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The sum of all the even integers

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The sum of all the even integers from 18 to 36 inclusive [#permalink] New post 24 Mar 2018, 02:23
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Question Stats:

40% (01:34) correct 60% (01:11) wrong based on 5 sessions
Quantity A
Quantity B
The sum of all the even integers from 18 to 36 inclusive
The sum of all the even integers from 22 to 38 inclusive


A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.

Drill 1
Question: 6
Page: 547
[Reveal] Spoiler: OA

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Re: The sum of all the even integers from 18 to 36 inclusive [#permalink] New post 25 Mar 2018, 10:44
sandy wrote:
Quantity A
Quantity B
The sum of all the even integers from 18 to 36 inclusive
The sum of all the even integers from 22 to 38 inclusive


A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.

Drill 1
Question: 6
Page: 547


Is there any way to solve this quest under 30 sec?
Also, my favorite short cut doesn't work here (which is Sum=average*#)
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Re: The sum of all the even integers from 18 to 36 inclusive [#permalink] New post 28 Mar 2018, 13:32
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Explanation

Even if you know the summation formula, you can avoid a lot of time-consuming calculation by disregarding the numbers that are common to both sums—the even integers
from 22 to 36, inclusive.

That leaves 18 + 20 = 38 as the sum of the unique terms in Quantity A, and 38 as the only unique term in Quantity B. The quantities are equal.
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The sum of all the even integers [#permalink] New post 04 Feb 2019, 04:48
Quantity A
Quantity B
The sum of all the even integers from 18 to 36 inclusive
The sum of all the even integers from 22 to 38 inclusive




A)Quantity A is greater.
B)Quantity B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Last edited by Carcass on 04 Feb 2019, 04:56, edited 1 time in total.
Edited by Carcass
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Re: The sum of all the even integers [#permalink] New post 04 Feb 2019, 05:38
SKH121 wrote:
Quantity A
Quantity B
The sum of all the even integers from 18 to 36 inclusive
The sum of all the even integers from 22 to 38 inclusive




A)Quantity A is greater.
B)Quantity B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.



Hello,

Could you please check the forum before posting, this is duplication of the question. Moreover plz check the questions already posted under Princeton Review. U will find most of them.

For your reference this question is answered here:

https://greprepclub.com/forum/the-sum-o ... 12325.html
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Re: The sum of all the even integers [#permalink] New post 04 Feb 2019, 06:23
pranab01 wrote:
SKH121 wrote:
Quantity A
Quantity B
The sum of all the even integers from 18 to 36 inclusive
The sum of all the even integers from 22 to 38 inclusive




A)Quantity A is greater.
B)Quantity B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.



Hello,

Could you please check the forum before posting, this is duplication of the question. Moreover plz check the questions already posted under Princeton Review. U will find most of them.

For your reference this question is answered here:

https://greprepclub.com/forum/the-sum-o ... 12325.html


Thank you for your reply.
The posted answer is exactly the same as the book explanation, and i still couldn't get it.
Maybe someone has another explanation.
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Re: The sum of all the even integers [#permalink] New post 04 Feb 2019, 08:11
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SKH121 wrote:
SKH121 wrote:
Quantity A
Quantity B
The sum of all the even integers from 18 to 36 inclusive
The sum of all the even integers from 22 to 38 inclusive




A)Quantity A is greater.
B)Quantity B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.



Thank you for your reply.
The posted answer is exactly the same as the book explanation, and i still couldn't get it.
Maybe someone has another explanation.


So we have two quantitites..
1) A=Sum of all even numbers from 18 to 36 = 18+20+22+24+26+...34+36.
2) B=Sum of all even numbers from 22 to 38 = 22+24+26+...34+36+38.
Let 22+24+...36 be a, so A=18+20+a=38+a and B=a+38..
Thus A=B

another way..
1) A=Sum of all even numbers from 18 to 36 = 18+20+22+24+26+...34+36
Sum of consecutive numbers, or consecutive even integers is average * number of terms
Average = \(\frac{first+last}{2}=\frac{18+36}{2}=27\)
Number of terms = \(\frac{36-18}{2}+1=9+1=10\)
Sum = 27*10=270

2) B=Sum of all even numbers from 22 to 38 = 22+24+26+...34+36+38.
Average = \(\frac{first+last}{2}=\frac{22+38}{2}=30\)
Number of terms = \(\frac{38-22}{2}+1=8+1=9\)
Sum = 30*9=270
so A=B

C
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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

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Re: The sum of all the even integers [#permalink] New post 04 Feb 2019, 09:15
SKH121 wrote:
Thank you for your reply.
The posted answer is exactly the same as the book explanation, and i still couldn't get it.
Maybe someone has another explanation.


Even if the u need an explanation to any post, just post a reply under the same post, u need not create a separate Question as it duplicates and the GRE moderator need to spend time in rectifying this.

I hope u do understand, and plz Next time first search in the forum, if u find a post reply there else create a new post.

For ur reference:

https://greprepclub.com/forum/the-sum-o ... 10659.html

IMPORTANT RULES TO FOLLOW BEFORE POSTING https://greprepclub.com/forum/rules-for ... -1083.html
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Re: The sum of all the even integers   [#permalink] 04 Feb 2019, 09:15
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