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Math Expert V
Joined: 02 Sep 2009
Posts: 58402
Math Revolution and GMAT Club Contest! If x=-1 and n is the sum of the  [#permalink]

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Question Stats: 83% (01:30) correct 17% (01:15) wrong based on 199 sessions

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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 Contest

The 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 6-months 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! _________________ Intern  Joined: 30 Sep 2013 Posts: 20 Re: Math Revolution and GMAT Club Contest! If x=-1 and n is the sum of the [#permalink] Show Tags 2 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  P Joined: 21 May 2013 Posts: 636 Re: Math Revolution and GMAT Club Contest! If x=-1 and n is the sum of the [#permalink] Show Tags 2 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+1-1+1=0 Answer C Intern  Joined: 12 Jul 2015 Posts: 25 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 3 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+1-1+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+1-1+1 = 0) Case 2: n = Even, n+1 = odd, n+2 = Even, n+3 = Odd (-1+1-1+1 = 0) Ans =C = 0 Current Student B Joined: 20 Jan 2015 Posts: 47 Re: Math Revolution and GMAT Club Contest! If x=-1 and n is the sum of the [#permalink] Show Tags 1 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  B Joined: 21 Jan 2013 Posts: 39 Concentration: General Management, Leadership Schools: LBS 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 1 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: 36 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 1 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 Marshall & McDonough Moderator D Joined: 13 Apr 2015 Posts: 1685 Location: India Re: Math Revolution and GMAT Club Contest! If x=-1 and n is the sum of the [#permalink] Show Tags 1 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 Intern  Joined: 09 Jul 2015 Posts: 49 Re: Math Revolution and GMAT Club Contest! If x=-1 and n is the sum of the [#permalink] Show Tags 1 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*(1-1+1-1) = 0. Hence answer is 0. _________________ Please kudos if you find this post helpful. I am trying to unlock the tests Intern  S Joined: 21 Nov 2014 Posts: 31 Location: Viet Nam GMAT 1: 760 Q50 V44 Re: Math Revolution and GMAT Club Contest! If x=-1 and n is the sum of the [#permalink] Show Tags 1 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/ Senior Manager  B Joined: 23 Sep 2015 Posts: 371 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 1 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: 1-1+1-1=0 and -1+1-1+1 =0 answer C _________________ 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 1 1 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+1-1-1=0 (order can vary ) Intern  B 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 1 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. Retired Moderator V Joined: 22 Jun 2014 Posts: 1093 Location: India Concentration: General Management, Technology GMAT 1: 540 Q45 V20 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 1 Given: x = -1 x^n + x^(n+1) + x^(n+2) + x^(n+3) can be re-written 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. _________________ Math Expert V Joined: 02 Sep 2009 Posts: 58402 Re: Math Revolution and GMAT Club Contest! If x=-1 and n is the sum of the [#permalink] Show Tags 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 Contest The 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 6-months 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.
_________________
Current Student D
Joined: 12 Aug 2015
Posts: 2568
Schools: Boston U '20 (M)
GRE 1: Q169 V154 Re: Math Revolution and GMAT Club Contest! If x=-1 and n is the sum of the  [#permalink]

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[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
_________________
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]

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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 V
Joined: 02 Sep 2009
Posts: 58402
Re: Math Revolution and GMAT Club Contest! If x=-1 and n is the sum of the  [#permalink]

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expertesp wrote:
Probably a stupid question: What does "second" mean here? I got the question right but just by plugging in -1 due to gutfeeling Agree the wording could be clearer.

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.
_________________
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]

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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 Intern  B
Joined: 17 Jan 2018
Posts: 44
Schools: ISB '20 (A)
Re: Math Revolution and GMAT Club Contest! If x=-1 and n is the sum of the  [#permalink]

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How is this question important?

No matter what n is, even or odd, the answer is always 0. :/

It takes 10 seconds to just look at the powers to be consecutive and answer this question. What was the entire point of the second sum of prime numbers to be 110? :/ Re: Math Revolution and GMAT Club Contest! If x=-1 and n is the sum of the   [#permalink] 22 Mar 2018, 00:42

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