 It is currently 29 Nov 2020, 18:36 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # The sum of all the multiples of 3 between 250 and 350  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Retired Moderator Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 175

Kudos [?]: 3037 , given: 394

The sum of all the multiples of 3 between 250 and 350 [#permalink]
Expert's post 00:00

Question Stats: 63% (01:06) correct 36% (02:00) wrong based on 86 sessions
 Quantity A Quantity B The sum of all the multiples of 3 between 250 and 350 9990

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.
[Reveal] Spoiler: OA

_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test Moderator  Joined: 07 Jan 2018
Posts: 697
Followers: 11

Kudos [?]: 785  , given: 88

Re: The sum of all the multiples of 3 between 250 and 350 [#permalink]
2
KUDOS
The first number divisible by $$3$$ after $$250$$ is $$252$$
The first number divisible by $$3$$ before $$350$$ is $$348$$
Hence there are altogether $$\frac{348 - 252}{3} + 1 = 33$$ numbers
Since the 33 numbers are equally spread apart with a difference of 3 the avg of those numbers = $$\frac{252 + 348}{2} = 300$$
Hence the sum is $$300 * 33 = 9900$$
option B > option A
_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos Retired Moderator Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 175

Kudos [?]: 3037  , given: 394

Re: The sum of all the multiples of 3 between 250 and 350 [#permalink]
3
KUDOS
Expert's post
Explanation

First, find the smallest multiple of 3 in this range: 250 is not a multiple of 3 (2 + 5 + 0 = 7, which is not a multiple of 3). The smallest multiple of 3 in this range is 252 (2 + 5 + 2 = 9, which is a multiple of 3).

Next, find the largest multiple of 3 in this range. Since 350 is not a multiple of 3 (3 + 5 + 0 = 8), the largest multiple of 3 in this range is 348.

The sum of an evenly spaced set of numbers equals the average value multiplied by the number of terms. The average value is the midpoint between 252 and 348: (252 + 348) ÷ 2 = 300. To find the number of terms, first subtract 348 – 252 = 96. This figure represents all numbers between 348 and 252, inclusive.

To count only the multiples of 3, divide 96 by the 3: 96 ÷ 3 = 32. Finally, “add 1 before you’re done” to count both end points of the range: 32 + 1 = 33.

The sum is 300 × 33 = 9,900. Since 9,900 is smaller than 9,990, Quantity B is greater.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Manager Joined: 23 Oct 2018
Posts: 57
Followers: 0

Kudos [?]: 0 , given: 0

Re: The sum of all the multiples of 3 between 250 and 350 [#permalink]
Supreme Moderator
Joined: 01 Nov 2017
Posts: 371
Followers: 12

Kudos [?]: 187 , given: 4

Re: The sum of all the multiples of 3 between 250 and 350 [#permalink]
Expert's post Intern Joined: 24 Sep 2018
Posts: 32
Followers: 0

Kudos [?]: 46  , given: 2

Re: The sum of all the multiples of 3 between 250 and 350 [#permalink]
2
KUDOS
Sum of Set = n[(last-first)/2) where n = [(last-first)/k]+1 and the value of K= the distance between numbers in a set.

Step 1: Find K.

The question is a sum of all multiples of 3, which would mean 3,6,9,12... the distance between each is (6-3)=3 or (9-6)=3 and so on. As such, the value of k for this problem is 3.

Step 2: determine the first and last values that fit the parameters of the question.

While we are given a range of 250 to 350, the first and last values are not 250 and 350 becuase they are NOT multiples of 3. The shorthand way to determine if something is a multiple of 3 is to add up all the digits. If the number you get from doing that is a number divisible by 3, then the larger original number is ALSO divisible by 3.

EX: 3312 is divisible by 3 because 3+3+1+2 =9 and 9 is clearly divisible by 3. Similarly, 23451321 is ALSO divisible by 3 because 2+3+4+5+1+3+2+1 = 21, a number you know is divisible by 3.

Anyway, 250 = 7, which is not divisible by 3 and 350 = 8 which is not divisible by 3. By testing numbers one by one above 250 and below 350 (within the range) we see that the first multiple of 3 is actually 251 and the last multiple of 3 in our range is 348.

Step 3: Solve for n

n = [(348-252)/3]+1 .... this is equal to (96/3)+1, which becomes 32+1 = 33

Step 4: With our n value in tow, we can now solve the original equation.

sum of set = n[(first+last)/2] = 33*[(252+348)/2] = 33* = 9900.

Step 5: Compare Quantity A and B

A = 9900. B = 9990. Therefore, B is greater than A and the answer is B Director  Joined: 22 Jun 2019
Posts: 517
Followers: 5

Kudos [?]: 108  , given: 161

Re: The sum of all the multiples of 3 between 250 and 350 [#permalink]
1
KUDOS
sandy wrote:
 Quantity A Quantity B The sum of all the multiples of 3 between 250 and 350 9990

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.

Another approach

The first number divisible by $$3$$ after $$250$$ is $$252$$ Like: 252= 84 * 3
The first number divisible by $$3$$ before $$350$$ is $$348$$ Like: 348 = 116 * 3
Hence there are altogether so the range means the total number here is, 84........116 = ( 116-84+1 )=33
Since the 33 numbers are equally spread so, 33/2 * (252 + 348) = 9900
option B > option A
_________________

New to the GRE, and GRE CLUB Forum?
Posting Rules: QUANTITATIVE | VERBAL

Questions' Banks and Collection:
ETS: ETS Free PowerPrep 1 & 2 All 320 Questions Explanation. | ETS All Official Guides
3rd Party Resource's: All In One Resource's | All Quant Questions Collection | All Verbal Questions Collection | Manhattan 5lb All Questions Collection
Books: All GRE Best Books
Scores: Average GRE Score Required By Universities in the USA
Tests: All Free & Paid Practice Tests | GRE Prep Club Tests
Extra: Permutations, and Combination
Vocab: GRE Vocabulary Re: The sum of all the multiples of 3 between 250 and 350   [#permalink] 06 Jul 2019, 01:12
Display posts from previous: Sort by

# The sum of all the multiples of 3 between 250 and 350  Question banks Downloads My Bookmarks Reviews Important topics  Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.