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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

\(0<1-\frac{c}{d}<1\) --> add \(-1\) to all three parts of this inequality --> \(-1<-\frac{c}{d}<0\) --> multiply by \(-1\) and as multiplying by negative, flip signs --> \(1>\frac{c}{d}>0\).

So we have that: \(1>\frac{c}{d}>0\)

I. \(c>0\) --> as \(\frac{c}{d}>0\) and \(d>0\), then \(c>0\). Always true.

II. \(\frac{c}{d}<1\) --> directly given as true.

III. \(c^2 + d^2 > 1\) --> if \(c=1\) and \(d=2\), then YES, but if \(c=0.1\) and \(d=0.2\), then No, hence this one is not always true.

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

\(0<1-\frac{c}{d}<1\) --> add \(-1\) to all three parts of this inequality --> \(-1<-\frac{c}{d}<0\) --> multiply by \(-1\) and as multiplying by negative, flip signs --> \(1>\frac{c}{d}>0\).

So we have that: \(1>\frac{c}{d}>0\)

I. \(c>0\) --> as \(\frac{c}{d}>0\) and \(d>0\), then \(c>0\). Always true.

II. \(\frac{c}{d}<1\) --> directly given as true.

III. \(c^2 + d^2 > 1\) --> if \(c=1\) and \(d=2\), then YES, but if \(c=0.1\) and \(d=0.2\), then No, hence this one is not always true.

Re: If d > 0 and 0 < 1 - c/d < 1, which of the following must be [#permalink]

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06 May 2015, 11:20

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If d > 0 and 0 < 1 - c/d < 1, which of the following must be [#permalink]

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09 May 2016, 00:54

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If d > 0 and 0 < 1 - c/d < 1, which of the following must be [#permalink]

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04 Jul 2017, 06:11

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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