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

 It is currently 05 Aug 2015, 03:15

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# The Discreet Charm of the DS

Author Message
TAGS:
Math Expert
Joined: 02 Sep 2009
Posts: 28785
Followers: 4607

Kudos [?]: 47722 [28] , given: 7132

The Discreet Charm of the DS [#permalink]  02 Feb 2012, 03:15
28
KUDOS
Expert's post
67
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
_________________
 Kaplan GMAT Prep Discount Codes Knewton GMAT Discount Codes Veritas Prep GMAT Discount Codes
Manager
Joined: 26 Jun 2011
Posts: 249
Location: India
GMAT 1: 760 Q51 V41
Followers: 11

Kudos [?]: 47 [1] , given: 26

Re: The Discreet Charm of the DS [#permalink]  03 Feb 2012, 16:37
1
KUDOS
Bunuel wrote:
sourabhsoni wrote:
2. Is xy<=1/2?
(1) x^2+y^2=1
(2) x^2-y^2=0

My funda - Area of square is largest among all the quadilateral with same perimeter.
Stmt 1 - Only possible values of x and y are 1/Sqrt(2). So sufficient as xy = 1/2
Stmt 2 - Only says x and y are equal. Not sufficient

You are close to correct reasoning for (1), though from it you can not say that xy=1/2 and the only possible value for x and y are 1/Sqrt(2). Consider the following example: 0^1+1^2=1.

As for (2): x^2-y^2=0 doesn't mean that x=y.

1) x2 + y2 = 1 is a circle with radius 1, and origin as center. We are only concerned with 1st and 3rd quad (think why? ), Draw a line y=x which intersects circle at x=y=1/sqrt(2). We can observe, as x becomes greater than 1/sqrt2, y gets lesser than 1/sqrt2 moving on the circle (below y=x line). Hence xy<= 1/2. Similarly, as y becomes greater than 1/sqrt2, x gets lesser than 1/sqrt2 moving on the circle (above y=x line). Hence xy<= 1/2. Hence sufficient.

For more mathematically inclined, draw graph of xy=1/2. It has only one point of contact with the circle, tangential at x=y=1/sqrt(2).
Attachments

gmatclub exp.png [ 10.25 KiB | Viewed 14999 times ]

_________________

The chase begins ...

Math Expert
Joined: 02 Sep 2009
Posts: 28785
Followers: 4607

Kudos [?]: 47722 [1] , given: 7132

Re: The Discreet Charm of the DS [#permalink]  03 Feb 2012, 17:08
1
KUDOS
Expert's post
IMO, if you can imagine drawing the circle and y=x line, it takes less than 30 sec. to figure it out. It only takes so much longer to explain in text. And ofcourse, no need to draw the xy graph.
Will wait though for the even faster method, if any.

If you answered this question in less than 30 sec using this approach then all I can say is great job!

As for the easier/faster solution, little hint: it involves simplest algebraic manipulation.
_________________
Manager
Joined: 26 Jun 2011
Posts: 249
Location: India
GMAT 1: 760 Q51 V41
Followers: 11

Kudos [?]: 47 [1] , given: 26

Re: The Discreet Charm of the DS [#permalink]  03 Feb 2012, 17:20
1
KUDOS
Bunuel wrote:
If you answered this question in less than 30 sec using this approach then all I can say is great job!

As for the easier/faster solution, little hint: it involves simplest algebraic manipulation.

F***ing good !

(x-y)2 = 1-2xy >=0 => xy>=1/2.

Now this should take 15sec !
_________________

The chase begins ...

Manager
Status: Retaking next month
Affiliations: None
Joined: 05 Mar 2011
Posts: 229
Location: India
Concentration: Marketing, Entrepreneurship
GMAT 1: 570 Q42 V27
GPA: 3.01
WE: Sales (Manufacturing)
Followers: 5

Kudos [?]: 29 [1] , given: 34

Re: The Discreet Charm of the DS [#permalink]  04 Feb 2012, 01:03
1
KUDOS
sourabhsoni wrote:
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.

prime # are always positive

Stmt 1 - |y| will be always positive to x*|y| to be prime z has to be positve. Sufficient
Stmt 2 - Same concept x will be positive number Sufficient

Statement 2: x can be zero or +. ( x*|y| is a non negative integer. i.eit can be 0 as well.. NS)
Math Expert
Joined: 02 Sep 2009
Posts: 28785
Followers: 4607

Kudos [?]: 47722 [1] , given: 7132

Re: The Discreet Charm of the DS [#permalink]  16 May 2012, 00:39
1
KUDOS
Expert's post
piyushksharma 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.

Hi bunuel,
Did not got how u solved option 2.Could you please explain in detail.
thanks.

(2) 2x - 3 < 3y - 4 --> $$x<1.5y-\frac{1}{2}$$ --> $$x<y+(0.5y-\frac{1}{2})$$. Now, since $$y$$ is a negative number then $$0.5y-\frac{1}{2}=negative$$ so, we have that: $$x<y+negative$$. $$y+negative$$ is less then $$y$$ and if $$x$$ is less than $$y+negative$$ then it must also be less than $$y$$ itself: $$x<y$$.

Hope it's clear.
_________________
Intern
Joined: 13 Mar 2012
Posts: 20
GMAT 1: 700 Q50 V34
Followers: 0

Kudos [?]: 22 [1] , given: 9

Re: The Discreet Charm of the DS [#permalink]  19 May 2012, 07:13
1
KUDOS
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 also 2 and 3: $$2+3=5=prime$$. $$x$$ can be 12 or 100. Not sufficient.

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

hey..., can sm1 pls explain how primes of 100 can be 2 and 3?...(2nd last line),,..
thanx..
Math Expert
Joined: 02 Sep 2009
Posts: 28785
Followers: 4607

Kudos [?]: 47722 [1] , given: 7132

Re: The Discreet Charm of the DS [#permalink]  19 May 2012, 07:20
1
KUDOS
Expert's post
vivekdhawan 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 also 2 and 3: $$2+3=5=prime$$. $$x$$ can be 12 or 100. Not sufficient.

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

hey..., can sm1 pls explain how primes of 100 can be 2 and 3?...(2nd last line),,..
thanx..

It should be: "... distinct primes of 100 are 2 and 5: $$2+5=7=prime$$. $$x$$ can be 12 or 100".
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 28785
Followers: 4607

Kudos [?]: 47722 [1] , given: 7132

Re: The Discreet Charm of the DS [#permalink]  10 Aug 2013, 23:33
1
KUDOS
Expert's post
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.

I followed a different approach but I am getting that (1) also answers the question.

From 3b=7c => 6b=14c.

So ac=6b - equation 1)
14c=6b - equation 2)

Dividing 1) by 2) =>a/14= 1

You cannot divide ac by 14c because c could be zero and division by zero is not allowed. The same applies to division of 6b by 6b.

Does this make sense?
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 28785
Followers: 4607

Kudos [?]: 47722 [1] , given: 7132

Re: The Discreet Charm of the DS [#permalink]  22 Oct 2014, 06:03
1
KUDOS
Expert's post
sagarjain90 wrote:
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.

Hi Bunuel,
I considered $$(x+y)^2$$ $$>=$$ 0 and arrived at $$xy >=$$ $$\frac{-1}{2}$$.
And hence concluded that the statement is insufficient.

Yes, you need to consider $$(x-y)^2\geq{0}$$ to get sufficiency.
_________________
Intern
Joined: 04 Aug 2011
Posts: 45
Location: United States
GMAT 1: 570 Q45 V25
GPA: 4
WE: Information Technology (Computer Software)
Followers: 0

Kudos [?]: 14 [0], given: 20

Re: The Discreet Charm of the DS [#permalink]  02 Feb 2012, 05:55
1. B
2. A
3. B
4. D
5. D
6. E
7. D
8. C
9. B
10. C
11. D
12. E
Manager
Joined: 06 Oct 2011
Posts: 165
Schools: Wharton '15, CBS '15
GMAT Date: 06-30-2012
GPA: 3.7
WE: Accounting (Insurance)
Followers: 3

Kudos [?]: 61 [0], given: 10

Re: The Discreet Charm of the DS [#permalink]  02 Feb 2012, 06:48
time to get cracking... thanks for posting
_________________

Reward wisdom with kudos

Intern
Joined: 16 Jan 2012
Posts: 32
Followers: 0

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

Re: The Discreet Charm of the DS [#permalink]  02 Feb 2012, 10:55
1-b
2-a
3-b
4-a
5-b
6-e
7-d
8-b
9-e
10-a
11-d
12-a
Intern
Joined: 13 Jul 2011
Posts: 45
Followers: 0

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

Re: The Discreet Charm of the DS [#permalink]  02 Feb 2012, 18:01
Ans:
1-B
2-A
3-A
4-E
5-D
6-E
7-C
8-A
9-C
10-A
11-D
12-D
Math Expert
Joined: 02 Sep 2009
Posts: 28785
Followers: 4607

Kudos [?]: 47722 [0], given: 7132

Re: The Discreet Charm of the DS [#permalink]  03 Feb 2012, 02:36
Expert's post
1.B
2.A
3.B
4.D
5.A
6.E

5 correct answers out of 6.

sourabhsoni wrote:
1. B
2. A
3. B
4. D
5. D
6. E
7. D
8. C
9. B
10. C
11. D
12. E

10 correct answers out of 12.

1-b
2-a
3-b
4-a
5-b
6-e
7-d
8-b
9-e
10-a
11-d
12-a

7 correct answers out of 12.

vinayaerostar wrote:
Ans:
1-B
2-A
3-A
4-E
5-D
6-E
7-C
8-A
9-C
10-A
11-D
12-D

4 correct answers out of 12.

Good job everyone! By the way it's better if you post the solutions along with the answers: others will benefit with your approaches and you'll get 1 Kudos point per correct solution.

Will post explanations in couple of days, so that to give some more time to those who want to participate.
_________________
Intern
Joined: 04 Aug 2011
Posts: 45
Location: United States
GMAT 1: 570 Q45 V25
GPA: 4
WE: Information Technology (Computer Software)
Followers: 0

Kudos [?]: 14 [0], given: 20

Re: The Discreet Charm of the DS [#permalink]  03 Feb 2012, 06:51
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

The catch is that they are working independently.

stmt 1 - no relation there are can be multiple values of x and y
stmt 2 - both started at same time, finished at same time with no breaks means they have same working rate proves x = y
sufficient

Intern
Joined: 04 Aug 2011
Posts: 45
Location: United States
GMAT 1: 570 Q45 V25
GPA: 4
WE: Information Technology (Computer Software)
Followers: 0

Kudos [?]: 14 [0], given: 20

Re: The Discreet Charm of the DS [#permalink]  03 Feb 2012, 06:56
2. Is xy<=1/2?
(1) x^2+y^2=1
(2) x^2-y^2=0

My funda - Area of square is largest among all the quadilateral with same perimeter.
Stmt 1 - Only possible values of x and y are 1/Sqrt(2). So sufficient as xy = 1/2
Stmt 2 - Only says x and y are equal. Not sufficient
Math Expert
Joined: 02 Sep 2009
Posts: 28785
Followers: 4607

Kudos [?]: 47722 [0], given: 7132

Re: The Discreet Charm of the DS [#permalink]  03 Feb 2012, 06:57
Expert's post
sourabhsoni wrote:
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

The catch is that they are working independently.

stmt 1 - no relation there are can be multiple values of x and y
stmt 2 - both started at same time, finished at same time with no breaks means they have same working rate proves x = y
sufficient

The logic for (2) is not correct, (though I'm not saying that (2) is insufficient). Even if two entities have different rates if they work together they both stop when the job is done.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 28785
Followers: 4607

Kudos [?]: 47722 [0], given: 7132

Re: The Discreet Charm of the DS [#permalink]  03 Feb 2012, 07:00
Expert's post
sourabhsoni wrote:
2. Is xy<=1/2?
(1) x^2+y^2=1
(2) x^2-y^2=0

My funda - Area of square is largest among all the quadilateral with same perimeter.
Stmt 1 - Only possible values of x and y are 1/Sqrt(2). So sufficient as xy = 1/2
Stmt 2 - Only says x and y are equal. Not sufficient

You are close to correct reasoning for (1), though from it you can not say that xy=1/2 and the only possible value for x and y are 1/Sqrt(2). Consider the following example: 0^1+1^2=1.

As for (2): x^2-y^2=0 doesn't mean that x=y.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 28785
Followers: 4607

Kudos [?]: 47722 [0], given: 7132

Re: The Discreet Charm of the DS [#permalink]  03 Feb 2012, 07:04
Expert's post
sourabhsoni wrote:
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

Funda for product abc to be even, if any one of them even then product will be even.

Stmt 1 - says b = (a+c)/2
means a+c is some even number.
E + E also results in even
O + O also results in Even and b can be anything even or odd
so not sufficient.

Stmt 2 - says a = b - c
say worst condition b an c are odd . will results in a even. or lets says any one among b or c is even then a off but since one number is even the product will be even so sufficient.

That's correct. +1.
_________________
Manager
Joined: 31 Jan 2012
Posts: 74
Followers: 2

Kudos [?]: 17 [0], given: 2

Re: The Discreet Charm of the DS [#permalink]  03 Feb 2012, 07:43
1)b
2)a
3)b
4)d
5)d
6)e
7)d
8)c
9)e
10)a
11)d
12)a
Re: The Discreet Charm of the DS   [#permalink] 03 Feb 2012, 07:43

Go to page   Previous    1   2   3   4   5   6   7   8   9    Next  [ 171 posts ]

Similar topics Replies Last post
Similar
Topics:
DS deduction 1 25 Jun 2011, 05:41
DS question 3 22 Apr 2011, 07:55
Inequalities - DS 4 16 Apr 2011, 05:28
ratio DS 11 08 Aug 2009, 08:34
5 DS Ques 10 24 Jun 2008, 23:17
Display posts from previous: Sort by