Find all School-related info fast with the new School-Specific MBA Forum

It is currently 19 Aug 2014, 22:58

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

The Discreet Charm of the DS

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Expert Post
30 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19020
Followers: 3358

Kudos [?]: 24331 [30] , given: 2676

The Discreet Charm of the DS [#permalink] New post 02 Feb 2012, 03:15
30
This post received
KUDOS
Expert's post
30
This post was
BOOKMARKED
I'm posting the next set of medium/hard DS questions. I'll post OA's with detailed explanations after some discussion. Please, post your solutions along with the answers. Good luck!

1. Bonnie can paint a stolen car in x hours, and Clyde can paint the same car in y hours. They start working simultaneously and independently at their respective constant rates at 9:45am. If both x and y are odd integers, is x=y?
(1) x^2+y^2<12
(2) Bonnie and Clyde complete the painting of the car at 10:30am

Solution: the-discreet-charm-of-the-ds-126962-20.html#p1039633

2. Is xy<=1/2?
(1) x^2+y^2=1
(2) x^2-y^2=0

Solution: the-discreet-charm-of-the-ds-126962-20.html#p1039634

3. If a, b and c are integers, is abc an even integer?
(1) b is halfway between a and c
(2) a = b - c

Solution: the-discreet-charm-of-the-ds-126962-40.html#p1039637

4. How many numbers of 5 consecutive positive integers is divisible by 4?
(1) The median of these numbers is odd
(2) The average (arithmetic mean) of these numbers is a prime number

Solution: the-discreet-charm-of-the-ds-126962-40.html#p1039645

5. What is the value of integer x?
(1) 2x^2+9<9x
(2) |x+10|=2x+8

Solution: the-discreet-charm-of-the-ds-126962-40.html#p1039650

6. If a and b are integers and ab=2, is a=2?
(1) b+3 is not a prime number
(2) a>b

Solution: the-discreet-charm-of-the-ds-126962-40.html#p1039651

7. A certain fruit stand sold total of 76 oranges to 19 customers. How many of them bought only one orange?
(1) None of the customers bought more than 4 oranges
(2) The difference between the number of oranges bought by any two customers is even

Solution: the-discreet-charm-of-the-ds-126962-40.html#p1039655

8. If x=0.abcd, where a, b, c and d are digits from 0 to 9, inclusive, is x>7/9?
(1) a+b>14
(2) a-c>6

Solution: the-discreet-charm-of-the-ds-126962-40.html#p1039662

9. If x and y are negative numbers, is x<y?
(1) 3x + 4 < 2y + 3
(2) 2x - 3 < 3y - 4

Solution: the-discreet-charm-of-the-ds-126962-40.html#p1039665

10. The function f is defined for all positive integers a and b by the following rule: f(a,b)=(a+b)/GCF(a,b), where GCF(a,b) is the greatest common factor of a and b. If f(10,x)=11, what is the value of x?
(1) x is a square of an integer
(2) The sum of the distinct prime factors of x is a prime number.

Solution: the-discreet-charm-of-the-ds-126962-40.html#p1039671

11. If x and y are integers, is x a positive integer?
(1) x*|y| is a prime number.
(2) x*|y| is non-negative integer.

Solution: the-discreet-charm-of-the-ds-126962-40.html#p1039678

12. If 6a=3b=7c, what is the value of a+b+c?
(1) ac=6b
(2) 5b=8a+4c

Solution: the-discreet-charm-of-the-ds-126962-40.html#p1039680
_________________

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.


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

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Kaplan Promo CodeKnewton GMAT Discount CodesGMAT Pill GMAT Discount Codes
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19020
Followers: 3358

Kudos [?]: 24331 [0], given: 2676

Re: The Discreet Charm of the DS [#permalink] New post 10 Dec 2012, 05:01
Expert's post
skamal7 wrote:
Bunnel,
Can you please explain once again why in 1st question statement2 is sufficient...If you dont mind.Thanks in adavance


You should tell me what didn't you understand in the solution provided.

Check other approaches here: the-discreet-charm-of-the-ds-126962-80.html#p1151803

Hope it 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.


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

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 12 Dec 2012
Posts: 4
Followers: 0

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

Re: The Discreet Charm of the DS [#permalink] New post 12 Dec 2012, 06:00
Amazing collection bunuel, thanks a ton. Helped me a lot.
Manager
Manager
avatar
Joined: 05 Nov 2012
Posts: 147
Followers: 1

Kudos [?]: 7 [0], given: 56

Re: The Discreet Charm of the DS [#permalink] New post 12 Dec 2012, 18:36
Bunuel wrote:
SOLUTIONS:

1. Bonnie can paint a stolen car in x hours, and Clyde can paint the same car in y hours. They start working simultaneously and independently at their respective constant rates at 9:45am. If both x and y are odd integers, is x=y?

Bonnie and Clyde when working together complete the painting of the car ins \frac{xy}{x+y} hours (sum of the rates equal to the combined rate or reciprocal of total time: \frac{1}{x}+\frac{1}{y}=\frac{1}{T} --> T=\frac{xy}{x+y}). Now, if x=y then the total time would be: \frac{x^2}{2x}=\frac{x}{2}, since x is odd then this time would be odd/2: 0.5 hours, 1.5 hours, 2.5 hours, ....

(1) x^2+y^2<12 --> it's possible x and y to be odd and equal to each other if x=y=1 but it's also possible that x=1 and y=3 (or vise-versa). Not sufficient.

(2) Bonnie and Clyde complete the painting of the car at 10:30am --> they complete the job in 3/4 of an hour (45 minutes), since it's not odd/2 then x and y are not equal. Sufficient.

Answer: B.
i didnot understand this..... the questions says if they are working independently.... why are you considering combined rate? my analysis I ended up at the same answer though
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19020
Followers: 3358

Kudos [?]: 24331 [0], given: 2676

Re: The Discreet Charm of the DS [#permalink] New post 13 Dec 2012, 02:24
Expert's post
Amateur wrote:
Bunuel wrote:
SOLUTIONS:

1. Bonnie can paint a stolen car in x hours, and Clyde can paint the same car in y hours. They start working simultaneously and independently at their respective constant rates at 9:45am. If both x and y are odd integers, is x=y?

Bonnie and Clyde when working together complete the painting of the car ins \frac{xy}{x+y} hours (sum of the rates equal to the combined rate or reciprocal of total time: \frac{1}{x}+\frac{1}{y}=\frac{1}{T} --> T=\frac{xy}{x+y}). Now, if x=y then the total time would be: \frac{x^2}{2x}=\frac{x}{2}, since x is odd then this time would be odd/2: 0.5 hours, 1.5 hours, 2.5 hours, ....

(1) x^2+y^2<12 --> it's possible x and y to be odd and equal to each other if x=y=1 but it's also possible that x=1 and y=3 (or vise-versa). Not sufficient.

(2) Bonnie and Clyde complete the painting of the car at 10:30am --> they complete the job in 3/4 of an hour (45 minutes), since it's not odd/2 then x and y are not equal. Sufficient.

Answer: B.
i didnot understand this..... the questions says if they are working independently.... why are you considering combined rate? my analysis I ended up at the same answer though


Because they are working simultaneously and independently to paint the same car.
_________________

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.


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

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Current Student
User avatar
Status: Waiting
Joined: 11 Dec 2012
Posts: 73
Location: Bahrain
Concentration: Healthcare, General Management
GMAT 1: 640 Q49 V24
GMAT 2: 720 Q49 V40
WE: Sales (Other)
Followers: 2

Kudos [?]: 42 [0], given: 144

Reviews Badge
Re: The Discreet Charm of the DS [#permalink] New post 29 Dec 2012, 06:37
Bunuel wrote:
2. Is xy<=1/2?

(1) x^2+y^2=1. Recall that (x-y)^2\geq{0} (square of any number is more than or equal to zero) --> x^2-2xy+y^2\geq{0} --> since x^2+y^2=1 then: 1-2xy\geq{0} --> xy\leq{\frac{1}{2}}. Sufficient.

(2) x^2-y^2=0 --> |x|=|y|. Clearly insufficient.

Answer: A.


Dear Bunuel

Why haven't we used (x+y)^2 instead of (x-y)^2 in statement 1 ? Sorry if its a silly question :?
_________________

--
Piyush Jain
GMAT Debrief | Personal Blog | Twitter | LinkedIn

Manager
Manager
avatar
Status: K... M. G...
Joined: 22 Oct 2012
Posts: 51
Concentration: General Management, Leadership
GMAT Date: 08-27-2013
GPA: 3.8
Followers: 0

Kudos [?]: 6 [0], given: 118

Re: The Discreet Charm of the DS [#permalink] New post 11 Feb 2013, 02:38
Bunuel wrote:
SOLUTIONS:

1. Bonnie can paint a stolen car in x hours, and Clyde can paint the same car in y hours. They start working simultaneously and independently at their respective constant rates at 9:45am. If both x and y are odd integers, is x=y?

Bonnie and Clyde when working together complete the painting of the car ins \frac{xy}{x+y} hours (sum of the rates equal to the combined rate or reciprocal of total time: \frac{1}{x}+\frac{1}{y}=\frac{1}{T} --> T=\frac{xy}{x+y}). Now, if x=y then the total time would be: \frac{x^2}{2x}=\frac{x}{2}, since x is odd then this time would be odd/2: 0.5 hours, 1.5 hours, 2.5 hours, ....

(1) x^2+y^2<12 --> it's possible x and y to be odd and equal to each other if x=y=1 but it's also possible that x=1 and y=3 (or vise-versa). Not sufficient.

(2) Bonnie and Clyde complete the painting of the car at 10:30am --> they complete the job in 3/4 of an hour (45 minutes), since it's not odd/2 then x and y are not equal. Sufficient.

Answer: B.



Hi,

Just a question, Only if we get a answer which is "odd/2" then x & y are considered to be equal . rite?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19020
Followers: 3358

Kudos [?]: 24331 [0], given: 2676

Re: The Discreet Charm of the DS [#permalink] New post 11 Feb 2013, 04:45
Expert's post
FTG wrote:
Bunuel wrote:
SOLUTIONS:

1. Bonnie can paint a stolen car in x hours, and Clyde can paint the same car in y hours. They start working simultaneously and independently at their respective constant rates at 9:45am. If both x and y are odd integers, is x=y?

Bonnie and Clyde when working together complete the painting of the car ins \frac{xy}{x+y} hours (sum of the rates equal to the combined rate or reciprocal of total time: \frac{1}{x}+\frac{1}{y}=\frac{1}{T} --> T=\frac{xy}{x+y}). Now, if x=y then the total time would be: \frac{x^2}{2x}=\frac{x}{2}, since x is odd then this time would be odd/2: 0.5 hours, 1.5 hours, 2.5 hours, ....

(1) x^2+y^2<12 --> it's possible x and y to be odd and equal to each other if x=y=1 but it's also possible that x=1 and y=3 (or vise-versa). Not sufficient.

(2) Bonnie and Clyde complete the painting of the car at 10:30am --> they complete the job in 3/4 of an hour (45 minutes), since it's not odd/2 then x and y are not equal. Sufficient.

Answer: B.



Hi,

Just a question, Only if we get a answer which is "odd/2" then x & y are considered to be equal . rite?


Yes, that's correct.
_________________

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.


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

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Director
Director
avatar
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 550
Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)
Followers: 2

Kudos [?]: 27 [0], given: 562

GMAT Tests User
Re: The Discreet Charm of the DS [#permalink] New post 13 Feb 2013, 23:31
Bunuel wrote:
12. If 6a=3b=7c, what is the value of a+b+c?

Given: 6a=3b=7c --> least common multiple of 6, 3, and 7 is 42 hence we ca write: 6a=3b=7c=42x, for some number x --> a=7x, b=14x and c=6x.

(1) ac=6b --> 7x*6x=6*14x --> x^2=2x --> x=0 or x=2. Not sufficient.

(2) 5b=8a+4c --> 5*14x=8*7x+4*14x --> 70x=80x --> 10x=0 --> x=0 --> a=b=c=0 --> a+b+c=0. Sufficient.

Answer: B.


Bunuel,
Here's how I did . I don't know why it is wrong. Please advise :

6a=3b=7c

=>
12a=6b=14c

From 1) ac=6b
=> ac=12a
=> c=12.. a can be cancelled because it is not inequality. .

so c =12..

however,

ac-12a=0 --> a(c-12)=0 so a=0 OR c=12 .. Is this the reason why my soln is wrong?
_________________

hope is a good thing, maybe the best of things. And no good thing ever dies.

Who says you need a 700 ?Check this out : http://gmatclub.com/forum/who-says-you-need-a-149706.html#p1201595

My GMAT Journey : end-of-my-gmat-journey-149328.html#p1197992

Manager
Manager
avatar
Joined: 28 Aug 2012
Posts: 52
Concentration: Operations, Marketing
GMAT 1: 510 Q36 V25
GPA: 4
WE: Information Technology (Other)
Followers: 0

Kudos [?]: 46 [0], given: 105

Re: The Discreet Charm of the DS [#permalink] New post 14 Feb 2013, 00:24
Bunuel wrote:
SOLUTIONS:

1. Bonnie can paint a stolen car in x hours, and Clyde can paint the same car in y hours. They start working simultaneously and independently at their respective constant rates at 9:45am. If both x and y are odd integers, is x=y?

Bonnie and Clyde when working together complete the painting of the car ins \frac{xy}{x+y} hours (sum of the rates equal to the combined rate or reciprocal of total time: \frac{1}{x}+\frac{1}{y}=\frac{1}{T} --> T=\frac{xy}{x+y}). Now, if x=y then the total time would be: \frac{x^2}{2x}=\frac{x}{2}, since x is odd then this time would be odd/2: 0.5 hours, 1.5 hours, 2.5 hours, ....

(1) x^2+y^2<12 --> it's possible x and y to be odd and equal to each other if x=y=1 but it's also possible that x=1 and y=3 (or vise-versa). Not sufficient.

(2) Bonnie and Clyde complete the painting of the car at 10:30am --> they complete the job in 3/4 of an hour (45 minutes), since it's not odd/2 then x and y are not equal. Sufficient.

Answer: B.


Bunuel,
I did not understand the reasoning behind statement 2 being sufficient. Line marked in red is my doubt. what does it mean ?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19020
Followers: 3358

Kudos [?]: 24331 [0], given: 2676

Re: The Discreet Charm of the DS [#permalink] New post 14 Feb 2013, 01:08
Expert's post
Sachin9 wrote:
Bunuel wrote:
12. If 6a=3b=7c, what is the value of a+b+c?

Given: 6a=3b=7c --> least common multiple of 6, 3, and 7 is 42 hence we ca write: 6a=3b=7c=42x, for some number x --> a=7x, b=14x and c=6x.

(1) ac=6b --> 7x*6x=6*14x --> x^2=2x --> x=0 or x=2. Not sufficient.

(2) 5b=8a+4c --> 5*14x=8*7x+4*14x --> 70x=80x --> 10x=0 --> x=0 --> a=b=c=0 --> a+b+c=0. Sufficient.

Answer: B.


Bunuel,
Here's how I did . I don't know why it is wrong. Please advise :

6a=3b=7c

=>
12a=6b=14c

From 1) ac=6b
=> ac=12a
=> c=12.. a can be cancelled because it is not inequality. .

so c =12..

however,

ac-12a=0 --> a(c-12)=0 so a=0 OR c=12 .. Is this the reason why my soln is wrong?


Never reduce an equation by a variable (or expression with a variable), if you are not certain that the variable (or the expression with a variable) doesn't equal to zero. We can not divide by zero.

So, if you divide (reduce) ac=12a by a, you assume, with no ground for it, that a does not equal to zero thus exclude a possible solution (notice that both a=0 AND c-12=0 satisfy the equation).

Hope it's clear.
_________________

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.


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

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19020
Followers: 3358

Kudos [?]: 24331 [0], given: 2676

Re: The Discreet Charm of the DS [#permalink] New post 14 Feb 2013, 01:16
Expert's post
thinktank wrote:
Bunuel wrote:
SOLUTIONS:

1. Bonnie can paint a stolen car in x hours, and Clyde can paint the same car in y hours. They start working simultaneously and independently at their respective constant rates at 9:45am. If both x and y are odd integers, is x=y?

Bonnie and Clyde when working together complete the painting of the car ins \frac{xy}{x+y} hours (sum of the rates equal to the combined rate or reciprocal of total time: \frac{1}{x}+\frac{1}{y}=\frac{1}{T} --> T=\frac{xy}{x+y}). Now, if x=y then the total time would be: \frac{x^2}{2x}=\frac{x}{2}, since x is odd then this time would be odd/2: 0.5 hours, 1.5 hours, 2.5 hours, ....

(1) x^2+y^2<12 --> it's possible x and y to be odd and equal to each other if x=y=1 but it's also possible that x=1 and y=3 (or vise-versa). Not sufficient.

(2) Bonnie and Clyde complete the painting of the car at 10:30am --> they complete the job in 3/4 of an hour (45 minutes), since it's not odd/2 then x and y are not equal. Sufficient.

Answer: B.


Bunuel,
I did not understand the reasoning behind statement 2 being sufficient. Line marked in red is my doubt. what does it mean ?


From the stem we got that if x=y then the total time would be: \frac{x^2}{2x}=\frac{x}{2}, since x is odd then this time would be odd/2: 0.5 hours (1/2 hours = 0.5 hours), 1.5 hours (3/2 hours = 1.5 hours), 2.5 hours (5/2 hours = 2.5 hours), 3.5 hours (7/2 hours = 3.5 hours), 4.5 hours (9/2 hours = 4.5 hours), ....

Now, from the second statement we got that they complete the job in 0.75 hours, since the total time (0.75 hours) is NOT odd/2 (0.5 hours, 1.5 hours, 2.5 hours, 3.5 hours, 4.5 hours, ....), then x and y are not equal.

Hope it's clear.
_________________

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.


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

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 28 Aug 2012
Posts: 52
Concentration: Operations, Marketing
GMAT 1: 510 Q36 V25
GPA: 4
WE: Information Technology (Other)
Followers: 0

Kudos [?]: 46 [0], given: 105

Re: The Discreet Charm of the DS [#permalink] New post 14 Feb 2013, 01:44
Crystal Clear..Thanks Bunuel :)
Director
Director
avatar
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 550
Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)
Followers: 2

Kudos [?]: 27 [0], given: 562

GMAT Tests User
Re: The Discreet Charm of the DS [#permalink] New post 14 Feb 2013, 01:48
Bunuel wrote:
Sachin9 wrote:
Bunuel wrote:
12. If 6a=3b=7c, what is the value of a+b+c?

Given: 6a=3b=7c --> least common multiple of 6, 3, and 7 is 42 hence we ca write: 6a=3b=7c=42x, for some number x --> a=7x, b=14x and c=6x.

(1) ac=6b --> 7x*6x=6*14x --> x^2=2x --> x=0 or x=2. Not sufficient.

(2) 5b=8a+4c --> 5*14x=8*7x+4*14x --> 70x=80x --> 10x=0 --> x=0 --> a=b=c=0 --> a+b+c=0. Sufficient.

Answer: B.


Bunuel,
Here's how I did . I don't know why it is wrong. Please advise :

6a=3b=7c

=>
12a=6b=14c

From 1) ac=6b
=> ac=12a
=> c=12.. a can be cancelled because it is not inequality. .

so c =12..

however,

ac-12a=0 --> a(c-12)=0 so a=0 OR c=12 .. Is this the reason why my soln is wrong?


Never reduce an equation by a variable (or expression with a variable), if you are not certain that the variable (or the expression with a variable) doesn't equal to zero. We can not divide by zero.

So, if you divide (reduce) ac=12a by a, you assume, with no ground for it, that a does not equal to zero thus exclude a possible solution (notice that both a=0 AND c-12=0 satisfy the equation).

Hope it's clear.


thanks alot. .you rock man!! r u a phd in maths ;) ?
_________________

hope is a good thing, maybe the best of things. And no good thing ever dies.

Who says you need a 700 ?Check this out : http://gmatclub.com/forum/who-says-you-need-a-149706.html#p1201595

My GMAT Journey : end-of-my-gmat-journey-149328.html#p1197992

Manager
Manager
avatar
Joined: 05 Nov 2012
Posts: 72
Concentration: International Business, Operations
Schools: Foster '15 (S)
GPA: 3.65
Followers: 1

Kudos [?]: 42 [0], given: 8

GMAT ToolKit User
Re: The Discreet Charm of the DS [#permalink] New post 23 Feb 2013, 15:17
Bunuel wrote:
3. If a, b and c are integers, is abc an even integer?

In order the product of the integers to be even at leas on of them must be even

(1) b is halfway between a and c --> on the GMAT we often see such statement and it can ALWAYS be expressed algebraically as b=\frac{a+c}{2}. Now, does that mean that at leas on of them is be even? Not necessarily, consider a=1, b=3 and c=5. Of course it's also possible that b=even, for example if a=1 and b=7. Not sufficient.

(2) a = b - c --> a+c=b. Since it's not possible that the sum of two odd integers to be odd then the case of 3 odd numbers is ruled out, hence at least on of them must be even. Sufficient.

Answer: B.


1) b = a+c/2 i.e. a+c = even (as it is divisible by 2) and an even# divided by another even# can be odd or even (e.g. 46/2 = 23 an odd, but 48/2 = 24 an even). now if a + c = odd + odd = even and if a+c/2 = odd then all 3 numbers are odd (e.g. a=21, b=23 and c=25) and abc = odd but if a+c = even+even then a+c/2 = odd and abc = even (a=22, b=24 and c=26). so insufficient
2) a = b - c i.e. a + c = b. from number properties we know that
i) odd+odd = even,
ii) even+odd = odd
iii) even+even = even
so in any of the 3 cases you will end up with atleast one number that is even and hence abc = even. sufficient. correct ans. B
_________________

___________________________________________
Consider +1 Kudos if my post helped

Intern
Intern
avatar
Joined: 27 Jul 2011
Posts: 47
Followers: 1

Kudos [?]: 16 [0], given: 2

Re: The Discreet Charm of the DS [#permalink] New post 23 May 2013, 14:59
Hi Brunnel,
I have trouble with question 9 for the second statement, 2x-3<3y-4, when I substitute x=-5; y= -1; the equation holds but when I substitute x=-2; y=-5; the equation collapsed. So, wouldn't the answer be E? Please help explain, Thanks.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19020
Followers: 3358

Kudos [?]: 24331 [0], given: 2676

Re: The Discreet Charm of the DS [#permalink] New post 23 May 2013, 15:09
Expert's post
smartyman wrote:
Hi Brunnel,
I have trouble with question 9 for the second statement, 2x-3<3y-4, when I substitute x=-5; y= -1; the equation holds but when I substitute x=-2; y=-5; the equation collapsed. So, wouldn't the answer be E? Please help explain, Thanks.


The question does not ask whether 2x - 3 < 3y - 4, it asks whether x<y. While 2x - 3 < 3y - 4 is given to be true by the second statement.
_________________

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.


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

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 16 Jan 2013
Posts: 5
Concentration: Marketing, International Business
GMAT Date: 07-05-2013
Followers: 0

Kudos [?]: 1 [0], given: 23

Re: The Discreet Charm of the DS [#permalink] New post 05 Jun 2013, 13:19
Bunuel wrote:
10. The function f is defined for all positive integers a and b by the following rule: f(a,b)=(a+b)/GCF(a,b), where GCF(a,b) is the greatest common factor of a and b. If f(10,x)=11, what is the value of x?

Notice that the greatest common factor of 10 and x, GCF(10,x), naturally must be a factor of 10: 1, 2, 5, and 10. Thus from f(10,x)=11 we can get four different values of x:

GCF(10,x)=1 --> f(10,x)=11=\frac{10+x}{1} --> x=1;
GCF(10,x)=2 --> f(10,x)=11=\frac{10+x}{2} --> x=12;
GCF(10,x)=5 --> f(10,x)=11=\frac{10+x}{5} --> x=45;
GCF(10,x)=10 --> f(10,x)=11=\frac{10+x}{10} --> x=100.

(1) x is a square of an integer --> x can be 1 or 100. Not sufficient.

(2) The sum of the distinct prime factors of x is a prime number ---> distinct primes of 12 are 2 and 3: 2+3=5=prime, distinct primes of 45 are 3 and 5: 3+5=8\neq{prime} and distinct primes of 100 are 2 and 5: 2+5=7=prime. x can be 12 or 100. Not sufficient.

(1)+(2) x can only be 100. Sufficient.

Answer: C.



I think the answer to the above questions should be "A" not "C".
Since the GCD for 10 and x can only be 1,2,5 and 10, the corresponding value for x can be 1, 12, 45 and 100. Given this information, the first clause leaves only 100 as the correct answer, which is a square of 10. Please let me know if there is any flaw in my reasoning.
Intern
Intern
avatar
Joined: 16 Jan 2013
Posts: 5
Concentration: Marketing, International Business
GMAT Date: 07-05-2013
Followers: 0

Kudos [?]: 1 [0], given: 23

Re: The Discreet Charm of the DS [#permalink] New post 05 Jun 2013, 22:17
Bunuel wrote:
9. If x and y are negative numbers, is x<y?

(1) 3x + 4 < 2y + 3 --> 3x<2y-1. x can be some very small number for instance -100 and y some large enough number for instance -3 and the answer would be YES, x<y BUT if x=-2 and y=-2.1 then the answer would be NO, x>y. Not sufficient.

(2) 2x - 3 < 3y - 4 --> x<1.5y-\frac{1}{2} --> x<y+(0.5y-\frac{1}{2})=y+negative --> x<y (as y+negative is "more negative" than y). Sufficient.

Answer: B.


Hi Bunuel,

First of all, great set of questions.

I have a little doubt around the explanation given for Q9 Clause 2. You mentioned the following as your explanation:


(2) 2x - 3 < 3y - 4 --> x<1.5y-\frac{1}{2} --> x<y+(0.5y-\frac{1}{2})=y+negative --> x<y (as y+negative is "more negative" than y). Sufficient.

However, the questions is whether x<y. If x< y-(any negative term) doesn't mean that X< Y. For example: if x= -5 y= -3 (Here x<Y) and according to the above equation -5<-3 but -5<-3 + (a negative term, say -3) will make the questions incorrect.

Please tell me where I am going wrong with this. Thanks!
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19020
Followers: 3358

Kudos [?]: 24331 [0], given: 2676

Re: The Discreet Charm of the DS [#permalink] New post 05 Jun 2013, 23:20
Expert's post
narulajasneet wrote:
Bunuel wrote:
10. The function f is defined for all positive integers a and b by the following rule: f(a,b)=(a+b)/GCF(a,b), where GCF(a,b) is the greatest common factor of a and b. If f(10,x)=11, what is the value of x?

Notice that the greatest common factor of 10 and x, GCF(10,x), naturally must be a factor of 10: 1, 2, 5, and 10. Thus from f(10,x)=11 we can get four different values of x:

GCF(10,x)=1 --> f(10,x)=11=\frac{10+x}{1} --> x=1;
GCF(10,x)=2 --> f(10,x)=11=\frac{10+x}{2} --> x=12;
GCF(10,x)=5 --> f(10,x)=11=\frac{10+x}{5} --> x=45;
GCF(10,x)=10 --> f(10,x)=11=\frac{10+x}{10} --> x=100.

(1) x is a square of an integer --> x can be 1 or 100. Not sufficient.

(2) The sum of the distinct prime factors of x is a prime number ---> distinct primes of 12 are 2 and 3: 2+3=5=prime, distinct primes of 45 are 3 and 5: 3+5=8\neq{prime} and distinct primes of 100 are 2 and 5: 2+5=7=prime. x can be 12 or 100. Not sufficient.

(1)+(2) x can only be 100. Sufficient.

Answer: C.



I think the answer to the above questions should be "A" not "C".
Since the GCD for 10 and x can only be 1,2,5 and 10, the corresponding value for x can be 1, 12, 45 and 100. Given this information, the first clause leaves only 100 as the correct answer, which is a square of 10. Please let me know if there is any flaw in my reasoning.


x could be 1, 12, 45 or 100.

(1) says that x is a square of an integer --> x could be 1^2=1 or 10^2=100. Two answers, thus the statement is insufficient.

Hope it's clear.
_________________

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.


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

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19020
Followers: 3358

Kudos [?]: 24331 [0], given: 2676

Re: The Discreet Charm of the DS [#permalink] New post 05 Jun 2013, 23:27
Expert's post
narulajasneet wrote:
Bunuel wrote:
9. If x and y are negative numbers, is x<y?

(1) 3x + 4 < 2y + 3 --> 3x<2y-1. x can be some very small number for instance -100 and y some large enough number for instance -3 and the answer would be YES, x<y BUT if x=-2 and y=-2.1 then the answer would be NO, x>y. Not sufficient.

(2) 2x - 3 < 3y - 4 --> x<1.5y-\frac{1}{2} --> x<y+(0.5y-\frac{1}{2})=y+negative --> x<y (as y+negative is "more negative" than y). Sufficient.

Answer: B.


Hi Bunuel,

First of all, great set of questions.

I have a little doubt around the explanation given for Q9 Clause 2. You mentioned the following as your explanation:

(2) 2x - 3 < 3y - 4 --> x<1.5y-\frac{1}{2} --> x<y+(0.5y-\frac{1}{2})=y+negative --> x<y (as y+negative is "more negative" than y). Sufficient.

However, the questions is whether x<y. If x< y-(any negative term) doesn't mean that X< Y. For example: if x= -5 y= -3 (Here x<Y) and according to the above equation -5<-3 but -5<-3 + (a negative term, say -3) will make the questions incorrect.

Please tell me where I am going wrong with this. Thanks!


It's the other way around: if x and y are negative numbers and IF x<y+negative, then x<y.
_________________

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.


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

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: The Discreet Charm of the DS   [#permalink] 05 Jun 2013, 23:27
    Similar topics Author Replies Last post
Similar
Topics:
4 Experts publish their posts in the topic Serious individual art collectors are usually discreet when espa 7 17 Jun 2013, 23:00
Third time's a charm. vwjetty 1 20 Jul 2010, 11:09
Discreet Profile Evaluation almostfamous 1 23 Oct 2009, 19:31
7 Experts publish their posts in the topic Second try is the charm 710 (48 q, 38 v) mohater 15 21 Jun 2009, 13:13
4 times the charm uclandru 4 13 Nov 2005, 23:12
Display posts from previous: Sort by

The Discreet Charm of the DS

  Question banks Downloads My Bookmarks Reviews Important topics  

Go to page   Previous    1   2   3   4   5   6   7   8    Next  [ 145 posts ] 



GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.