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

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If d > 0 and 0 < 1 - c/d < 1, which of the following must be [#permalink] New post 03 Sep 2005, 05:16
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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
[Reveal] Spoiler: OA

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Last edited by Bunuel on 01 Apr 2012, 12:10, edited 1 time in total.
Edited the question and added the OA
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If d > 0 and 0 < 1 - c/d < 1, which of the following must be [#permalink] New post 01 Apr 2012, 12:09
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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[/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.
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Re: If d > 0 and 0 < 1 - c/d < 1, which of the following must be [#permalink] New post 01 Apr 2012, 14:12
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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.
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Re: If d > 0 and 0 < 1 - c/d < 1, which of the following must be [#permalink] New post 19 Jun 2013, 10:29
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0 < 1 - c/d < 1

Multiply by d,
0 < d - c < d

Implies that c>0

Now, d - c > 0 implies that d>c and hence c/d < 1

information we now have is c>0, d>0 and d>c

c^2 + d^2 > 0 but it may or may not be greater than 1.

Hence I & II only.
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Re: If d > 0 and 0 < 1 - c/d < 1, which of the following must be [#permalink] New post 21 Sep 2013, 15:58
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\(0<1-\frac{c}{d}<1\)

First Part:
\(0<1-\frac{c}{d}\)
\(\frac{c}{d}<1\) This satisfies Choice II

Second Part:
\(1-\frac{c}{d}<1\)
\(0<\frac{c}{d}\) This satisfies Choice I as \(d>0\)

As for Choice III, if c and d are decimals then this gives us "False" but if they are integers, then "True"
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Re: If d > 0 and 0 < 1 - c/d < 1, which of the following must be [#permalink] New post 21 Nov 2014, 08:50
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sunaimshadmani wrote:
Bunuel I have just one confusion here, 1> c/d > 0, however st 2 says c/d <1, doesnt the statement also include the cases where c/d<0, where the inequality wont hold so it isnt a MUST BE TRUE statement.
Thanks in advance


We got that \(0 < \frac{c}{d} < 1\). So, the answer to the question whether \(\frac{c}{d} < 1\) is true, is YES. How else?
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 [#permalink] New post 03 Sep 2005, 12:13
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
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Re: If d > 0 and 0 < 1 - c/d < 1, which of the following must be [#permalink] New post 01 Apr 2012, 13:27
Inequalities !!
is it possible to get some tips and tools to solve these "sign" (< = > ) questions?
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Re: If d > 0 and 0 < 1 - c/d < 1, which of the following must be [#permalink] New post 02 Apr 2012, 17:18
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.
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Re: If d > 0 and 0 < 1 - c/d < 1, which of the following must be [#permalink] New post 19 Jun 2013, 03:51
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If d > 0 and 0 < 1 - c/d < 1, which of the following must be [#permalink] New post 08 Nov 2014, 16:16
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Hey Guys

May I raise a small question regarding the third statement? If it would be INSTEAD of c^2 + d^2 > 1 be c^2 + d^2 > 0 , would the third statement be considered sufficient? My thinking is as follows:

1. as we know (out of proven first statement) that c>0: multiply the IE with itself leads to: c^2 >0
2. as we know (out of the question stem) that d>0: multiply the IE with itself leads to: d^2 >0
3. Combining the two IE from above by adding them up: c^2 + d^2 >0
4. The MODIFIED Statement 3 is considered sufficient

Would highly appreciate your inputs on my thought...

Cheers, Rene
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Re: If d > 0 and 0 < 1 - c/d < 1, which of the following must be [#permalink] New post 09 Nov 2014, 04:19
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DarkMight wrote:
Hey Guys

May I raise a small question regarding the third statement? If it would be INSTEAD of c^2 + d^2 > 1 be c^2 + d^2 > 0 , would the third statement be considered sufficient? My thinking is as follows:

1. as we know (out of proven first statement) that c>0: multiply the IE with itself leads to: c^2 >0
2. as we know (out of the question stem) that d>0: multiply the IE with itself leads to: d^2 >0
3. Combining the two IE from above by adding them up: c^2 + d^2 >0
4. The MODIFIED Statement 3 is considered sufficient

Would highly appreciate your inputs on my thought...

Cheers, Rene

______________
Yes, that's correct.
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

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. ,11 Mixed Questions, 12 Fresh Meat

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., 11 New DS set.


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Re: If d > 0 and 0 < 1 - c/d < 1, which of the following must be [#permalink] New post 09 Nov 2014, 05:18
Bunuel, thanks very much for the feedback
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Re: If d > 0 and 0 < 1 - c/d < 1, which of the following must be [#permalink] New post 21 Nov 2014, 07:42
Bunuel I have just one confusion here, 1> c/d > 0, however st 2 says c/d <1, doesnt the statement also include the cases where c/d<0, where the inequality wont hold so it isnt a MUST BE TRUE statement.
Thanks in advance
Re: If d > 0 and 0 < 1 - c/d < 1, which of the following must be   [#permalink] 21 Nov 2014, 07:42
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If d > 0 and 0 < 1 - c/d < 1, which of the following must be

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