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when to simplify ?

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when to simplify ?

by beat_gmat_09 » Wed May 12, 2010 6:55 am
Question 1:

If a,b,c are integers, is a-b+c greater than a+b-c ?

1) b is negative.
2) c is positive.

Question 2:

If x!=-y (x is not equal to -y), is x-y/x+y >1 ?

1) x>0
2) y<0

Both problems are from OG 11. For the first problem the question is simplified a-b+c > a+b-c to c> b
but in the second question x-y/x+y > 1 is not simplified (if simplified would have been y<0).

Simplification and picking numbers gives different answers.

Can anyone please explain when to simplify and when not to.
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by tpr-becky » Wed May 12, 2010 3:35 pm
The problem is that when you multiply or divide by a negative number you must switch the sign. in the first problem you are only dealing with addition and subtraction so the rule doesn't come into play and you can simplify all you want.

in the second problem you must multiplyby x+y to get the fration out of the equation - you can't tell if x+y is positive or negative so you can't simplify easily (you would need two statements, one for the instance in which x+y is positive and one in which x+y is negative) and here it would be easier to use numbers.

so you simplify when you know the rules and can easily do it - when you get into multiplication and division with inequalities it is a difficult area so unless you truly understand all the elements of the rule pluggin in numbers is a safer approach.
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by beat_gmat_09 » Fri May 14, 2010 6:41 am
Hi becky,

Thanks for your valuable tips, but I have one doubt in the first problem, here the denominator a+b-c can be considered +ve and -ve both, then why to simplify instead of picking numbers?
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by kevincanspain » Fri May 14, 2010 7:40 am
beat_gmat_09 wrote:Hi becky,

Thanks for your valuable tips, but I have one doubt in the first problem, here the denominator a+b-c can be considered +ve and -ve both, then why to simplify instead of picking numbers?
We refer to the top and bottom parts of a fraction as the numerator and demoninator. In the first question, there are no fractions
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by beat_gmat_09 » Fri May 14, 2010 10:02 am
kevincanspain wrote:
beat_gmat_09 wrote:Hi becky,

Thanks for your valuable tips, but I have one doubt in the first problem, here the denominator a+b-c can be considered +ve and -ve both, then why to simplify instead of picking numbers?
We refer to the top and bottom parts of a fraction as the numerator and demoninator. In the first question, there are no fractions
a-b+c greater than a+b-c
can we not consider above as a-b+c/a+b-c>1?
this too is a fraction and is similar to x-y/x+y>1
Please correct me if i am wrong.
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by tpr-becky » Fri May 14, 2010 10:37 am
The rule is only for division and in the first problem there is only addition and subtraction - no simplifying will create a fraction.
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by kevincanspain » Fri May 14, 2010 10:46 am
beat_gmat_09 wrote:
kevincanspain wrote:
beat_gmat_09 wrote:Hi becky,

Thanks for your valuable tips, but I have one doubt in the first problem, here the denominator a+b-c can be considered +ve and -ve both, then why to simplify instead of picking numbers?
We refer to the top and bottom parts of a fraction as the numerator and demoninator. In the first question, there are no fractions
a-b+c greater than a+b-c
can we not consider above as a-b+c/a+b-c>1?
this too is a fraction and is similar to x-y/x+y>1
Please correct me if i am wrong.
In dividing both sides by a + b - 1 without changing sides, you are assuming that a + b - 1 is positive!
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by manjus_mailme » Fri May 14, 2010 11:26 am
Can you please tell me what is the answer for the second question ?
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by beat_gmat_09 » Fri May 14, 2010 9:37 pm
Answer for 2nd question is E.
Thanks Kevin and Becky.
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by irmakyolcu » Sat May 15, 2010 8:50 am
answer for the first one is it c?
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