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

Oldest

Best Reply

Author

Message

TAGS:

Director

Joined: 15 Aug 2005

Posts: 810

Location: Singapore

Followers: 2

Kudos [?]: 1 [0], given: 0

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

03 Sep 2005, 06:16

00:00

Question Stats:

59% (02:04) correct

40% (01:39) wrong

based on 2 sessions

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

[Reveal] Spoiler: OA

_________________

Cheers, Rahul.

Last edited by Bunuel on 01 Apr 2012, 13:10, edited 1 time in total.

Edited the question and added the OA

GMAT Club team member

Joined: 02 Sep 2009

Posts: 11505

Followers: 1790

Kudos [?]: 9507 [2] , given: 826

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

01 Apr 2012, 13:09

This post received
KUDOS

mymbadreamz wrote:

I didn't understand this. could someone explain? thanks.

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[/quote]

0<1-\frac{c}{d}<1 --> add -1 to all three parts of this inequality --> -1<-\frac{c}{d}<0 --> mutliply 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, hences this one is not always true.

Answer: C (I and II only).

Hope it's clear.
_________________

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!

What are GMAT Club Tests?
25 extra-hard Quant Tests

Find out what's new at GMAT Club - latest features and updates

GMAT Club team member

Joined: 02 Sep 2009

Posts: 11505

Followers: 1790

Kudos [?]: 9507 [1] , given: 826

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

01 Apr 2012, 15:12

This post received
KUDOS

kashishh wrote:

Inequalities !!
is it possible to get some tips and tools to solve these "sign" (< = > ) questions?

DS questions on inequalities: search.php?search_id=tag&tag_id=184
PS questions on inequalities: search.php?search_id=tag&tag_id=189

Hard inequality and absolute value questions with detailed solutions check this: inequality-and-absolute-value-questions-from-my-collection-86939-40.html

The following threads might also be helpful:
x2-4x-94661.html#p731476
inequalities-trick-91482.html
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html?hilit=extreme#p873535
everything-is-less-than-zero-108884.html?hilit=extreme#p868863

Hope it helps.
_________________

SVP

Joined: 05 Apr 2005

Posts: 1745

Followers: 2

Kudos [?]: 17 [0], given: 0

Re: PS Inequalities [#permalink]

03 Sep 2005, 07:04

C. I and II only.

C > and c/d>0. then only 0 < 1 - c/d < 1 holds.

Senior Manager

Joined: 04 May 2005

Posts: 287

Location: CA, USA

Followers: 1

Kudos [?]: 4 [0], given: 0

[#permalink]

03 Sep 2005, 13:13

0 < 1 - c/d < 1 => 0<c/d<1
with d>0

we get: c>0 and c/d<1

not true for c^2 + d^2 > 1
example: c=0.1 d=0.2

C

Manager

Joined: 15 Apr 2011

Posts: 71

Followers: 0

Kudos [?]: 13 [0], given: 45

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

01 Apr 2012, 12:59

I didn't understand this. could someone explain? thanks.
_________________

http://mymbadreamz.blogspot.com

Manager

Joined: 02 Jun 2011

Posts: 160

Followers: 1

Kudos [?]: 4 [0], given: 11

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

01 Apr 2012, 14:27

Inequalities !!
is it possible to get some tips and tools to solve these "sign" (< = > ) questions?

Intern

Joined: 11 Apr 2011

Posts: 43

Followers: 0

Kudos [?]: 1 [0], given: 3

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

02 Apr 2012, 18:18

kashishh wrote:

Inequalities !!
is it possible to get some tips and tools to solve these "sign" (< = > ) questions?

i dunno if my method can help you but i solved it in two ways.

0 < 1 - (c/d) < 1

the way i looked at this problem was to first simply the equation by subtracting 1 in the middle to both sides:
-1 < -(c/d) < 0

and the given statement is that d is greater than zero, so d must be positive. if we know a variable is positive, you can safely multiply the variable without changing the signs. so i multiplied d to isolate c.
-1(d) < -c < 0(d)

so we get
-d < -c < 0

and then i divided the negative out and switched the signs.
d > c > 0

the above answers statement I. c > 0 is true.
for statement II, i manipulated the above equation by dividing d and i get
1 > c/d > 0
this answers statement II. c/d < 1

the last statement i just tested numbers using the d > c > 0 by using whole numbers and decimals.

the second way i solved this was using bunuel's way.

Intern

Joined: 19 Aug 2011

Posts: 30

Concentration: Finance, Entrepreneurship

Followers: 0

Kudos [?]: 5 [0], given: 2

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

03 Apr 2012, 02:33

I just picked numbers and tried to prove the options wrong.

Re: If d > 0 and 0 < 1 - c/d < 1, which of the following must be [#permalink] 03 Apr 2012, 02:33

		Similar topics	Author	Replies	Last post
Similar Topics:		If d>0 and 0<1-c/d<1 which of the following is	shubhangi	4	21 Nov 2003, 13:26
		If d>0, and 0 < 1 - (c/d) < 1, which of the	jcgoodchild	3	14 Apr 2006, 09:04
		If 0<x<1, which of the following must be true? 1.	2times	14	20 Aug 2006, 18:05
		If d>0 and 0< 1-c/d <1, which of the following	bigfernhead	5	22 Oct 2008, 21:14
	1	If -1< x <0 or x >1 then which of the following must be true	Joy111	1	25 May 2012, 07:56

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

Main navigation

GMAT Resources

Partners

MBA Resources

GMAT ® is a registered trademark of the Graduate Management Admission Council ® (GMAC ®). GMAT Club's website has not been reviewed or endorsed by GMAC.

GMAT Courses

Admissions Consulting

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

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

Main navigation

GMAT Resources

Partners

MBA Resources