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# Is a-3b an even number? 1). b=3a+3 2). b-a is an odd number

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Manager
Joined: 04 Dec 2005
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Is a-3b an even number? 1). b=3a+3 2). b-a is an odd number [#permalink]  26 Sep 2006, 06:06
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Is a-3b an even number?
1). b=3a+3
2). b-a is an odd number

When the question description is like this without informing anything about whether a and b are integers or real numbers, how do we proceed. What does GMAT/OG say when nothing is given on what type of numbers we should use by default.

Solve the above problem and highlight below for the Question.

When a and b are integers you wil get the answer as D. However when you consider a and b as real numbers you will get a different answer. For ex: Try b=5 and a = 2, b = 3.5 and a = 1.5, your choice D fails.
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Current Student
Joined: 29 Jan 2005
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For a number to be even it has to be a integer, either pos or negative.

any integers chosen here result in a odd integer.

(D)
GMAT Instructor
Joined: 04 Jul 2006
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Re: DS- Even or Odd - Very important [#permalink]  26 Sep 2006, 06:49
withme wrote:
Is a-3b an even number?
1). b=3a+3
2). b-a is an odd number

(1) a-3b=a-3(3a+3)= -8a-9 which may be even, odd, integer, non-integer, rational, irrational... NOTE THAT WE ARE NOT TOLD ABOUT THE PROPERTIES OF a. NOT SUFF

(2) b=(2k+1)+a where k is an integer

a-3b= a-3((2k+1)+a)= -2a -6k-3 NOT SUFF for the same reason

Together we see that -8a-9=-2a-6k-3 for some integer k

-6a=-6k+6=-6(k+1) => a=k+1

Thus a is an integer, either odd or even

(2) tells us that b is also an integer and that exactly one of {a,b} is even

If a is even and b is odd, a-3b is odd
If b is even and a is odd a-3b is odd

(1) and (2) combined tell us that a-3b is an odd number, not an even one
SUFF

Manager
Joined: 12 Sep 2006
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GMATT73 is right

only integers can be considered positive or negative. therefore the answer must be D

statement A:
b=3a+3
so 3a-b=-3, which is odd
that means a or b must be odd and the other even, so a-3b= odd
SUFF

statement B
b-a=odd
same as above, one of them must be odd and the other even, therefore a-3b=odd
SUFF

Manager
Joined: 04 Dec 2005
Posts: 79
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The question is asking to find whether a-3b is even but did not say anything on what should a and b can assume.

For example: take a = 0.5 and b = 3.5

which will give you a-3b = 0.5 - 10.5 = -10, an even number
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