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If d > 0 and 0 < 1  c/d < 1, which of the following must be
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06 Mar 2014, 03:05
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The Official Guide For GMAT® Quantitative Review, 2ND EditionIf 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 Problem Solving Question: 134 Category: Algebra Inequalities Page: 79 Difficulty: 600 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you!
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Re: If d > 0 and 0 < 1  c/d < 1, which of the following must be
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SOLUTIONIf 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. Answer: C (I and II only).
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Re: If d > 0 and 0 < 1  c/d < 1, which of the following must be
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06 Mar 2014, 03:58
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 IIISol: Given d>0 and 0 < 1  c/d < 1> Eq a Subtract from Eq a we get 1<c/d<0 Mulitply by each term by 1 we get 1>c/d>0 Since d>0 and c/d>0 this implies c>0 also we can clearly see c/d> 1. At this stage options A,B and D can be rejected Consider c^2+d^2> 1 If c=3 and d=5 then c^2+d^2>1 But if c=1/2 and d=3/4 then we have 1/4+9/25 or (25+36)/100 or 61 /100 which is less than 1 Ans is C
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If d > 0 and 0 < 1  c/d < 1, which of the following must be
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30 Aug 2017, 08:59
Answer is C:0<1c/d<1 1c/d>0 c/d>1 c/d<1 ________________________ ii point is proved 1c/d<1 c/d<0 c/d>0 , d>0 given so c/d to be >0 , implies c>0 ______i point proved 0<c/d<1 c=1 d=2______________c^2+d^2 =5 wow c=0.1 d=0.2__________c^2 + d^2 = 0.05 ohh no. hence only 1 and 2 are correct....
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Re: If d > 0 and 0 < 1  c/d < 1, which of the following must be
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03 Oct 2017, 07:13
0<1c/d<1
0<dc/d<1
0<dc<d
Ie d is >dc and both d and c are positive (if c is ve then dc cannot be <d) and d is>c.
c>0 proved above
c/d<1 a smaller postive number divided by a larger +ve no will result in a decimalPossible
c^2+d^2>1 if c and d are decimals then this inequality is not true.
Only 1 and II are a 'must' case.



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If d > 0 and 0 < 1  c/d < 1, which of the following must be tru
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25 Jan 2018, 16:39
Bunuel, can we plug in smart numbers for statement #1? When I plug in a "2" for "d", it turns out to be false.
0 < 1  c/2 < 1
According to I, C is supposed to be a positive number. This statement works when C = 1, but it doesn't work when C = 2.
Plugging in numbers works with #2, making it true.



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Re: If d > 0 and 0 < 1  c/d < 1, which of the following must be
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25 Jan 2018, 20:22
OCDianaOC wrote: Bunuel, can we plug in smart numbers for statement #1? When I plug in a "2" for "d", it turns out to be false.
0 < 1  c/2 < 1
According to I, C is supposed to be a positive number. This statement works when C = 1, but it doesn't work when C = 2.
Plugging in numbers works with #2, making it true. It's the other way around. We are given that \(d >0\) and \(0 < 1  \frac{c}{d} < 1\) are true. If these two inequalities are true, then c will be positive. So you should consider only those numbers which satisfy \(d >0\) and \(0 < 1  \frac{c}{d} < 1\). For c and d, which satisfy \(d >0\) and \(0 < 1  \frac{c}{d} < 1\), c will turn out to be positive.
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Re: If d > 0 and 0 < 1  c/d < 1, which of the following must be
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29 Jan 2018, 11:06
rahulraao wrote: 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 Simplifying the given inequality we have: 0 < 1  c/d < 1 1 < c/d < 0 d < c < 0 d > c > 0 So we see that c must be positive but less than d. Thus, I and II must be true. III does not have to be true since c and d could be some proper fractions, say both less than 1/2. Answer: C
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Re: If d > 0 and 0 < 1  c/d < 1, which of the following must be
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Re: If d > 0 and 0 < 1  c/d < 1, which of the following must be
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