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

It is currently 17 Dec 2014, 18:24

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

If X is the sum of first 50 positive even integers and Y is

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 10 Jan 2011
Posts: 244
Location: India
GMAT Date: 07-16-2012
GPA: 3.4
WE: Consulting (Consulting)
Followers: 0

Kudos [?]: 23 [0], given: 25

Reviews Badge
If X is the sum of first 50 positive even integers and Y is [#permalink] New post 11 Sep 2012, 04:11
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

68% (01:41) correct 32% (00:45) wrong based on 149 sessions
If X is the sum of first 50 positive even integers and Y is the sum of first 50 positive odd integers, what is the value of x-y?

A. 0
B. 25
C. 50
D. 75
E. 100

-----------------------------------------------
Please try to explain your answers
[Reveal] Spoiler: OA

_________________

-------Analyze why option A in SC wrong-------

Expert Post
5 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 24572
Followers: 3800

Kudos [?]: 32737 [5] , given: 3556

Re: If X is the sum of first 50 positive even integers and Y is [#permalink] New post 11 Sep 2012, 04:21
5
This post received
KUDOS
Expert's post
nishtil wrote:
If X is the sum of first 50 positive even integers and Y is the sum of first 50 positive odd integers, what is the value of x-y?

A. 0
B. 25
C. 50
D. 75
E. 100

-----------------------------------------------
Please try to explain your answers


We can solve this question even if we don't know any formula for such sums:

First even minus first odd = 2-1 = 1;
The sum of first 2 even integers minus the sum of first 2 odd integers = (2+4)-(1+3) = 2;
The sum of first 3 even integers minus the sum of first 3 odd integers = (2+4+6)-(1+3+5) = 3;
...
We can see the patterns here, so the sum of first 50 positive even integers minus the sum of first 50 positive odd integers will be 50.

Answer: C.

OR: each even minus its preceding odd is one, so x-y=50 (x-y=(even1+even2+...+even50)-(odd1+odd2+..+odd50)=(even1-odd1)+(even2-odd2)+...+(even50-odd50)=1+1+...+1=50).

Answer: C.

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

Senior Manager
Senior Manager
avatar
Joined: 06 Aug 2011
Posts: 409
Followers: 2

Kudos [?]: 70 [0], given: 82

Re: If X is the sum of first 50 positive even integers and Y is [#permalink] New post 11 Sep 2012, 05:15
Nice way bunuel..!!

and i did it in this way..

first even and last even ..2 and 100 respectively, 100+2=102/2=51..51 is average of first 50 even integers=num of terms*average =50*51=2550..so sum of first 50 integers is 2550

first odd and last odd of first 50 intergers is =99 and 1..99+1=100/2=50.. so 50*50=2500..sum of first 50 odd integers is 2500..

2550-2500=50... ans c.
_________________

Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !

1 KUDOS received
Manager
Manager
avatar
Joined: 24 Jul 2011
Posts: 77
Location: India
Concentration: Strategy, General Management
GMAT 1: 670 Q49 V33
WE: Asset Management (Manufacturing)
Followers: 2

Kudos [?]: 72 [1] , given: 5

Re: If X is the sum of first 50 positive even integers and Y is [#permalink] New post 12 Sep 2012, 09:37
1
This post received
KUDOS
nishtil wrote:
If X is the sum of first 50 positive even integers and Y is the sum of first 50 positive odd integers, what is the value of x-y?

A. 0
B. 25
C. 50
D. 75
E. 100

-----------------------------------------------
Please try to explain your answers



Let's use this process,

x= 2+ 4+ 6+ ...... (up to 50th term)
y= 1+ 3 +5+ .......(up to 50th term)
-------------------------------------------------
(x-y)= 1+1+1+ .......... up to 50th term = 50
_________________

My mantra for cracking GMAT:
Everyone has inborn talent, however those who complement it with hard work we call them 'talented'.


+1 Kudos = Thank You Dear :)
Are you saying thank you?

Director
Director
avatar
Joined: 24 Aug 2009
Posts: 508
Schools: Harvard, Columbia, Stern, Booth, LSB,
Followers: 9

Kudos [?]: 408 [0], given: 241

Re: If X is the sum of first 50 positive even integers and Y is [#permalink] New post 12 Sep 2012, 10:03
Shortcut way without even a single calculation:-

Sum of first 'n' even integers is given by - n(n+1)
Sum of first 'n' odd integers is given by - n^2

x = n(n+1) = 50 x 51
y= n^2 = 50 x 50
x-y = 50 (51-50) = 50 (1) = 50
Answer C

Hope It helps
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS.
Kudos always maximizes GMATCLUB worth
-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

Manager
Manager
avatar
Joined: 21 Jul 2012
Posts: 61
Followers: 0

Kudos [?]: 6 [0], given: 32

Re: If X is the sum of first 50 positive even integers and Y is [#permalink] New post 26 Mar 2013, 14:12
fameatop wrote:
Shortcut way without even a single calculation:-

Sum of first 'n' even integers is given by - n(n+1)
Sum of first 'n' odd integers is given by - n^2

x = n(n+1) = 50 x 51
y= n^2 = 50 x 50
x-y = 50 (51-50) = 50 (1) = 50
Answer C

Hope It helps


do these above formulas always hold true? And what is the formula for the first 100 positive integers?
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 24572
Followers: 3800

Kudos [?]: 32737 [1] , given: 3556

Re: If X is the sum of first 50 positive even integers and Y is [#permalink] New post 27 Mar 2013, 03:33
1
This post received
KUDOS
Expert's post
jmuduke08 wrote:
fameatop wrote:
Shortcut way without even a single calculation:-

Sum of first 'n' even integers is given by - n(n+1)
Sum of first 'n' odd integers is given by - n^2

x = n(n+1) = 50 x 51
y= n^2 = 50 x 50
x-y = 50 (51-50) = 50 (1) = 50
Answer C

Hope It helps


do these above formulas always hold true? And what is the formula for the first 100 positive integers?



Sum of n first positive integers: 1+2+...+n=\frac{1+n}{2}*n. So, the sum of 100 first positive integers is (1+100)/2*100.

Sum of n first positive odd numbers: a_1+a_2+...+a_n=1+3+...+a_n=n^2, where a_n is the last, n_{th} term and given by: a_n=2n-1. Given n=5 first odd positive integers, then their sum equals to 1+3+5+7+9=5^2=25.

Sum of n first positive even numbers: a_1+a_2+...+a_n=2+4+...+a_n=n(n+1), where a_n is the last, n_{th} term and given by: a_n=2n. Given n=4 first positive even integers, then their sum equals to 2+4+6+8=4(4+1)=20.

For more check here: math-number-theory-88376.html

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

Manager
Manager
avatar
Joined: 21 Jul 2012
Posts: 61
Followers: 0

Kudos [?]: 6 [0], given: 32

Re: If X is the sum of first 50 positive even integers and Y is [#permalink] New post 30 Mar 2013, 12:06
Bunuel wrote:
jmuduke08 wrote:
fameatop wrote:
Shortcut way without even a single calculation:-

Sum of first 'n' even integers is given by - n(n+1)
Sum of first 'n' odd integers is given by - n^2

x = n(n+1) = 50 x 51
y= n^2 = 50 x 50
x-y = 50 (51-50) = 50 (1) = 50
Answer C

Hope It helps


do these above formulas always hold true? And what is the formula for the first 100 positive integers?



Sum of n first positive integers: 1+2+...+n=\frac{1+n}{2}*n. So, the sum of 100 first positive integers is (1+100)/2*100.

Sum of n first positive odd numbers: a_1+a_2+...+a_n=1+3+...+a_n=n^2, where a_n is the last, n_{th} term and given by: a_n=2n-1. Given n=5 first odd positive integers, then their sum equals to 1+3+5+7+9=5^2=25.

Sum of n first positive even numbers: a_1+a_2+...+a_n=2+4+...+a_n=n(n+1), where a_n is the last, n_{th} term and given by: a_n=2n. Given n=4 first positive even integers, then their sum equals to 2+4+6+8=4(4+1)=20.

For more check here: math-number-theory-88376.html

Hope it helps.


Bunuel, if I wanted to find the sum of the even integers between 26 and 62, inclusive, then the formula above for even integers n(n+1) would not work, because this formula is only for the first n even positive integers meaning we would need to start at 2. Is this the correct way to think about it?
Manager
Manager
User avatar
Joined: 24 Nov 2012
Posts: 175
Concentration: Sustainability, Entrepreneurship
GMAT 1: 770 Q50 V44
WE: Business Development (Internet and New Media)
Followers: 19

Kudos [?]: 109 [0], given: 73

Re: If X is the sum of first 50 positive even integers and Y is [#permalink] New post 16 Apr 2013, 10:21
[quote=
Bunuel, if I wanted to find the sum of the even integers between 26 and 62, inclusive, then the formula above for even integers n(n+1) would not work, because this formula is only for the first n even positive integers meaning we would need to start at 2. Is this the correct way to think about it?[/quote]


Sum of x consecutive even integers = 2xn + x(x+1)/2 (n = (First term of series/2) - 1)

Sum of x consecutive odd integers = (x+n)^2 - (n)^2 (n=(first term of series - 1)/2)
_________________

You've been walking the ocean's edge, holding up your robes to keep them dry. You must dive naked under, and deeper under, a thousand times deeper! - Rumi

http://www.manhattangmat.com/blog/index ... nprep-com/ - This is worth its weight in gold

Economist GMAT Test - 730, Q50, V41 Aug 9th, 2013
Manhattan GMAT Test - 670, Q45, V36 Aug 11th, 2013
Manhattan GMAT Test - 680, Q47, V36 Aug 17th, 2013
GmatPrep CAT 1 - 770, Q50, V44 Aug 24th, 2013
Manhattan GMAT Test - 690, Q45, V39 Aug 30th, 2013
Manhattan GMAT Test - 710, Q48, V39 Sep 13th, 2013
GmatPrep CAT 2 - 740, Q49, V41 Oct 6th, 2013

GMAT - 770, Q50, V44, Oct 7th, 2013
My Debrief - from-the-ashes-thou-shall-rise-770-q-50-v-44-awa-5-ir-162299.html#p1284542

Manager
Manager
avatar
Joined: 05 Nov 2012
Posts: 164
Followers: 1

Kudos [?]: 10 [0], given: 56

Re: If X is the sum of first 50 positive even integers and Y is [#permalink] New post 16 Apr 2013, 10:56
X = 2+4+6+8+.... +100
Y = 1+3+5+7+.... +99

X-Y= (2-1) + (4-3) + (6-5) + .... +(100-99) there are 50 terms
X-Y= 1 + 1 + 1 + .... +1 50 terms
=> X-Y=50
Answer C
Current Student
User avatar
Joined: 23 Oct 2010
Posts: 387
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Followers: 13

Kudos [?]: 160 [0], given: 73

GMAT ToolKit User
Re: If X is the sum of first 50 positive even integers and Y is [#permalink] New post 25 Apr 2013, 00:30
sum of the 1st even integers =n(n+2)=25*27
sum of the 1st odd integers =k^2=25*25

25*27-25*25=25*(27-25)=50
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

1 KUDOS received
Intern
Intern
User avatar
Status: Currently Preparing the GMAT
Joined: 15 Feb 2013
Posts: 31
Location: United States
GMAT 1: 550 Q47 V23
GPA: 3.7
WE: Analyst (Consulting)
Followers: 1

Kudos [?]: 4 [1] , given: 11

Re: If X is the sum of first 50 positive even integers and Y is [#permalink] New post 25 Apr 2013, 02:06
1
This post received
KUDOS
I'll post two ways to solve this question : The formal way (in order for you guys to better understand the theory behind it) and the GMAT way (within the 2-minute scope).

Let's start.

1st method : The GMAT way

Bunuel actually proposed the easiest and fastest method to solve this question. That is you should look for patterns through examples.

First 2 even numbers : 2, 4 => summed up : (2+4) = 6
First 2 odd numbers : 1, 3 => summed up : (1+3) = 4

Their difference will be 2.

First 3 even numbers : 2, 4, 6 => summed up : (2+4+6) = 12
First 3 odd numbers : 1, 3, 5 => summed up : (1+3+5) = 9

Their difference will be 3.

And so forth. So eventually the difference between the sum of the first 50 even integers and the first 50 odd integers will be 50. Which is answer choice C.

2nd method : The formal way

To use this method you should be familiar and comfortable with :

- The general form of an even integer which is 2n ;
- The general form of an odd integer which is 2n+1 ;
- Counting the number of consecutive integers within a list which is given by the following formula : (Last number - First number) + 1 ;
- The sum operator and manipulating it.

Therefore the difference between the sum of the 50 first even integers and the 50 first odd integers is written as such :
Attachment:
pic3.jpg
pic3.jpg [ 6.93 KiB | Viewed 3951 times ]


You'll notice two things :

- I chose to index the sums from 0 to 49 since the first even integer is 0 and the first odd integer is 1 ;
- I inverted the difference since I've written Y-X instead of X-Y. This is due to the general form of the odd integer which if left as the original question stem suggests would leave me with a (-1) instead of 1.

If we develop the difference above we get :
Attachment:
pic4.jpg
pic4.jpg [ 10.55 KiB | Viewed 3951 times ]


Which, unsuprisingly, yields 50 which is answer choice C.

Note that you can combine two sums if and only if they have the same index range (0 to 49 in both cases).

Hope that helped. :-D
Intern
Intern
avatar
Joined: 09 Jul 2013
Posts: 19
Concentration: Operations, Marketing
Schools: CUHK '15
GPA: 3.6
Followers: 0

Kudos [?]: 1 [0], given: 14

Re: If X is the sum of first 50 positive even integers and Y is [#permalink] New post 08 Dec 2013, 21:38
Y not consider zero as zero is also an even number.....
correct me if i m wrong


Kindly let me know :)
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 24572
Followers: 3800

Kudos [?]: 32737 [0], given: 3556

Re: If X is the sum of first 50 positive even integers and Y is [#permalink] New post 09 Dec 2013, 00:03
Expert's post
Intern
Intern
avatar
Joined: 09 Jul 2013
Posts: 19
Concentration: Operations, Marketing
Schools: CUHK '15
GPA: 3.6
Followers: 0

Kudos [?]: 1 [0], given: 14

Re: If X is the sum of first 50 positive even integers and Y is [#permalink] New post 09 Dec 2013, 00:16
Question: Is the number 0 even or odd?
Answer: 0/2 = 0. The result is an integer, so the number 0 is divisible by 2. As a result, the number 0 is even


i read this in one of the manhatttan forums...hence the doubt..... :) could you throw some light based on the above info
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 24572
Followers: 3800

Kudos [?]: 32737 [0], given: 3556

Re: If X is the sum of first 50 positive even integers and Y is [#permalink] New post 09 Dec 2013, 00:23
Expert's post
iyersu wrote:
Question: Is the number 0 even or odd?
Answer: 0/2 = 0. The result is an integer, so the number 0 is divisible by 2. As a result, the number 0 is even


i read this in one of the manhatttan forums...hence the doubt..... :) could you throw some light based on the above info


As written above: yes, zero is an even number but the questions talks about positive even numbers and since zero is neither positive nor negative, we do not consider 0 for this question.

THEORY:
1. EVEN/ODD

An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder.

An odd number is an integer that is not evenly divisible by 2.

According to the above both negative and positive integers can be even or odd.

2. ZERO

Zero is an even integer. Zero is nether positive nor negative, but zero is definitely an even number.

An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even (in fact zero is divisible by every integer except zero itself).

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

Re: If X is the sum of first 50 positive even integers and Y is   [#permalink] 09 Dec 2013, 00:23
    Similar topics Author Replies Last post
Similar
Topics:
19 Experts publish their posts in the topic The sum of the first 50 positive even integers is 2550. What CasperMonday 28 03 Sep 2009, 05:35
The sum of the first 50 positive even integers is 2,550. rpmodi 10 27 Apr 2008, 18:33
The sum of the first 50 positive even integers is 2,550. djhouse81 11 22 Jun 2007, 03:36
The sum of the first 50 positive even integers is 2550. what enola 4 12 Dec 2006, 05:54
The sum of the first 50 positive even integers is 2550. What Matador 4 15 Apr 2006, 13:37
Display posts from previous: Sort by

If X is the sum of first 50 positive even integers and Y is

  Question banks Downloads My Bookmarks Reviews Important topics  


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®.