November 18, 2018 November 18, 2018 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score. November 18th, 7 AM PST November 20, 2018 November 20, 2018 09:00 AM PST 10:00 AM PST The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 10 Jan 2011
Posts: 158
Location: India
GMAT Date: 07162012
GPA: 3.4
WE: Consulting (Consulting)

If X is the sum of first 50 positive even integers and Y is
[#permalink]
Show Tags
11 Sep 2012, 04:11
Question Stats:
73% (01:18) correct 27% (01:35) wrong based on 668 sessions
HideShow timer Statistics
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 xy? A. 0 B. 25 C. 50 D. 75 E. 100  Please try to explain your answers
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Analyze why option A in SC wrong




Math Expert
Joined: 02 Sep 2009
Posts: 50621

Re: If X is the sum of first 50 positive even integers and Y is
[#permalink]
Show Tags
11 Sep 2012, 04:21
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 xy?
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 = 21 = 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 xy=50 (xy=(even1+even2+...+even50)(odd1+odd2+..+odd50)=(even1odd1)+(even2odd2)+...+(even50odd50)=1+1+...+1=50). Answer: C. Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  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




Senior Manager
Joined: 24 Aug 2009
Posts: 472
Schools: Harvard, Columbia, Stern, Booth, LSB,

Re: If X is the sum of first 50 positive even integers and Y is
[#permalink]
Show Tags
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 xy = 50 (5150) = 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




Senior Manager
Joined: 06 Aug 2011
Posts: 340

Re: If X is the sum of first 50 positive even integers and Y is
[#permalink]
Show Tags
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.. 25502500=50... ans c.
_________________
Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !



Manager
Joined: 24 Jul 2011
Posts: 70
Location: India
Concentration: Strategy, General Management
WE: Asset Management (Manufacturing)

Re: If X is the sum of first 50 positive even integers and Y is
[#permalink]
Show Tags
12 Sep 2012, 09:37
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 xy?
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)  (xy)= 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?



Manager
Joined: 21 Jul 2012
Posts: 65

Re: If X is the sum of first 50 positive even integers and Y is
[#permalink]
Show Tags
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 xy = 50 (5150) = 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?



Math Expert
Joined: 02 Sep 2009
Posts: 50621

Re: If X is the sum of first 50 positive even integers and Y is
[#permalink]
Show Tags
27 Mar 2013, 03:33
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 xy = 50 (5150) = 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: \(a_n=2n1\). 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: mathnumbertheory88376.htmlHope it helps.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  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: 21 Jul 2012
Posts: 65

Re: If X is the sum of first 50 positive even integers and Y is
[#permalink]
Show Tags
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 xy = 50 (5150) = 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: \(a_n=2n1\). 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: mathnumbertheory88376.htmlHope 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
Joined: 24 Nov 2012
Posts: 157
Concentration: Sustainability, Entrepreneurship
WE: Business Development (Internet and New Media)

Re: If X is the sum of first 50 positive even integers and Y is
[#permalink]
Show Tags
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.php/author/cbermanmanhattanprepcom/  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  http://gmatclub.com/forum/fromtheashesthoushallrise770q50v44awa5ir162299.html#p1284542



Manager
Joined: 05 Nov 2012
Posts: 149

Re: If X is the sum of first 50 positive even integers and Y is
[#permalink]
Show Tags
16 Apr 2013, 10:56
X = 2+4+6+8+.... +100 Y = 1+3+5+7+.... +99
XY= (21) + (43) + (65) + .... +(10099) there are 50 terms XY= 1 + 1 + 1 + .... +1 50 terms => XY=50 Answer C



Senior Manager
Joined: 23 Oct 2010
Posts: 353
Location: Azerbaijan
Concentration: Finance

Re: If X is the sum of first 50 positive even integers and Y is
[#permalink]
Show Tags
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*2725*25=25*(2725)=50
_________________
Happy are those who dream dreams and are ready to pay the price to make them come true
I am still on all gmat forums. msg me if you want to ask me smth



Intern
Status: Currently Preparing the GMAT
Joined: 15 Feb 2013
Posts: 29
Location: United States
GPA: 3.7
WE: Analyst (Consulting)

Re: If X is the sum of first 50 positive even integers and Y is
[#permalink]
Show Tags
25 Apr 2013, 02:06
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 2minute scope). Let's start. 1st method : The GMAT wayBunuel 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 wayTo 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 [ 6.93 KiB  Viewed 18054 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 YX instead of XY. 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 [ 10.55 KiB  Viewed 18051 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.



Intern
Joined: 09 Jul 2013
Posts: 14
Concentration: Operations, Marketing
GPA: 3.6

Re: If X is the sum of first 50 positive even integers and Y is
[#permalink]
Show Tags
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



Math Expert
Joined: 02 Sep 2009
Posts: 50621

Re: If X is the sum of first 50 positive even integers and Y is
[#permalink]
Show Tags
09 Dec 2013, 00:03



Intern
Joined: 09 Jul 2013
Posts: 14
Concentration: Operations, Marketing
GPA: 3.6

Re: If X is the sum of first 50 positive even integers and Y is
[#permalink]
Show Tags
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



Math Expert
Joined: 02 Sep 2009
Posts: 50621

Re: If X is the sum of first 50 positive even integers and Y is
[#permalink]
Show Tags
09 Dec 2013, 00:23
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/ODDAn 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. ZEROZero 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 the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  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



VP
Joined: 07 Dec 2014
Posts: 1114

Re: If X is the sum of first 50 positive even integers and Y is
[#permalink]
Show Tags
08 Aug 2016, 12:49
sum of first 5 even integers=30 sum of first 5 odd integers=25 3025=5 5*(50/5)=50



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830

Re: If X is the sum of first 50 positive even integers and Y is
[#permalink]
Show Tags
12 Oct 2017, 17:14
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 xy?
A. 0 B. 25 C. 50 D. 75 E. 100 The sum of the first 50 positive even integers is: sum = average x quantity sum = (100 + 2)/2 x 50 = 51 x 50 The sum of the first 50 positive odd integers is: sum = (99 + 1)/2 x 50 = 50 x 50 Thus, x  y is 51 x 50  50 x 50 = 50(51  50) = 50. Alternate solution: The first 50 positive even integers are: 2, 4, 6, 8, …, 98, 100. The first 50 positive odd integers are: 1, 3, 5, 7, …, 97, 99. We see that each even integer is 1 more than its odd counterpart (2 is 1 more than 1, 4 is 1 more than 3, etc). Since there are 50 numbers in each set, the sum of the even integers will be 50 x 1 = 50 more than the sum of the odd integers. Answer: C
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



VP
Joined: 09 Mar 2016
Posts: 1079

If X is the sum of first 50 positive even integers and Y is
[#permalink]
Show Tags
09 Jun 2018, 02:41
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 xy?
A. 0 B. 25 C. 50 D. 75 E. 100
 Please try to explain your answers Hi pushpitkc i used the formalus from my post https://gmatclub.com/forum/arithmeticp ... l#p2035478but somrthing went wrong:? the formula for finding sum of even numbers confiused me.... pls explain where am i wrong. thanks HOW TO FIND THE SUM OF THE FIRST EVEN NUMBERS \(\frac{n(n+2)}{4}\) where \(n\) is number of terms HOW TO FIND NUMBER OF TERMS FROM A TO Z \(\frac{last..term  first..term}{2} +1\) Number of Even Terms \(\frac{502}{2} +1 = 25\) Sum of Even Terms \(\frac{25(25+2)}{4}\) ??? HOW TO FIND SUM OF ODD NUMBERS FROM A TO B Step one: \(find..the..number...of..terms\) Step two: \(\frac{first..term+last..term}{2}\) \(* number..of.. terms\) Number of Odd terms \(\frac{491}{2} +1 = 25\) Sum of Odd numbers \(\frac{49+1}{2}*25 = 625\)



Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3307
Location: India
GPA: 3.12

If X is the sum of first 50 positive even integers and Y is
[#permalink]
Show Tags
09 Jun 2018, 03:44
dave13 wrote: 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 xy?
A. 0 B. 25 C. 50 D. 75 E. 100
 Please try to explain your answers Hi pushpitkc i used the formalus from my post https://gmatclub.com/forum/arithmeticp ... l#p2035478but somrthing went wrong:? the formula for finding sum of even numbers confiused me.... pls explain where am i wrong. thanks HOW TO FIND THE SUM OF THE FIRST EVEN NUMBERS \(\frac{n(n+2)}{4}\) where \(n\) is number of terms HOW TO FIND NUMBER OF TERMS FROM A TO Z \(\frac{last..term  first..term}{2} +1\) Number of Even Terms \(\frac{502}{2} +1 = 25\) Sum of Even Terms \(\frac{25(25+2)}{4}\) ??? HOW TO FIND SUM OF ODD NUMBERS FROM A TO B Step one: \(find..the..number...of..terms\) Step two: \(\frac{first..term+last..term}{2}\) \(* number..of.. terms\) Number of Odd terms \(\frac{491}{2} +1 = 25\) Sum of Odd numbers \(\frac{49+1}{2}*25 = 625\) Hi dave13Unfortunately, the formula for the sum of even numbers is wrong. The correct formula for the sum of even numbers is \(N(N+1)\). Also, we have another formula for the sum of odd numbers, which is \(N^2\). Let's check this by means of an example. If N = 3, the even numbers are 2,4, and 6. The sum of the even numbers is 12. If the formula was \(\frac{N(N+2)}{4} = \frac{3(5)}{4} = \frac{15}{4}\), we will not get the right answer. Coming back to our problem, we have been asked to find the sum of the first 50 even numbers. However, you have found the details for the first 25 numbers(till 50) We could go about doing this problem as follows: The sum of the first 50 even numbers is 50*(50+1) = 50*51 = 2550(which is X) The sum of the first 50 odd numbers is 50^2 = 2500(which is Y) Therefore, the difference between X and Y is 2550  2500 = 50(Option C)Hope this helps you!
_________________
You've got what it takes, but it will take everything you've got




If X is the sum of first 50 positive even integers and Y is &nbs
[#permalink]
09 Jun 2018, 03:44



Go to page
1 2
Next
[ 24 posts ]



