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Inequality problem [#permalink]
21 Aug 2004, 23:45

Hi,
This question is from the OG. It's question 299 from the quantitative section. I don't quite agree with the OA, so I'm posting it here to see what you guys think.

OG Q299) If d > 0, and 0< 1-c/d < 1, which of the following must be true?

I. c > 0
II. c/d < 1
III. c^2 + d^2 > 1

A) I only
B) II only
C) I and II only
D) II and III only
E) I, II and III

My answer is I only (A), which the OA says is wrong. I won't reveal the OA just yet, and have some discussion about II and III with you guys.

OOPS, the following is wrong, please ignore (edited)

/************************************************************
Okay we know d > 0. Let's restate the next equation by subtracting 1 from all 3 expressions (this does not effect the inequality). Hence,

-1 < c/d < 0.

This means c/d must be < 0 and II is true.

Since c/d is a fraction < 0 and we know d > 0, c must be < 0. Hence I must be true.

Finally, while we know something about the ratio of c to d, we cannot limit the absolute values of c and d. If c = -1000 and d = 2000 then III is true, but is c = -.00001 and d = .00002, then III is not. Hence, only I and II must be true and the answer is C.
*********************************************************/
The answer still is C (read my next post).

_________________

Best,

AkamaiBrah Former Senior Instructor, Manhattan GMAT and VeritasPrep Vice President, Midtown NYC Investment Bank, Structured Finance IT MFE, Haas School of Business, UC Berkeley, Class of 2005 MBA, Anderson School of Management, UCLA, Class of 1993

Last edited by AkamaiBrah on 22 Aug 2004, 07:58, edited 1 time in total.

OG Q299) If d > 0, and 0< 1-c/d < 1, which of the following must be true?

By rewriting the equation 0 < 1-c/d < 1, this is what I got:

-1 < -c/d < 0
0 < c/d < 1

So since we are given d > 0, for c/d < 1 and c/d > 0, we know c must be positive as well. So I is correct.

But II is suspect, c/d < 1 is okay, but it can mean c/d can get become a negative number and so won't satisfy the left hand side of the inequality, whic is c/d > 0. So that's why I ruled II out. What do you think?
Anything wrong with this reasoning ?

OG Q299) If d > 0, and 0< 1-c/d < 1, which of the following must be true?

By rewriting the equation 0 < 1-c/d < 1, this is what I got:

-1 < -c/d < 0 0 < c/d < 1

So since we are given d > 0, for c/d < 1 and c/d > 0, we know c must be positive as well. So I is correct.

But II is suspect, c/d < 1 is okay, but it can mean c/d can get become a negative number and so won't satisfy the left hand side of the inequality, whic is c/d > 0. So that's why I ruled II out. What do you think? Anything wrong with this reasoning ?

Oops. Forget what I said in previous post (it was 4am on a Saturday after playing poker and drinking beer).

You are right that the statement mean 0 < c/d < 1. Since we are GIVEN than 0 < 1-c/d < 1, then it is also GIVEN that 0 < c/d < 1. Hence, II is true. The stuff about III still holds true, but take out the negative sign.

_________________

Best,

AkamaiBrah Former Senior Instructor, Manhattan GMAT and VeritasPrep Vice President, Midtown NYC Investment Bank, Structured Finance IT MFE, Haas School of Business, UC Berkeley, Class of 2005 MBA, Anderson School of Management, UCLA, Class of 1993