GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 25 Jun 2018, 12:27

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Set X consists of the first 100 positive even integers. Set Y consists

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

1 KUDOS received
Intern
Intern
avatar
B
Joined: 02 Mar 2016
Posts: 5
GMAT ToolKit User
Set X consists of the first 100 positive even integers. Set Y consists [#permalink]

Show Tags

New post 06 Feb 2017, 13:16
1
6
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

66% (03:24) correct 34% (03:33) wrong based on 111 sessions

HideShow timer Statistics

Set X consists of the first 100 positive even integers. Set Y consists of the first 100 positive multiples of 5. If the terms in both sets are combined to create a new set with no repeat elements, what is the sum of all unique terms in the new set?

a) 33250

b) 34350

c) 35750

d) 36300

e) 37500
2 KUDOS received
Senior Manager
Senior Manager
avatar
G
Joined: 24 Apr 2016
Posts: 333
Re: Set X consists of the first 100 positive even integers. Set Y consists [#permalink]

Show Tags

New post 06 Feb 2017, 14:36
2
1
Sum of first 100 positive even integers: 2 + 4 + 6 + 8 + ....+ 200 = [100 (2+200)]/2 = 10100

Sum of first 100 positive multiples of 5: 5 + 10 + 15 + ... + 500 = [100 (5+500)]/2 = 25250

Sum of multiples of 10 till 200: 10 + 20 + 30 + ... + 200 = [20 (10+200)]/2 = 2100

Therefore: Sum of all unique terms in the new set = 10100 + 25250 - 2100 = 33250 (A)
2 KUDOS received
Senior SC Moderator
User avatar
V
Joined: 14 Nov 2016
Posts: 1315
Location: Malaysia
GMAT ToolKit User Premium Member CAT Tests
Re: Set X consists of the first 100 positive even integers. Set Y consists [#permalink]

Show Tags

New post 12 Feb 2017, 07:32
2
Matruco wrote:
Set X consists of the first 100 positive even integers. Set Y consists of the first 100 positive multiples of 5. If the terms in both sets are combined to create a new set with no repeat elements, what is the sum of all unique terms in the new set?

a) 33250

b) 34350

c) 35750

d) 36300

e) 37500


Official solution from Veritas Prep.

This problem heavily rewards you for knowing how to quickly calculate the sum of an evenly-spaced set. When you look at the two sets, you have:

\(Set X\): \(2, 4, 6, 8, 10….198, 200\)
\(Set Y\): \(5, 10, 15, 20…495, 500\)

And note that you do not need to perform a “count” to make sure you have exactly 100 terms in each set. Multiples of 2 are defined as 2 times an integer, so the first 100 terms will be 1 * 2, 2 * 2, 3 * 2… up to 100 * 2. Same for multiples of 5: 1 * 5, 2 * 5, 3 * 5…100 * 5. So you know that your ending number for each set will be 100 times the common multiple.
When you’re dealing with evenly-spaced set, the median equals the mean. So you can quickly calculate the average by averaging the first and last term. For Set X, that’s \(\frac{(2 + 200)}{2} = 101\), and for Set Y that’s \(\frac{(5 + 500)}{2} = 252.5\).

Now you’ll use the Average = Sum of Terms / Number of Terms rule to your advantage. The sum of the terms (what you want) can be calculated by multiplying the average times the number of terms. So for Set X that’s 100(101) = 10100. And for Set Y that’s 100(252.5) = 25250.

At this point you can sum those two sets to arrive at 35350. But wait – the question specified “unique terms” and “no repeat elements.” So here you will have to subtract out the numbers that are multiples of both 2 and 5. Which are those? The multiples of 10.

But be careful: Here you do not have 100 multiples of 10; you only have the multiples of 10 up to 200 (where the set of even numbers stops). So you’ll calculate the multiples of 10 between 10 and 200, inclusive. Again, take the average (105) and multiply by the number of terms (20) to get 2100. When you subtract that from 35350 you’ll have the correct answer, 33250.
_________________

"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

Rules for posting in verbal forum | Please DO NOT post short answer in your post!

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46305
Re: Set X consists of the first 100 positive even integers. Set Y consists [#permalink]

Show Tags

New post 14 Feb 2017, 01:20
Matruco wrote:
Set X consists of the first 100 positive even integers. Set Y consists of the first 100 positive multiples of 5. If the terms in both sets are combined to create a new set with no repeat elements, what is the sum of all unique terms in the new set?

a) 33250

b) 34350

c) 35750

d) 36300

e) 37500


Similar question: https://gmatclub.com/forum/set-x-consis ... 86754.html
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
S
Joined: 03 Jan 2017
Posts: 180
Re: Set X consists of the first 100 positive even integers. Set Y consists [#permalink]

Show Tags

New post 18 Mar 2017, 13:48
find sum of 100 even intergers
find sum of 100 multiplies of 5
and then deduct the sum of multiplies of 10 from 10 to 200
10100+25250-2100=33250 (A)
Director
Director
User avatar
S
Joined: 08 Jun 2015
Posts: 517
Location: India
GMAT 1: 640 Q48 V29
GMAT 2: 700 Q48 V38
Premium Member CAT Tests
Re: Set X consists of the first 100 positive even integers. Set Y consists [#permalink]

Show Tags

New post 20 Apr 2018, 02:52
+1 for option A.

First find sum of all multiples of 2 = 10100
Next, find sum of all multiples of 5 = 25250

Sum of all common numbers = 2100

The final value = 35350-2100 = 33250.

Option A it is
_________________

" The few , the fearless "

Re: Set X consists of the first 100 positive even integers. Set Y consists   [#permalink] 20 Apr 2018, 02:52
Display posts from previous: Sort by

Set X consists of the first 100 positive even integers. Set Y consists

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


cron

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.