Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 44352

Math Revolution and GMAT Club Contest! If x=1 and n is the sum of the [#permalink]
Show Tags
19 Dec 2015, 08:42
Question Stats:
85% (01:02) correct 15% (01:03) wrong based on 181 sessions
HideShow timer Statistics
Math Revolution and GMAT Club Contest Starts! QUESTION #13:If x=1 and n is the sum of the second 101 prime numbers, what is the value of \(x^n + x^{(n+1)} + x^{(n+2)} + x^{(n+3)}\)? A. 2 B. 1 C. 0 D. 1 E. 2 Check conditions below: Math Revolution and GMAT Club ContestThe Contest Starts November 28th in Quant Forum We are happy to announce a Math Revolution and GMAT Club Contest For the following four (!) weekends we'll be publishing 4 FRESH math questions per weekend (2 on Saturday and 2 on Sunday). To participate, you will have to reply with your best answer/solution to the new questions that will be posted on Saturday and Sunday at 9 AM Pacific. Then a week later, the forum moderator will be selecting 2 winners who provided most correct answers to the questions, along with best solutions. Those winners will get 6months access to GMAT Club Tests. PLUS! Based on the answers and solutions for all the questions published during the project ONE user will be awarded with ONE Grand prize: PS + DS course with 502 videos that is worth $299! All announcements and winnings are final and no whining GMAT Club reserves the rights to modify the terms of this offer at any time. NOTE: Test Prep Experts and Tutors are asked not to participate. We would like to have the members maximize their learning and problem solving process.
Thank you!
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
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





Intern
Joined: 30 Sep 2013
Posts: 22

Re: Math Revolution and GMAT Club Contest! If x=1 and n is the sum of the [#permalink]
Show Tags
19 Dec 2015, 09:59
1
This post received KUDOS
There are total 25 prime numbers from 1 to 100 There are total 26 prime numbers from 1 to 101
Now given , " second 101 prime numbers " , I think that prime number starts from 3 to 101 . Excluding 2 [first prime number]
List of second 101 prime numbers are 3,5,7,11,13,17.....101 There are total 25 second 101 primer numbers.
If we can calculate n as even or odd, that will results into the solution as X = 1
Sum of second 2 prime numbers is even Sum of second 3 prime numbers is odd Sum of second 4 prime numbers is even Sum of second 5 prime numbers is odd . . . . Sum of second 25 prime numbers is odd
There n is odd.
x^n + x^(n+1) + x^(n+2) + x^(n+3) is
(1)^odd + (1)^(odd + 1) + (1)^(odd + 2) + (1)^(odd + 3)
1 + (1)^(even) + (1)^(odd) + (1)^(even)
1 + 1  1 + 1
0
Answer is C



Director
Joined: 21 May 2013
Posts: 613

Re: Math Revolution and GMAT Club Contest! If x=1 and n is the sum of the [#permalink]
Show Tags
19 Dec 2015, 10:13
1
This post received KUDOS
n=sum of second 101 prime numbers Now , all prime numbers except 2 are odd. Therefore, sum of odd no of prime nos=odd and sum of even no of prime nos=even Therefore, sum of second 101 primes nos(in which all are odd)=odd or n=odd Reqd equation= 1+11+1=0 Answer C



Intern
Joined: 12 Jul 2015
Posts: 27
Location: United States
Concentration: Strategy, General Management
WE: General Management (Pharmaceuticals and Biotech)

Re: Math Revolution and GMAT Club Contest! If x=1 and n is the sum of the [#permalink]
Show Tags
19 Dec 2015, 11:05
3
This post received KUDOS
Given: x=1 n = Sum of the second 101 prime nos
In the second set of 101 prime nos, 1. There are no even nos 2. Sum of any two odd nos is a Even no
Since n is the sum of 101 prime nos, n = odd
Now, (1)^n+(1)^(n+1)+(1)^(n+2)+(1)^(n+3)
As n = odd, n+1= Even n+2=Odd n+3=Even and (1)^odd = (1), and (1)^Even = +1
On Solving, 1+11+1=0
Alternatively, irrespective of whether n= odd/even, ans =0 Case 1: n = odd, n+1 = Even ,n+2 = odd, n+3 = Even (1+11+1 = 0) Case 2: n = Even, n+1 = odd, n+2 = Even, n+3 = Odd (1+11+1 = 0)
Ans =C = 0



Current Student
Joined: 20 Jan 2015
Posts: 60

Re: Math Revolution and GMAT Club Contest! If x=1 and n is the sum of the [#permalink]
Show Tags
20 Dec 2015, 00:40
1
This post received KUDOS
First, the sum of second 101 prime numbers needs to be calculated. Now, second 101 prime numbers means that the 101 prime numbers after 2. We also know that the sum of the 101 prime numbers after 2 will be an odd number since all these prime numbers are odd. => n is odd. Now to find the value = (1)^odd + (1)^even + (1)^odd + (1)^even = 1 + 1 + (1) + 1 = 0 Option C.
_________________
Please take a moment to hit Kudos if you like my post



Intern
Joined: 21 Jan 2013
Posts: 46
Concentration: General Management, Leadership
GPA: 3.82
WE: Engineering (Computer Software)

Re: Math Revolution and GMAT Club Contest! If x=1 and n is the sum of the [#permalink]
Show Tags
20 Dec 2015, 04:42
1
This post received KUDOS
If x=1 and n is the sum of the second 101 prime numbers, what is the value of xn+x(n+1)+x(n+2)+x(n+3)? A. 2 B. 1 C. 0 D. 1 E. 2  x = 1 ; n = sum of second 101 "prime" numbers; Given that all prime numbers above 2 are ODD , sum of 101 second prime numbers is a sum of ALL ODD INTEGERS, odd integer + odd integer = even integer Extending this observation, sum of EVEN NUMBER of odd INTEGERS is always EVEN, sum of ODD number of ODD INTEGERS is always ODD. Therefore, we need not really deduce the value of n, but we can infer that n is definitely an ODD integer. Plugging it back into the equation, we're looking at (1)^(odd) + (1)^(even) + (1)^(odd) + (1)^(even) = 1 + (+1) + (1) + (+1) = 0 Correct answer : C
_________________

Consider +1 Kudos if you find my post useful



Intern
Joined: 01 Nov 2015
Posts: 38
Location: India
Concentration: Marketing, Entrepreneurship
WE: Engineering (Computer Software)

Re: Math Revolution and GMAT Club Contest! If x=1 and n is the sum of the [#permalink]
Show Tags
20 Dec 2015, 19:22
1
This post received KUDOS
Since n is the sum of 2nd 101 Prime Numbers, n Must be Odd
Therefore, (1)^odd + (1)^even + (1)^odd + (1)^even =1 +1 1 +1 = 0
Answer is C



SC Moderator
Joined: 13 Apr 2015
Posts: 1600
Location: India
Concentration: Strategy, General Management
WE: Analyst (Retail)

Re: Math Revolution and GMAT Club Contest! If x=1 and n is the sum of the [#permalink]
Show Tags
21 Dec 2015, 01:45
1
This post received KUDOS
x = 1
n = Sum of second 101 prime numbers is odd. (odd + odd + .... 101 times = odd)
Now, the question can be rephrased as > (1)^odd + (1)^even + (1)^odd + (1)^(even) = 1 + 1  1 + 1 = 0
Answer: C



Manager
Joined: 09 Jul 2015
Posts: 58

Re: Math Revolution and GMAT Club Contest! If x=1 and n is the sum of the [#permalink]
Show Tags
21 Dec 2015, 17:41
1
This post received KUDOS
Answer is C. xn+x(n+1)+x(n+2)+x(n+3) can be written as x^n(1+x+x^2+x^3). Apply x=1 in this equation. (1)^n*(11+11) = 0. Hence answer is 0.
_________________
Please kudos if you find this post helpful. I am trying to unlock the tests



Intern
Joined: 21 Nov 2014
Posts: 31
Location: Viet Nam

Re: Math Revolution and GMAT Club Contest! If x=1 and n is the sum of the [#permalink]
Show Tags
22 Dec 2015, 02:34
1
This post received KUDOS
Since n is an integer, in \(n, (n+1), (n+2), (n+3)\) there will be two odd numbers and two even numbers. \(1^{2k} = 1\) and \(1^{(2k+1)} = 1\) => \(x^n + x^{(n+1)} + x^{(n+2)} + x^{(n+3)} = 0\), as it's the sum of two (1) and two (1) Answer C.
_________________
GMAT Group for Vietnamese:
https://www.facebook.com/groups/644070009087525/



Retired Moderator
Joined: 23 Sep 2015
Posts: 401
Location: France
GMAT 1: 690 Q47 V38 GMAT 2: 700 Q48 V38
WE: Real Estate (Mutual Funds and Brokerage)

Re: Math Revolution and GMAT Club Contest! If x=1 and n is the sum of the [#permalink]
Show Tags
23 Dec 2015, 06:56
1
This post received KUDOS
We are looking for the sum of 4 consecutive powers of x.  Since n in the sum of prime numbers, n is an integer. (in this case, excluding prime number 2, n is odd) however we don't need to know that.  Since x is negative, the even powers will yield 1 and the odd powers 1. Therefore the answer will always be zero: 11+11=0 and 1+11+1 =0 answer C
_________________
New Application Tracker : update your school profiles instantly!



Intern
Joined: 17 Aug 2014
Posts: 10

Re: Math Revolution and GMAT Club Contest! If x=1 and n is the sum of the [#permalink]
Show Tags
24 Dec 2015, 10:06
1
This post received KUDOS
1
This post was BOOKMARKED
The answer is 0 What ever may be the value of n ( either odd or even), the expression x^n+x^n+1+x^n+2+x^n+3 will have two even power of x and two odd powers of x. Since x is 1, the expression reduces to +1+111=0 (order can vary )



Intern
Joined: 05 Jun 2013
Posts: 35

Re: Math Revolution and GMAT Club Contest! If x=1 and n is the sum of the [#permalink]
Show Tags
25 Dec 2015, 05:33
1
This post received KUDOS
x=1 n = the sum of the second 101 prime numbers, value of xn+x(n+1)+x(n+2)+x(n+3) Except 2, all prime numbers are odd.So sum of all odd numbers 101 times is again odd . So n is odd number.
(1)^odd number + (1)^even number + (1)^odd number + (1)^even number = 0
which is answer choice C.



Moderator
Joined: 22 Jun 2014
Posts: 1002
Location: India
Concentration: General Management, Technology
GPA: 2.49
WE: Information Technology (Computer Software)

Re: Math Revolution and GMAT Club Contest! If x=1 and n is the sum of the [#permalink]
Show Tags
25 Dec 2015, 13:53
1
This post received KUDOS
Given: x = 1x^n + x^(n+1) + x^(n+2) + x^(n+3) can be rewritten as the following by taking x^n as common: = x^n ( 1 + x + x^2 + x^3)  put the value of x = (1)^n * ( 1 + (1) + (1)^2 + (1)^3) = (1)^n * 0 = 0 Option C is the correct answer.
_________________
 Target  720740 http://gmatclub.com/forum/informationonnewgmatesrreportbeta221111.html http://gmatclub.com/forum/listofoneyearfulltimembaprograms222103.html



Math Expert
Joined: 02 Sep 2009
Posts: 44352

Re: Math Revolution and GMAT Club Contest! If x=1 and n is the sum of the [#permalink]
Show Tags
27 Dec 2015, 12:21
Bunuel wrote: Math Revolution and GMAT Club Contest Starts! QUESTION #13:If x=1 and n is the sum of the second 101 prime numbers, what is the value of \(x^n + x^{(n+1)} + x^{(n+2)} + x^{(n+3)}\)? A. 2 B. 1 C. 0 D. 1 E. 2 Check conditions below: Math Revolution and GMAT Club ContestThe Contest Starts November 28th in Quant Forum We are happy to announce a Math Revolution and GMAT Club Contest For the following four (!) weekends we'll be publishing 4 FRESH math questions per weekend (2 on Saturday and 2 on Sunday). To participate, you will have to reply with your best answer/solution to the new questions that will be posted on Saturday and Sunday at 9 AM Pacific. Then a week later, the forum moderator will be selecting 2 winners who provided most correct answers to the questions, along with best solutions. Those winners will get 6months access to GMAT Club Tests. PLUS! Based on the answers and solutions for all the questions published during the project ONE user will be awarded with ONE Grand prize: PS + DS course with 502 videos that is worth $299! All announcements and winnings are final and no whining GMAT Club reserves the rights to modify the terms of this offer at any time. NOTE: Test Prep Experts and Tutors are asked not to participate. We would like to have the members maximize their learning and problem solving process.
Thank you! MATH REVOLUTION OFFICIAL SOLUTION:The sum of the second 101 prime numbers is the sum of the all prime numbers from the second prime number to the next 101 prime numbers. Except 2, every prime number is an odd number. So, n=3+5+…………..+prime=odd. Then, \(x^n + x^{(n+1)} + x^{(n+2)} + x^{(n+3)}=(1)^{odd}+(1)^{even}+(1)^{odd}+(1)^{even}=(1)+1+(1)+1=0\), and the correct answer is C.
_________________
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



BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2500
GRE 1: 323 Q169 V154

Re: Math Revolution and GMAT Club Contest! If x=1 and n is the sum of the [#permalink]
Show Tags
07 Mar 2016, 04:00
[quote="Bunuel"][quote="Bunuel"] Math Revolution and GMAT Club Contest Starts! QUESTION #13:If x=1 and n is the sum of the second 101 prime numbers, what is the value of \(x^n + x^{(n+1)} + x^{(n+2)} + x^{(n+3)}\)? A. 2 B. 1 C. 0 D. 1 E. 2 Answer is Zero Irrespective of the value of N
_________________
Getting into HOLLYWOOD with an MBA The MOST AFFORDABLE MBA programs!STONECOLD's BRUTAL Mock Tests for GMATQuant(700+)Average GRE Scores At The Top Business Schools!



Intern
Joined: 23 Apr 2016
Posts: 14

Re: Math Revolution and GMAT Club Contest! If x=1 and n is the sum of the [#permalink]
Show Tags
11 Jul 2016, 06:52
Probably a stupid question: What does "second" mean here? I got the question right but just by plugging in 1 due to gutfeeling



Math Expert
Joined: 02 Sep 2009
Posts: 44352

Re: Math Revolution and GMAT Club Contest! If x=1 and n is the sum of the [#permalink]
Show Tags
11 Jul 2016, 07:12



Intern
Joined: 23 Apr 2016
Posts: 14

Re: Math Revolution and GMAT Club Contest! If x=1 and n is the sum of the [#permalink]
Show Tags
11 Jul 2016, 14:37
Thank you! So add on to this what does "25 second 101 primer numbers" stand for? Also one I figured out there is 25 prime numbers between 2 and 101 exclusive why do I plug in 1 for n? Which I did because of my gutfeeling but I rather have a mathematical explanation



NonHuman User
Joined: 09 Sep 2013
Posts: 6531

Re: Math Revolution and GMAT Club Contest! If x=1 and n is the sum of the [#permalink]
Show Tags
26 Sep 2017, 02:09
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: Math Revolution and GMAT Club Contest! If x=1 and n is the sum of the
[#permalink]
26 Sep 2017, 02:09






