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If AB/7 > 1/14 and A = B, which of the following must be gre

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If AB/7 > 1/14 and A = B, which of the following must be gre [#permalink] New post 19 Feb 2014, 01:10
00:00
A
B
C
D
E

Difficulty:

  25% (low)

Question Stats:

73% (02:13) correct 27% (01:07) wrong based on 37 sessions
If AB/7 > 1/14 and A = B, which of the following must be greater than 1?

A. A+B
B. 1-A
C. 2A^2
D. A^2 - 1/2
E. A

[Reveal] Spoiler:
OA is C but It seems A also satisfies this condition...

I calculated it as below;
AB/7 > 1/14
multiplying both sides by 14
2AB > 1
as A=B
2A^2 >1 and 2 B^2 > 1
Option (C) is true as per this logic
While analyzing other options this is what I got...
2A^2>1
A^2>1/2
A>1/sqrt(2)
as A=B, B >1/sqrt(2)

so A+B > 1/sqrt(2) + 1/sqrt(2)
A+B > 2/sqrt(2)
A+B > sqrt(2)
This is also going to be greater than 1
[Reveal] Spoiler: OA

Last edited by Bunuel on 19 Feb 2014, 02:52, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Inequalities MGMAT [#permalink] New post 19 Feb 2014, 02:51
Expert's post
Conquistador22 wrote:
This problem is from MGMAT Algebra Strategy Guide:

If AB/7 > 1/14 and A=B While of the following must be greater than 1 ?
a) A+B
b) 1-A
c) 2A^2
d) A^2-1/2
e) A

OA is C but It seems A also satisfies this condition...

I calculated it as below;
AB/7 > 1/14
multiplying both sides by 14
2AB > 1
as A=B
2A^2 >1 and 2 B^2 > 1
Option (C) is true as per this logic
While analyzing other options this is what I got...
2A^2>1
A^2>1/2
A>1/sqrt(2)
as A=B, B >1/sqrt(2)

so A+B > 1/sqrt(2) + 1/sqrt(2)
A+B > 2/sqrt(2)
A+B > sqrt(2)
This is also going to be greater than 1


If AB/7 > 1/14 and A = B, which of the following must be greater than 1?

A. A+B
B. 1-A
C. 2A^2
D. A^2 - 1/2
E. A

First of all notice that the question asks which of the following MUST be true, not COULD be true.

\frac{AB}{7} > \frac{1}{14} --> 2AB>1. Since A = B, then 2A^2>1.

Answer: C.

As for option A: notice that from A^2>\frac{1}{2} it follows that A, and therefore B, since A = B, can be negative numbers, for example, -1, and in this case A + B = -2 < 1. The problem with your solution is that A^2>\frac{1}{2} means that A>\frac{1}{\sqrt{2}} OR A<-\frac{1}{\sqrt{2}}, not only A>\frac{1}{\sqrt{2}}.

Hope it's clear.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rules 3, 5, and 7. Also, please hide the OA under the spoiler. Thank you.

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Re: Inequalities MGMAT [#permalink] New post 19 Feb 2014, 04:01
Thanks Bunuel, Your explanation is awesome as usual. :)

But I am a bit confused about below part.
Bunuel wrote:
The problem with your solution is that A^2>\frac{1}{2} means that A>\frac{1}{\sqrt{2}} OR A<-\frac{1}{\sqrt{2}}, not only A>\frac{1}{\sqrt{2}}.
.

As per my understanding
A^2>\frac{1}{2} means that A>+\frac{1}{\sqrt{2}} OR A>-\frac{1}{\sqrt{2}}. Could you please elaborate why A<-\frac{1}{\sqrt{2}} ?
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Re: Inequalities MGMAT [#permalink] New post 19 Feb 2014, 04:06
Expert's post
Conquistador22 wrote:
Thanks Bunuel, Your explanation is awesome as usual. :)

But I am a bit confused about below part.
Bunuel wrote:
The problem with your solution is that A^2>\frac{1}{2} means that A>\frac{1}{\sqrt{2}} OR A<-\frac{1}{\sqrt{2}}, not only A>\frac{1}{\sqrt{2}}.
.

As per my understanding
A^2>\frac{1}{2} means that A>+\frac{1}{\sqrt{2}} OR A>-\frac{1}{\sqrt{2}}. Could you please elaborate why A<-\frac{1}{\sqrt{2}} ?


Let me ask you a question: does x^2>4 mean x>2 or x>-2? What does x>2 or x>-2 even mean?

x^2>4 --> |x|>2 --> x>2 or x<-2.

Go through the links below to brush up fundamentals on inequalities:


Hope this helps.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

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; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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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Kudos [?]: 8 [0], given: 13

Re: Inequalities MGMAT [#permalink] New post 19 Feb 2014, 06:56
Bunuel wrote:

Let me ask you a question: does x^2>4 mean x>2 or x>-2? What does x>2 or x>-2 even mean?

x^2>4 --> |x|>2 --> x>2 or x<-2.

This conclusion is based on below logic.
x^2=25 has TWO solutions, +5 and -5 so I thought x^2>4 would also have two solutions +2 & -2, this is how I got x>2 or x>-2
Could you please let me know why this is not valid ?

I am asking very basic question but I know only after getting my basics clear, I will be able to get good score.... Thanks for bearing with me and my stupid questions :) .
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Re: Inequalities MGMAT [#permalink] New post 19 Feb 2014, 07:03
Expert's post
Conquistador22 wrote:
Bunuel wrote:

Let me ask you a question: does x^2>4 mean x>2 or x>-2? What does x>2 or x>-2 even mean?

x^2>4 --> |x|>2 --> x>2 or x<-2.

This conclusion is based on below logic.
x^2=25 has TWO solutions, +5 and -5 so I thought x^2>4 would also have two solutions +2 & -2, this is how I got x>2 or x>-2
Could you please let me know why this is not valid ?

I am asking very basic question but I know only after getting my basics clear, I will be able to get good score.... Thanks for bearing with me and my stupid questions :) .


Guess you did not follow the links I proposed...

Again, what does x is more than 2 or x is more than -2 mean? What are the possible values of x in this case? For example, can x be 1, since it's more than -2?

x^2>4 indeed has two ranges, which are x>2 or x<-2. Please follow the links in my previous post for more.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

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; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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: Inequalities MGMAT   [#permalink] 19 Feb 2014, 07:03
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