Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 39702

The Discreet Charm of the DS [#permalink]
Show Tags
02 Feb 2012, 04:15
23
This post received KUDOS
Expert's post
125
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: thediscreetcharmoftheds12696220.html#p10396332. Is xy<=1/2? (1) x^2+y^2=1 (2) x^2y^2=0 Solution: thediscreetcharmoftheds12696220.html#p10396343. 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: thediscreetcharmoftheds12696240.html#p10396374. 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: thediscreetcharmoftheds12696240.html#p10396455. What is the value of integer x?(1) 2x^2+9<9x (2) x+10=2x+8 Solution: thediscreetcharmoftheds12696240.html#p10396506. If a and b are integers and ab=2, is a=2?(1) b+3 is not a prime number (2) a>b Solution: thediscreetcharmoftheds12696240.html#p10396517. 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: thediscreetcharmoftheds12696240.html#p10396558. 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) ac>6 Solution: thediscreetcharmoftheds12696240.html#p10396629. If x and y are negative numbers, is x<y?(1) 3x + 4 < 2y + 3 (2) 2x  3 < 3y  4 Solution: thediscreetcharmoftheds12696240.html#p103966510. 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: thediscreetcharmoftheds12696240.html#p103967111. If x and y are integers, is x a positive integer?(1) x*y is a prime number. (2) x*y is nonnegative integer. Solution: thediscreetcharmoftheds12696240.html#p103967812. If 6a=3b=7c, what is the value of a+b+c?(1) ac=6b (2) 5b=8a+4c Solution: thediscreetcharmoftheds12696240.html#p1039680
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  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.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 12 Dec 2012
Posts: 4

Re: The Discreet Charm of the DS [#permalink]
Show Tags
12 Dec 2012, 07:00
Amazing collection bunuel, thanks a ton. Helped me a lot.



Manager
Joined: 05 Nov 2012
Posts: 170

Re: The Discreet Charm of the DS [#permalink]
Show Tags
12 Dec 2012, 19:36
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 viseversa). 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



Math Expert
Joined: 02 Sep 2009
Posts: 39702

Re: The Discreet Charm of the DS [#permalink]
Show Tags
13 Dec 2012, 03:24
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 viseversa). 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 the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  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.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Status: Waiting
Joined: 11 Dec 2012
Posts: 53
Location: Bahrain
Concentration: Healthcare, General Management
GMAT 1: 640 Q49 V24 GMAT 2: 720 Q49 V40
WE: Sales (Other)

Re: The Discreet Charm of the DS [#permalink]
Show Tags
29 Dec 2012, 07:37
Bunuel wrote: 2. Is xy<=1/2?
(1) x^2+y^2=1. Recall that \((xy)^2\geq{0}\) (square of any number is more than or equal to zero) > \(x^22xy+y^2\geq{0}\) > since \(x^2+y^2=1\) then: \(12xy\geq{0}\) > \(xy\leq{\frac{1}{2}}\). Sufficient.
(2) x^2y^2=0 > \(x=y\). Clearly insufficient.
Answer: A. Dear Bunuel Why haven't we used (x+y)^2 instead of (xy)^2 in statement 1 ? Sorry if its a silly question



Manager
Status: K... M. G...
Joined: 22 Oct 2012
Posts: 51
Concentration: General Management, Leadership
GMAT Date: 08272013
GPA: 3.8

Re: The Discreet Charm of the DS [#permalink]
Show Tags
11 Feb 2013, 03:38
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 viseversa). 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?



Math Expert
Joined: 02 Sep 2009
Posts: 39702

Re: The Discreet Charm of the DS [#permalink]
Show Tags
11 Feb 2013, 05:45
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 viseversa). 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 the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  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.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Director
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 520
Location: India
GMAT 1: 640 Q43 V34 GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)

Re: The Discreet Charm of the DS [#permalink]
Show Tags
14 Feb 2013, 00:31
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, ac12a=0 > a(c12)=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/whosaysyouneeda149706.html#p1201595
My GMAT Journey : http://gmatclub.com/forum/endofmygmatjourney149328.html#p1197992



Manager
Joined: 28 Aug 2012
Posts: 52
Concentration: Operations, Marketing
GPA: 4
WE: Information Technology (Other)

Re: The Discreet Charm of the DS [#permalink]
Show Tags
14 Feb 2013, 01:24
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 viseversa). 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 ?



Math Expert
Joined: 02 Sep 2009
Posts: 39702

Re: The Discreet Charm of the DS [#permalink]
Show Tags
14 Feb 2013, 02:08
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, ac12a=0 > a(c12)=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 c12=0 satisfy the equation). Hope it's clear.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  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.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Math Expert
Joined: 02 Sep 2009
Posts: 39702

Re: The Discreet Charm of the DS [#permalink]
Show Tags
14 Feb 2013, 02:16
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 viseversa). 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 the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  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.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 28 Aug 2012
Posts: 52
Concentration: Operations, Marketing
GPA: 4
WE: Information Technology (Other)

Re: The Discreet Charm of the DS [#permalink]
Show Tags
14 Feb 2013, 02:44
Crystal Clear..Thanks Bunuel



Director
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 520
Location: India
GMAT 1: 640 Q43 V34 GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)

Re: The Discreet Charm of the DS [#permalink]
Show Tags
14 Feb 2013, 02:48
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, ac12a=0 > a(c12)=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 c12=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/whosaysyouneeda149706.html#p1201595
My GMAT Journey : http://gmatclub.com/forum/endofmygmatjourney149328.html#p1197992



Manager
Joined: 05 Nov 2012
Posts: 71
Concentration: International Business, Operations
GPA: 3.65

Re: The Discreet Charm of the DS [#permalink]
Show Tags
23 Feb 2013, 16:17
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



Manager
Joined: 27 Jul 2011
Posts: 61

Re: The Discreet Charm of the DS [#permalink]
Show Tags
23 May 2013, 15:59
Hi Brunnel, I have trouble with question 9 for the second statement, 2x3<3y4, 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.



Math Expert
Joined: 02 Sep 2009
Posts: 39702

Re: The Discreet Charm of the DS [#permalink]
Show Tags
23 May 2013, 16:09



AGSM Thread Master
Joined: 17 Jan 2013
Posts: 18
Location: India

Re: The Discreet Charm of the DS [#permalink]
Show Tags
05 Jun 2013, 14:19
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.



AGSM Thread Master
Joined: 17 Jan 2013
Posts: 18
Location: India

Re: The Discreet Charm of the DS [#permalink]
Show Tags
05 Jun 2013, 23:17
Bunuel wrote: 9. If x and y are negative numbers, is x<y?
(1) 3x + 4 < 2y + 3 > \(3x<2y1\). \(x\) 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!



Math Expert
Joined: 02 Sep 2009
Posts: 39702

Re: The Discreet Charm of the DS [#permalink]
Show Tags
06 Jun 2013, 00:20
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, t he 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 the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  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.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Math Expert
Joined: 02 Sep 2009
Posts: 39702

Re: The Discreet Charm of the DS [#permalink]
Show Tags
06 Jun 2013, 00:27
narulajasneet wrote: Bunuel wrote: 9. If x and y are negative numbers, is x<y?
(1) 3x + 4 < 2y + 3 > \(3x<2y1\). \(x\) 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 the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  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.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



AGSM Thread Master
Joined: 17 Jan 2013
Posts: 18
Location: India

Re: The Discreet Charm of the DS [#permalink]
Show Tags
06 Jun 2013, 01:29
Bunuel wrote: narulajasneet wrote: Bunuel wrote: 9. If x and y are negative numbers, is x<y?
(1) 3x + 4 < 2y + 3 > \(3x<2y1\). \(x\) 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. Sorry for confusion. I was actually taking x<y to be true and thinking how it can prove x < y(negative number). Thanks a lot!
Your posts are amazing and great learning!




Re: The Discreet Charm of the DS
[#permalink]
06 Jun 2013, 01:29



Go to page
Previous
1 2 3 4 5 6 7 8 9 10
Next
[ 190 posts ]




