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inequality confusion..pls help

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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inequality confusion..pls help

by arslan » Tue Aug 07, 2012 12:48 am
okay i dont know if ive been studying for too long and have gone nuts..or its just that inequalities are not my thing..

If d>0 and 0 < 1-c/d < 1, which of the following must be true:

1. c>0
2. c/d < 1
3. c^2+d^2 >1

I totally understand the solution to this problem..and its not that what i looking for..i just want to know WHY CANT IT BE : C/D<1<1+C/D

If thats possible..then the answer to this question will be different. So can someone please help?
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by Brent@GMATPrepNow » Tue Aug 07, 2012 7:41 am
arslan wrote: If d>0 and 0 < 1-c/d < 1, which of the following must be true:
1. c>0
2. c/d < 1
3. c^2+d^2 >1
From the notation you have used, it's hard to tell what the given conditions are.
"1-c/d" could be interpreted as (1-c)/d, or it could be interpreted as 1-(c/d).
Once this is clarified, we can go about answering your question.

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by Kobe_Kassidy » Tue Aug 07, 2012 8:22 am
As far as the correct answer goes, wouldn't it be statements I and II that must be true, but non necessarily statement III?
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by arslan » Tue Aug 07, 2012 2:09 pm
oh my bad. this is the question..

If d>0 and 0 < 1-(c/d) < 1, which of the following must be true:

1. c>0
2. c/d < 1
3. c^2+d^2 >1

and my question is : Why cant it be : (C/D)< 1 <1+(C/D)


Edit: Okay guys nevermind..i guess i was just too tired and sleepy last night when doing this problem..thanks for the responding though Brent =)

@Kobe..The correct asnwer to this probelm is C which states that only I AND II are correct.
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by Brent@GMATPrepNow » Tue Aug 07, 2012 2:23 pm
arslan wrote: If d>0 and 0 < 1-(c/d) < 1, which of the following must be true:

1. c>0
2. c/d < 1
3. c^2+d^2 >1
Let's deal with this in parts:

Part 1: 0 < 1-(c/d)
Add c/d to both sides to get: c/d < 1
Since we're told that d is positive, we'll multiply both sides by d to get: c < d

Part 2: 1-(c/d) < 1
Add c/d to both sides to get: 1 < 1 + c/d
Subtract 1 from both sides to get: 0 < c/d
If d is positive and c/d is positive, then c must be positive.
In other words, 0 < c

Combining the two parts, we get 0 < c < d

What kinds of conclusions can we make from this information?

1. c>0 (yes, this must be true)
2. c/d < 1 (since c < d, and since c and d are both positive, this must be true)
3. c^2+d^2 >1 (no, this need not be true. For example, we could have c=0.1 and d=0.2, in which case c^2 + d^2 is not greater than 1.)

Cheers,
Brent
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