat Oct 24, 2009 4:43 pm; Thanked: 22 times; GMAT Score:710

by palvarez » Thu Nov 12, 2009 11:00 pm

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

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heshamelaziry: Legendary Member; Posts: 869; Joined: Wed Aug 26, 2009 3:49 pmFollowed by: 3 members; Location: California; Thanked: 13 times

by heshamelaziry » Fri Nov 13, 2009 8:46 am

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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mp2437: Master | Next Rank: 500 Posts; Posts: 177; Joined: Thu Aug 14, 2008 11:59 am; Thanked: 25 times

by mp2437 » Fri Nov 13, 2009 9:55 am

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

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heshamelaziry: Legendary Member; Posts: 869; Joined: Wed Aug 26, 2009 3:49 pmFollowed by: 3 members; Location: California; Thanked: 13 times

by heshamelaziry » Fri Nov 13, 2009 10:02 am

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 ?

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mp2437: Master | Next Rank: 500 Posts; Posts: 177; Joined: Thu Aug 14, 2008 11:59 am; Thanked: 25 times

by mp2437 » Fri Nov 13, 2009 10:20 am

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.

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heshamelaziry: Legendary Member; Posts: 869; Joined: Wed Aug 26, 2009 3:49 pmFollowed by: 3 members; Location: California; Thanked: 13 times

by heshamelaziry » Fri Nov 13, 2009 10:36 am

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 ?

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mp2437: Master | Next Rank: 500 Posts; Posts: 177; Joined: Thu Aug 14, 2008 11:59 am; Thanked: 25 times

by mp2437 » Fri Nov 13, 2009 12:24 pm

# 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.

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heshamelaziry: Legendary Member; Posts: 869; Joined: Wed Aug 26, 2009 3:49 pmFollowed by: 3 members; Location: California; Thanked: 13 times

by heshamelaziry » Fri Nov 13, 2009 12:34 pm

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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gmatv09: Master | Next Rank: 500 Posts; Posts: 256; Joined: Mon Aug 10, 2009 6:31 pm; Thanked: 3 times

by gmatv09 » Fri Nov 13, 2009 12:48 pm

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

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Fri Nov 13, 2009 4:55 pm

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 .

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

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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