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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
If d > 0 and 0 < 1 - c/d < 1, which of the following must be true? I.
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20 Sep 2021, 04:46
20 Sep 2021, 04:46
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If \(d > 0\) and \(0 < 1 - \frac{c}{d} < 1,\) which of the following must be true?
I. \(c > 0\)
II. \(\frac{c}{d} < 1\)
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
I. \(c > 0\)
II. \(\frac{c}{d} < 1\)
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
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If d > 0 and 0 < 1 - c/d < 1, which of the following must be true? I.
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20 Sep 2021, 05:20
20 Sep 2021, 05:20
2
GeminiHeat wrote:
If \(d > 0\) and \(0 < 1 - \frac{c}{d} < 1,\) which of the following must be true?
I. \(c > 0\)
II. \(\frac{c}{d} < 1\)
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
I. \(c > 0\)
II. \(\frac{c}{d} < 1\)
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
Take the inequality: 0 < 1 - c/d < 1
Subtract 1 from all sides: -1 < -c/d < 0
Multiply all sides by -1 to get: 1 > c/d > 0 [when we multiply an inequality by a NEGATIVE value, we must REVERSE the direction of the inequality symbols]
Rearrange to get: 0 < c/d < 1
We can immediately see that statement II (c/d < 1) is true
Also, since 0 < c/d, we know that c/d is positive.
Since we're told d is positive, we can conclude that c must also be positive
In other words, c > 0, which means statement I is true.
Now let's analyze statement III
Notice that the values c = 0.1 and d = 0.2 satisfy all of the given information.
Now recognize that c² + d² = 0.1² + 0.2² = 0.01 + 0.04 = 0.05
So, it's not necessarily the case that c² + d² > 1
In other words, statement III need not be true.
Answer: C
General Discussion
Re: If d > 0 and 0 < 1 - c/d < 1, which of the following must be true? I.
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27 Mar 2025, 17:57
27 Mar 2025, 17:57
Hello from the GRE Prep Club BumpBot!
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Thanks to another GRE Prep 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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