Last visit was: 18 Dec 2024, 12:23 It is currently 18 Dec 2024, 12:23

Close

GRE Prep 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
Your Progress

every week, we’ll send you an estimated GRE 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.

Close

Request Expert Reply

Confirm Cancel
avatar
Retired Moderator
Joined: 20 Apr 2016
Posts: 1307
Own Kudos [?]: 2280 [7]
Given Kudos: 251
WE:Engineering (Energy and Utilities)
Send PM
avatar
Intern
Intern
Joined: 12 Sep 2019
Posts: 5
Own Kudos [?]: 6 [0]
Given Kudos: 0
Send PM
Manager
Manager
Joined: 05 Aug 2020
Posts: 101
Own Kudos [?]: 245 [0]
Given Kudos: 14
Send PM
avatar
Intern
Intern
Joined: 15 Aug 2020
Posts: 5
Own Kudos [?]: 9 [0]
Given Kudos: 0
Send PM
Re: The sum of the multiples of 3 between -93 and 252, inclusive [#permalink]
2
grenico wrote:
pranab223 wrote:
Quantity A
Quantity B
The sum of the multiples of 3 between -93 and 252, inclusive
\(9162\)


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



First note the following about the sequence from -93 to 252:

-93,-92,-91,-90,.......-1,0,1,....90,91,92,93,.....251,252

So when we're summing our multiples of 3, we can exclude the sequence {-93,93}, since those will add up to 0.

Our new sequence is {94,252}.

\(252 - 94 + 1 = 159\)

There are 159 terms in the sequence. Dividing this number by 3 will give us the number of multiples of 3 in the sequence.

\(\frac{159}{3} = 53\)

So there are 53 multiples of 3 in the sequence. We want to use the Gaussian trick and make pairs out of the multiples, so we'll pull out 96 from the sequence and we'll be left with 52 multiples of 3 in order to divide by 2. (Keep that 96 in mind, we'll need it later).

Using the Gaussian trick to sum numbers in a sequence:

\(252 + 99 = 351\)
\(249 + 102 = 351\)
\(246 + 105 = 351\)
.
.
.

Since there are 52 multiples, there are 26 pairs of multiples of 3 that we can arrange in the way we did above which sum to 351. Since we pulled out the 96 from before, we need to add that back in as well.

This can all be written as:

\(26*(351) + 96 = 9222\)


Therefore A is greater.



Nice explanation, instead of Gaussian trick we can try sum of Arithmetic progression as well.

96+99+....+252 which is written as 3(32+33+34....+52), where 32+33+.. is an AP the sum is 3074
3074*3 = 9222 which is greater than 9162

Just an alternative approach
Manager
Manager
Joined: 10 Dec 2020
Posts: 50
Own Kudos [?]: 90 [2]
Given Kudos: 955
GRE 1: Q166 V162
Send PM
Re: The sum of the multiples of 3 between -93 and 252, inclusive [#permalink]
2
For an equally spaced set:-

Average = (First term + Last term)/2 = (-93 + 252) / 2 = 79.5
No. of terms (multiple of 3) = [(Last multiple - First multiple)/3 + 1]= [(252+93)/3] + 1 = 116

Sum = Avg. * No. = 79.5 * 116 = 9222

A)The quantity in Column A is greater.



pranab223 wrote:
Quantity A
Quantity B
The sum of the multiples of 3 between -93 and 252, inclusive
\(9162\)


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given
Prep Club for GRE Bot
Re: The sum of the multiples of 3 between -93 and 252, inclusive [#permalink]
Moderators:
GRE Instructor
88 posts
GRE Forum Moderator
37 posts
Moderator
1115 posts
GRE Instructor
234 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne