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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # For each integer n>1, if S(n) denote the sum of even integer  Question banks Downloads My Bookmarks Reviews Important topics
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TAGS: GRE Prep Club Legend  Joined: 07 Jun 2014
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GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
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For each integer n>1, if S(n) denote the sum of even integer [#permalink]
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Expert's post 00:00

Question Stats: 61% (01:24) correct 38% (01:49) wrong based on 34 sessions
For each integer $$n>1$$, if S(n) denote the sum of even integer upto $$n$$ (not inclusive of $$n$$). For example, $$S(10)= 2+4+6+8=20$$. What is value of $$S(300)$$?

(A) $$22050$$
(B) $$22350$$
(C) $$22650$$
(D) $$45150$$
(E) $$90300$$
[Reveal] Spoiler: OA

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Sandy
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Manager Joined: 29 Nov 2017
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Location: United States
GRE 1: Q142 V146 WE: Information Technology (Computer Software)
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Kudos [?]: 79 , given: 99

Re: For each integer n>1, if S(n) denote the sum of even integer [#permalink]
hi

can anyone tell whats the shortcut to such questions?
GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 112

Kudos [?]: 1865 , given: 397

Re: For each integer n>1, if S(n) denote the sum of even integer [#permalink]
Expert's post
IshanGre wrote:
hi

can anyone tell whats the shortcut to such questions?

You need to be well versed with arithmetic progression formulas. It is not super complex just needs practice
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Sandy
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Intern Joined: 17 Sep 2017
Posts: 21
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Kudos [?]: 14 , given: 3

Re: For each integer n>1, if S(n) denote the sum of even integer [#permalink]
IshanGre wrote:
hi

can anyone tell whats the shortcut to such questions?

First, you need to memorize the formula for the sum of arithmetic progression. Second, you need to know how to count number of terms. Third, practice and practice.
Intern Joined: 10 Aug 2018
Posts: 29
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Kudos [?]: 6 , given: 2

Re: For each integer n>1, if S(n) denote the sum of even integer [#permalink]
please tell the shortcut method to solve this question. Intern Joined: 27 Oct 2018
Posts: 49
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Kudos [?]: 13  , given: 27

Re: For each integer n>1, if S(n) denote the sum of even integer [#permalink]
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S(300) = 2+..........+298

for number of terms, l = a+(n-1)*2
298 = a+(n-1)*2 = 2+(n-1)*2 => 296/2 = n-1 => n=149

for sum,

S(300) = n/2 * (a+l) = (149/2)*(298+2) = 149*150 = 22350

Answer is B!

Last edited by indiragre18 on 11 Nov 2018, 00:16, edited 1 time in total.
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Kudos [?]: 111 , given: 4

Re: For each integer n>1, if S(n) denote the sum of even integer [#permalink]
Expert's post
sandy wrote:
For each integer $$n>1$$, if S(n) denote the sum of even integer upto $$n$$ (not inclusive of $$n$$). For example, $$S(10)= 2+4+6+8=20$$. What is value of $$S(300)$$?

(A) $$22050$$
(B) $$22350$$
(C) $$22650$$
(D) $$45150$$
(E) $$90300$$

there are three ways to do it ....

(I) If you know that Sum of first n integers is $$\frac{n(n+1)}{2}$$
Sum = $$2+4+6+...+300) = 2(1+2+3....+150)= 2 *\frac{150*151}{2}=150*151=22650$$

(II) If you know that Sum of first n integers is $$\frac{n(n+1)[}{fraction]$$
Now we have $$[fraction]300/2}=150$$ terms till 300, inclusive.
Sum = $$2+4+6+...+300 = 150*151=150*151=22650$$

(III) since it is an AP. the sum will be equal to Number of integers* average
so $$150 * \frac{(300+2)}{2} = 150*151 = 22650$$

Now subtract 300 from each result as the answered has to be exclusive of 300, that is 300 is not be included in total..
Therefore answer is 22650-300=22350

B

To know more about Arithmetic progressions
https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
_________________

Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

Intern Joined: 15 Sep 2018
Posts: 23
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Kudos [?]: 6 , given: 2

Re: For each integer n>1, if S(n) denote the sum of even integer [#permalink]
chetan2u wrote:
sandy wrote:
For each integer $$n>1$$, if S(n) denote the sum of even integer upto $$n$$ (not inclusive of $$n$$). For example, $$S(10)= 2+4+6+8=20$$. What is value of $$S(300)$$?

(A) $$22050$$
(B) $$22350$$
(C) $$22650$$
(D) $$45150$$
(E) $$90300$$

there are three ways to do it ....

(I) If you know that Sum of first n integers is $$\frac{n(n+1)}{2}$$
Sum = $$2+4+6+...+300) = 2(1+2+3....+150)= 2 *\frac{150*151}{2}=150*151=22650$$

(II) If you know that Sum of first n integers is $$\frac{n(n+1)[}{fraction]$$
Now we have $$[fraction]300/2}=150$$ terms till 300, inclusive.
Sum = $$2+4+6+...+300 = 150*151=150*151=22650$$

(III) since it is an AP. the sum will be equal to Number of integers* average
so $$150 * \frac{(300+2)}{2} = 150*151 = 22650$$

C

To know more about Arithmetic progressions
https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048

According to the initial problem, the answer is B. Also it seems you are doing inclusive of n=300, while the prompt states NON-inclusive.
Supreme Moderator
Joined: 01 Nov 2017
Posts: 370
Followers: 5

Kudos [?]: 111 , given: 4

Re: For each integer n>1, if S(n) denote the sum of even integer [#permalink]
Expert's post
projectoffset wrote:
chetan2u wrote:
sandy wrote:
For each integer $$n>1$$, if S(n) denote the sum of even integer upto $$n$$ (not inclusive of $$n$$). For example, $$S(10)= 2+4+6+8=20$$. What is value of $$S(300)$$?

(A) $$22050$$
(B) $$22350$$
(C) $$22650$$
(D) $$45150$$
(E) $$90300$$

there are three ways to do it ....

(I) If you know that Sum of first n integers is $$\frac{n(n+1)}{2}$$
Sum = $$2+4+6+...+300) = 2(1+2+3....+150)= 2 *\frac{150*151}{2}=150*151=22650$$

(II) If you know that Sum of first n integers is $$\frac{n(n+1)[}{fraction]$$
Now we have $$[fraction]300/2}=150$$ terms till 300, inclusive.
Sum = $$2+4+6+...+300 = 150*151=150*151=22650$$

(III) since it is an AP. the sum will be equal to Number of integers* average
so $$150 * \frac{(300+2)}{2} = 150*151 = 22650$$

C

To know more about Arithmetic progressions
https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048

According to the initial problem, the answer is B. Also it seems you are doing inclusive of n=300, while the prompt states NON-inclusive.

Yes, thank you.
I had included 300 in each case.
B will be the correct answer.
_________________

Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html Re: For each integer n>1, if S(n) denote the sum of even integer   [#permalink] 26 Nov 2018, 18:05
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