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

 It is currently 01 Jul 2016, 17:26

### 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:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 33600
Followers: 5956

Kudos [?]: 74025 [28] , given: 9906

The Discreet Charm of the DS [#permalink]

### Show Tags

02 Feb 2012, 04:15
28
KUDOS
Expert's post
88
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
_________________
Manager
Joined: 31 Jan 2012
Posts: 74
Followers: 2

Kudos [?]: 19 [0], given: 2

Re: The Discreet Charm of the DS [#permalink]

### Show Tags

06 Feb 2012, 08:43
Hey Bunuel can I ask a question for 12?

We know 6a=3b

And for statement one:

ac =6b. Can't 6b =12a

Then it becomes ac=12a ==> c=12. I know it's wrong since if a is 0 then they will be equal regardless, but can you explain why what I did was wrong?
Intern
Joined: 29 Jan 2012
Posts: 21
Location: United Kingdom
Concentration: Finance, General Management
GMAT 1: 660 Q45 V35
GMAT 2: 720 Q47 V42
GPA: 3.53
Followers: 0

Kudos [?]: 7 [0], given: 4

Re: The Discreet Charm of the DS [#permalink]

### Show Tags

06 Feb 2012, 09:24
kys123 wrote:
Hey Bunuel can I ask a question for 12?

We know 6a=3b

And for statement one:

ac =6b. Can't 6b =12a

Then it becomes ac=12a ==> c=12. I know it's wrong since if a is 0 then they will be equal regardless, but can you explain why what I did was wrong?

Also,

6a = 3b = 7c

Can we say a/b= 1/2, b/c = 7/3, and a/c = 7/6
a) ac = 6b, therefore c = 6b/a
substituting this in b/c => b / (6b/a) = 7/3 => a =14, b=28, c = 12

Isnt A also sufficient? Am I ignoring something?
Math Expert
Joined: 02 Sep 2009
Posts: 33600
Followers: 5956

Kudos [?]: 74025 [0], given: 9906

Re: The Discreet Charm of the DS [#permalink]

### Show Tags

06 Feb 2012, 09:54
Expert's post
kys123 wrote:
Hey Bunuel can I ask a question for 12?

We know 6a=3b

And for statement one:

ac =6b. Can't 6b =12a

Then it becomes ac=12a ==> c=12. I know it's wrong since if a is 0 then they will be equal regardless, but can you explain why what I did was wrong?

ac=12a (here you can not reduce by a and write c=12 as you exclude possibility of a=0) --> a(c-12)=0 --> either a=0 OR c=12. So, we get either a=b=c=0 or a=14, b=28 and c=12.

nhemdani wrote:
Also,

6a = 3b = 7c

Can we say a/b= 1/2, b/c = 7/3, and a/c = 7/6
a) ac = 6b, therefore c = 6b/a
substituting this in b/c => b / (6b/a) = 7/3 => a =14, b=28, c = 12

Isnt A also sufficient? Am I ignoring something?

Your doubt is partially addressed above, though there is another thing: from 6a = 3b you can not write a/b=1/2 because b can be zero and we can not divide by zero. The same for other ratios you wrote.

Hope it's clear.
_________________
Manager
Joined: 03 Oct 2009
Posts: 62
Followers: 0

Kudos [?]: 85 [0], given: 8

Re: The Discreet Charm of the DS [#permalink]

### Show Tags

06 Feb 2012, 20:52
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 did this for option 1 -

ac=6b
ac=2 * 3 * b

since 6a=3b=7c

a c = 2 * 6a
c = 12
now we can find a and b also, so seems sufficient.

so where am i going wrong?
Manager
Joined: 31 Jan 2012
Posts: 74
Followers: 2

Kudos [?]: 19 [0], given: 2

Re: The Discreet Charm of the DS [#permalink]

### Show Tags

07 Feb 2012, 00:11
Well cause there is 2 options for statement 1.

ac = 3b ==>
ac = 12a
Now if a was 0 then 0*12 = 0*c ==> 6*0=3*0=7*0
a+b+c= 0
or

12a = ca
c=12
7*12(c)=3*28(b)=6*14(a)
a+b+c= 54.

There is 2 possible solutions, so you do not know if it's 0 or 54
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 [?]: 69 [0], given: 42

Re: The Discreet Charm of the DS [#permalink]

### Show Tags

09 Feb 2012, 02:12
HI Bunuel,

I personally dont feel very comfortable with your solution for Q9. Just not very intuitive for me.

Note: I really enjoyed doing these set of questions. U r taking GMAT club Quant practice questions to a next level alltogether. Thanks
Manager
Joined: 06 Jan 2012
Posts: 88
Followers: 0

Kudos [?]: 9 [0], given: 20

Re: The Discreet Charm of the DS [#permalink]

### Show Tags

24 Feb 2012, 14:52
I have seen references to use your guides in many threads, Bunuel. Now I can see why. I will be sure to use your challenge sets in the coming weeks to hopefully boost my quant score into the 48-50 range. Thank you so much for your invaluable contributions for relative GMAT newbies, like myself.
Intern
Joined: 08 Jan 2012
Posts: 7
Followers: 0

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

Re: The Discreet Charm of the DS [#permalink]

### Show Tags

25 Feb 2012, 05:27
All,

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

In respect to the question above, I assumed that any two of those 19 customer might have bought 5 & 3 oranges and hence I, marked the option insufficient. Bunnel have equated and treated the option in totally different way. I ,lack the skill to convert these sort of condition in to equation.

please can some post or point to the list of similar Word translation sentences and how to convert them in to equation. Im very new to GMAT club so please forgie me if this is the repeated posting.

Thanks,
Vids
Math Expert
Joined: 02 Sep 2009
Posts: 33600
Followers: 5956

Kudos [?]: 74025 [0], given: 9906

Re: The Discreet Charm of the DS [#permalink]

### Show Tags

25 Feb 2012, 05:53
Expert's post
vidhya16 wrote:
All,

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

In respect to the question above, I assumed that any two of those 19 customer might have bought 5 & 3 oranges and hence I, marked the option insufficient. Bunnel have equated and treated the option in totally different way. I ,lack the skill to convert these sort of condition in to equation.

please can some post or point to the list of similar Word translation sentences and how to convert them in to equation. Im very new to GMAT club so please forgie me if this is the repeated posting.

Thanks,
Vids

I did not use any equation for this question.

Statement (2) says: the difference between the number of oranges bought by ANY two customers is even --> in order the difference between ANY number of oranges bought to be even, either all customers must have bought odd number of oranges or all customers must have bough even number of oranges.

Now, the sum of 19 odd integers is odd and we have that fruit stand sold total of 76, so even number of oranges, which means that the case where all customers buy odd number of oranges is not possible. And since 1 is odd then no one bought only one orange. Sufficient.

As for word translation check this: word-problems-made-easy-87346.html

Hope it helps.
_________________
Senior Manager
Joined: 12 Dec 2010
Posts: 282
Concentration: Strategy, General Management
GMAT 1: 680 Q49 V34
GMAT 2: 730 Q49 V41
GPA: 4
WE: Consulting (Other)
Followers: 9

Kudos [?]: 44 [0], given: 23

Re: The Discreet Charm of the DS [#permalink]

### Show Tags

24 Mar 2012, 09:38
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?

(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 neither an integer nor integer/2 then $$x$$ and $$y$$ are not equal. Sufficient.

please consider adding "working together" to the stmt 2- as I deciphered they both worked separately and ended at the same time so cool enough (though same answer but got carried away by the wording)

Thanks once again for nice collection!!
_________________

My GMAT Journey 540->680->730!

~ When the going gets tough, the Tough gets going!

Math Expert
Joined: 02 Sep 2009
Posts: 33600
Followers: 5956

Kudos [?]: 74025 [0], given: 9906

Re: The Discreet Charm of the DS [#permalink]

### Show Tags

24 Mar 2012, 15:08
Expert's post
yogesh1984 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?

(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 neither an integer nor integer/2 then $$x$$ and $$y$$ are not equal. Sufficient.

please consider adding "working together" to the stmt 2- as I deciphered they both worked separately and ended at the same time so cool enough (though same answer but got carried away by the wording)

Thanks once again for nice collection!!

Thank you for the suggestion.
_________________
Manager
Joined: 12 Feb 2012
Posts: 136
Followers: 1

Kudos [?]: 46 [0], given: 28

Re: The Discreet Charm of the DS [#permalink]

### Show Tags

14 May 2012, 16:40
Bunuel wrote:
5. What is the value of integer x?

(1) 2x^2+9<9x --> factor qudratics: $$(x-\frac{3}{2})(x-3)<0$$ --> roots are $$\frac{3}{2}$$ and 3 --> "<" sign indicates that the solution lies between the roots: $$1.5<x<3$$ --> since there only integer in this range is 2 then $$x=2$$. Sufficient.

(2) |x+10|=2x+8 --> LHS is an absolute value, which is always non negative, hence RHS must also be non-negative: $$2x+8\geq{0}$$ --> $$x\geq{-4}$$, for this range $$x+10$$ is positive hence $$|x+10|=x+10$$ --> $$x+10=2x+8$$ --> $$x=2$$. Sufficient.

Check this for more on solving inequalities like the one in the first statement:
x2-4x-94661.html#p731476
inequalities-trick-91482.html
everything-is-less-than-zero-108884.html?hilit=extreme#p868863

Hope it helps.

Hey Bunuel,

Two questions.

1) How did you factor 2x^2+9<9x (ie 2x^2-9x+9<0) so quickly? I always struggle with factoring polynomials in which a coefficient other than 1 is on the x^2. Did you use the quadratic formula? I am interested in knowing if there is a quicker way than the quadratic formula method.

2) Once you determined that 1.5 and 3 were the roots of the equation, how did you figure that the solution was in between 1.5 and 3 from just looking at the sign "<"??
I used the dumb method of just plugging values that lie from (-infinity , 1.5), (1.5, 3) and (3, +infinity). How did you know the sign "<" told you the solution was in in between (1.5,3)?

Many thanks Bunuel! Your my hero dude!
Math Expert
Joined: 02 Sep 2009
Posts: 33600
Followers: 5956

Kudos [?]: 74025 [0], given: 9906

Re: The Discreet Charm of the DS [#permalink]

### Show Tags

14 May 2012, 23:19
Expert's post
alphabeta1234 wrote:
Bunuel wrote:
5. What is the value of integer x?

(1) 2x^2+9<9x --> factor qudratics: $$(x-\frac{3}{2})(x-3)<0$$ --> roots are $$\frac{3}{2}$$ and 3 --> "<" sign indicates that the solution lies between the roots: $$1.5<x<3$$ --> since there only integer in this range is 2 then $$x=2$$. Sufficient.

(2) |x+10|=2x+8 --> LHS is an absolute value, which is always non negative, hence RHS must also be non-negative: $$2x+8\geq{0}$$ --> $$x\geq{-4}$$, for this range $$x+10$$ is positive hence $$|x+10|=x+10$$ --> $$x+10=2x+8$$ --> $$x=2$$. Sufficient.

Check this for more on solving inequalities like the one in the first statement:
x2-4x-94661.html#p731476
inequalities-trick-91482.html
everything-is-less-than-zero-108884.html?hilit=extreme#p868863

Hope it helps.

Hey Bunuel,

Two questions.

1) How did you factor 2x^2+9<9x (ie 2x^2-9x+9<0) so quickly? I always struggle with factoring polynomials in which a coefficient other than 1 is on the x^2. Did you use the quadratic formula? I am interested in knowing if there is a quicker way than the quadratic formula method.

2) Once you determined that 1.5 and 3 were the roots of the equation, how did you figure that the solution was in between 1.5 and 3 from just looking at the sign "<"??
I used the dumb method of just plugging values that lie from (-infinity , 1.5), (1.5, 3) and (3, +infinity). How did you know the sign "<" told you the solution was in in between (1.5,3)?

Many thanks Bunuel! Your my hero dude!

2. Solving inequalities:
x2-4x-94661.html#p731476 (Check this first)
inequalities-trick-91482.html
everything-is-less-than-zero-108884.html?hilit=extreme#p868863

Hope it helps.
_________________
Manager
Joined: 21 Feb 2012
Posts: 115
Location: India
Concentration: Finance, General Management
GMAT 1: 600 Q49 V23
GPA: 3.8
WE: Information Technology (Computer Software)
Followers: 1

Kudos [?]: 81 [0], given: 15

Re: The Discreet Charm of the DS [#permalink]

### Show Tags

15 May 2012, 11:39
Bunuel wrote:
5. What is the value of integer x?

(1) 2x^2+9<9x --> factor qudratics: $$(x-\frac{3}{2})(x-3)<0$$ --> roots are $$\frac{3}{2}$$ and 3 --> "<" sign indicates that the solution lies between the roots: $$1.5<x<3$$ --> since there only integer in this range is 2 then $$x=2$$. Sufficient.

(2) |x+10|=2x+8 --> LHS is an absolute value, which is always non negative, hence RHS must also be non-negative: $$2x+8\geq{0}$$ --> $$x\geq{-4}$$, for this range $$x+10$$ is positive hence $$|x+10|=x+10$$ --> $$x+10=2x+8$$ --> $$x=2$$. Sufficient.

Hope it helps.

Hi bunuel,
Isn't |x+10|=2x+8 be written as
Either x+10=2x+8 or x+10=-(2x+8) ? and then this should be solved?
Math Expert
Joined: 02 Sep 2009
Posts: 33600
Followers: 5956

Kudos [?]: 74025 [0], given: 9906

Re: The Discreet Charm of the DS [#permalink]

### Show Tags

15 May 2012, 11:43
Expert's post
piyushksharma wrote:
Bunuel wrote:
5. What is the value of integer x?

(1) 2x^2+9<9x --> factor qudratics: $$(x-\frac{3}{2})(x-3)<0$$ --> roots are $$\frac{3}{2}$$ and 3 --> "<" sign indicates that the solution lies between the roots: $$1.5<x<3$$ --> since there only integer in this range is 2 then $$x=2$$. Sufficient.

(2) |x+10|=2x+8 --> LHS is an absolute value, which is always non negative, hence RHS must also be non-negative: $$2x+8\geq{0}$$ --> $$x\geq{-4}$$, for this range $$x+10$$ is positive hence $$|x+10|=x+10$$ --> $$x+10=2x+8$$ --> $$x=2$$. Sufficient.

Hope it helps.

Hi bunuel,
Isn't |x+10|=2x+8 be written as
Either x+10=2x+8 or x+10=-(2x+8) ? and then this should be solved?

We goth that x is more than or equal to 4. Now, for this range x+10>0 so |x+10| expands only as x+10 (|x+10|=x+10).
_________________
Manager
Joined: 21 Feb 2012
Posts: 115
Location: India
Concentration: Finance, General Management
GMAT 1: 600 Q49 V23
GPA: 3.8
WE: Information Technology (Computer Software)
Followers: 1

Kudos [?]: 81 [0], given: 15

Re: The Discreet Charm of the DS [#permalink]

### Show Tags

15 May 2012, 12:16
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.
Senior Manager
Joined: 08 Apr 2012
Posts: 464
Followers: 1

Kudos [?]: 38 [0], given: 58

Re: The Discreet Charm of the DS [#permalink]

### Show Tags

21 May 2012, 06:32
I plugged in number for question 2 statement (1).

Any numbers that I could think of really met the inequasion.

But do you have an algebric way of showing this rule?
Math Expert
Joined: 02 Sep 2009
Posts: 33600
Followers: 5956

Kudos [?]: 74025 [0], given: 9906

Re: The Discreet Charm of the DS [#permalink]

### Show Tags

21 May 2012, 06:35
Expert's post
ronr34 wrote:
I plugged in number for question 2 statement (1).

Any numbers that I could think of really met the inequasion.

But do you have an algebric way of showing this rule?

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.

_________________
Intern
Joined: 07 Jul 2011
Posts: 1
Followers: 0

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

Re: The Discreet Charm of the DS [#permalink]

### Show Tags

25 May 2012, 11:58
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: $$a=1$$, $$b=5$$ and $$c=3$$, of course it's also possible that for example $$b=even$$, for $$a=1$$ 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.

What about the case when all a,b,c are zero. In this case, abc = 0 and 0 is neither odd nor even. Hence 'E'.
Math Expert
Joined: 02 Sep 2009
Posts: 33600
Followers: 5956

Kudos [?]: 74025 [0], given: 9906

Re: The Discreet Charm of the DS [#permalink]

### Show Tags

25 May 2012, 12:29
Expert's post
avinash2603 wrote:
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: $$a=1$$, $$b=5$$ and $$c=3$$, of course it's also possible that for example $$b=even$$, for $$a=1$$ 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.

What about the case when all a,b,c are zero. In this case, abc = 0 and 0 is neither odd nor even. Hence 'E'.

Notice that zero is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder. Since 0/2=0=integer then zero is even.

For more on this subject please check Number Theory chapter of Math Book: math-number-theory-88376.html

Hope it helps.
_________________
Re: The Discreet Charm of the DS   [#permalink] 25 May 2012, 12:29

Go to page   Previous    1   2   3   4   5   6   7   8   9   10    Next  [ 183 posts ]

Similar topics Replies Last post
Similar
Topics:
ds inequalities 0 27 May 2016, 20:27
DS-Modulus 2 05 Jul 2011, 02:46
DS deduction 1 25 Jun 2011, 06:41
5 DS Ques 10 25 Jun 2008, 00:17
1 GMATprep DS: Number theory 8 09 Feb 2007, 03:23
Display posts from previous: Sort by